Trusted AI system optimization scheme based on double-domain extension and quantum fusion

Abstract

The invention relates to a technical supplement of a credible AI system solution based on double-domain modeling and quantum computing, and aims to improve the theoretical basis and application capability of the credible AI system solution. The cross-culture adaptability, the physical correctness and the decision real-time performance of the system are remarkably improved by proposing a double-domain kinetic equation, defining a specific implementation mode of a hypergraph-tensor hybrid architecture and defining 25 expansion deformation forms. Definitions of a cognitive dependent domain (CDR) and a non-cognitive domain (NCR) are optimized. Besides, specific implementation schemes are respectively designed for mature and immature scenes of the quantum technology, and under the support of a simplified model and a classical calculation method, the universality of the system in a complex scene is ensured. According to the invention, extension forms of multi-domain correlation, learning and optimization correlation and architecture and communication correlation are also listed in detail, flexible solutions are provided for different application scenes, and the expansibility and adaptability of the system are further enhanced.

Description

Technical Field

[0001] The present invention relates to trusted system design in the field of artificial intelligence (AI), and in particular to a technical supplement to "a trusted AI system solution based on dual-domain modeling and quantum computing." Background Art

[0002] In existing technologies, the trustworthiness design of AI systems faces numerous challenges, particularly in terms of cross-cultural adaptability, robustness under the constraints of physical laws, and real-time performance in high-dimensional decision spaces. "A Trustworthy AI System Solution Based on Dual-Domain Modeling and Quantum Computing" proposes a trustworthy AI architecture that integrates modern mathematical tools (such as tensor analysis and gauge field theory), quantum computing concepts (such as path optimization algorithms), and engineering optimization techniques. This architecture achieves the unity of subjective cognition and objective laws through a dual-domain modeling framework of the cognitive dependency domain (CDR) and the non-cognitive domain (NCR). It demonstrates strong universality and commercial potential in a variety of fields, including autonomous driving, industrial control, and financial risk management.

[0003] Improvement and optimization of CDR and NCR definitions:

[0004] To further enhance the technical integrity and theoretical depth of "A Trusted AI System Solution Based on Dual-Domain Modeling and Quantum Computing," this paper provides a more detailed description and optimization of the definitions of the Cognitive Dependent Domain (CDR) and the Non-Cognitive Domain (NCR):

[0005] Cognitive-Dependent Realm (CDR):

[0006] It refers to the knowledge system constructed and continuously interacted by human cognitive activities. Its existence and evolution path are highly dependent on the perception, interpretation and value judgment of the subjective cognitive subject. This field consists of three levels, forming a hierarchical structure of cognitive emergence from individual to society:

[0007] 1. Individual level (S): Private cognitive framework formed by personal perception, experience, memory construction and subjective initiative;

[0008] 2. Group level (OS): collective cognitive paradigm formed through symbolic systems, value consensus and interactive practices within a specific community;

[0009] 3. Social layer (IS): A macro-cognitive structure formed based on cultural traditions, institutional norms and civilization forms.

[0010] This field has significant temporal and spatial relativity, and its connotation is dynamically reconstructed with the changes in civilization process, cultural context and social form.

[0011] Non-Cognitive Realm (NCR):

[0012] Refers to the objective reality that exists independently of human cognition, whose essential attributes and operating laws follow the inevitability of natural laws. It includes three basic types of existence:

[0013] 1. Basic physics layer: space-time structure, basic interactions and the objective laws of material movement;

[0014] 2. Formalized systems: abstract structures such as mathematical axiom systems and logical deduction rules;

[0015] 3. Pre-observational entities: quantum systems that are not disturbed by observation, natural evolution processes on a cosmological scale, etc.

[0016] This field is cognitively irrelevant, its existence has nothing to do with human cognitive activities, and it exhibits regular stability that transcends time and space conditions.

[0017] However, in actual applications, it was found that although the "Trusted AI System Solution Based on Dual-Domain Modeling and Quantum Computing" provides a basic dual-domain modeling framework, there is still room for improvement in the following aspects:

[0018] 1. Insufficient theoretical depth: There is a lack of clear mathematical expressions to describe the dynamic interaction between the two domains, such as the two-domain dynamics equation.

[0019] 2. Lack of architectural details: The specific implementation of the hypergraph-tensor hybrid architecture has not been disclosed in detail, resulting in limited performance in representing multicultural relationships and verifying kinematic equations.

[0020] 3. Ambiguity in the combination method: "A Trusted AI System Solution Based on Dual-Domain Modeling and Quantum Computing" does not clearly explain the synergy between the dual-domain dynamics equations and the hypergraph-tensor hybrid architecture, making it difficult to fully utilize the complementary advantages of the two in practical applications.

[0021] 4. Limited scalability: The extended deformation forms of the dual-domain modeling framework have not been fully developed, which limits its flexibility and adaptability in different application scenarios.

[0022] To solve the above problems, the present invention supplements and improves the above technical gaps, specifically including:

[0023] 1. A dual-domain dynamic equation is proposed to accurately describe the dynamic coupling relationship between the cognitive dependence domain (CDR) and the non-cognitive domain (NCR).

[0024] 2. Clarify the specific implementation method of the hypergraph-tensor hybrid architecture to enhance the system's performance in multicultural relationship representation and kinematic equation verification.

[0025] 3. Explain how to combine the dual-domain dynamics equations with the hypergraph-tensor hybrid architecture to ensure efficient collaboration between the two in practical applications.

[0026] 4. Detailedly list and define 25 extended deformation forms including but not limited to dual-domain modeling to further improve the scalability and adaptability of the system.

[0027] Through the above-mentioned technical supplements, the present invention not only enhances the technical integrity and theoretical depth of "a trusted AI system solution based on dual-domain modeling and quantum computing", but also provides stronger support capabilities for it in a wider range of practical application scenarios. Summary of the Invention

[0028] The present invention further improves and optimizes the definitions of cognitive dependency domain (CDR) and non-cognitive domain (NCR), specifically including the following:

[0029] Cognitive-Dependent Realm (CDR):

[0030] It refers to the knowledge system constructed and continuously interacted by human cognitive activities. Its existence and evolution path are highly dependent on the perception, interpretation and value judgment of the subjective cognitive subject. This field consists of three levels, forming a hierarchical structure of cognitive emergence from individual to society:

[0031] 1. Individual level (S): Private cognitive framework formed by personal perception, experience, memory construction and subjective initiative;

[0032] 2. Group level (OS): collective cognitive paradigm formed through symbolic systems, value consensus and interactive practices within a specific community;

[0033] 3. Social layer (IS): A macro-cognitive structure formed based on cultural traditions, institutional norms and civilization forms.

[0034] This field has significant temporal and spatial relativity, and its connotation is dynamically reconstructed with the changes in civilization process, cultural context and social form.

[0035] Non-Cognitive Realm (NCR):

[0036] Refers to the objective reality that exists independently of human cognition, whose essential attributes and operating laws follow the inevitability of natural laws. It includes three basic types of existence:

[0037] 1. Basic physics layer: space-time structure, basic interactions and the objective laws of material movement;

[0038] 2. Formalized systems: abstract structures such as mathematical axiom systems and logical deduction rules;

[0039] 3. Pre-observational entities: quantum systems that are not disturbed by observation, natural evolution processes on a cosmological scale, etc.

[0040] This field is cognitively irrelevant, its existence has nothing to do with human cognitive activities, and it exhibits regular stability that transcends time and space conditions.

[0041] The present invention also involves improving "a trusted AI system solution based on dual-domain modeling and quantum computing":

[0042] 1. The theoretical depth is insufficient, and there is a lack of clear mathematical expressions to describe the dynamic interaction between the two domains, such as the two-domain dynamic equations.

[0043] 2. Lack of architectural details: The specific implementation of the hypergraph-tensor hybrid architecture has not been disclosed in detail, resulting in limited performance in representing multicultural relationships and verifying kinematic equations.

[0044] To address the above issues, the present invention aims to supplement and improve the aforementioned technical gaps. Based on the development level of quantum technology, it can be applied to the following two main scenarios:

[0045] Mature scenarios for quantum technology: Make full use of quantum effects (such as entangled potential energy terms) to build accurate dynamic models.

[0046] 1. Under the premise of mature quantum technology, the specific form of the dual-domain dynamics equation

[0047] (1) Dual-domain dynamic equation:

[0048]

[0049] Where: Ψ: dual-domain state function, describing the comprehensive state of subjective cognition (CDR) and objective law (NCR); H NCR : Hamiltonian operator in the non-cognitive domain (NCR), representing the constraints of physical laws; D CDR : The diffusion coefficient matrix in the cognitive dependency domain (CDR) reflects the changes in cultural dynamics and individual subjective experience; Laplace operator, describing changes in space; Γ: gauge field operator, derived from gauge field theory, used to describe the constraints of social rules on behavioral trajectories; V ent (r1, r2): entanglement potential energy term, describing the non-local correlation between different nodes or individuals; t: time variable; Reduced Planck constant;

[0050] (2) Origin and derivation process of the formula:

[0051] 1. Basic equations of quantum mechanics:

[0052] According to the Schrödinger equation:

[0053]

[0054] Here, H is the Hamiltonian operator of the system.

[0055] 2. Introduce diffusion term:

[0056] In the cognitive dependency domain (CDR), cultural transmission is uncertain and can be described by the diffusion term:

[0057]

[0058] 3. Introducing gauge field operators:

[0059] Gauge field theory is used to describe the constraints that social rules impose on behavioral trajectories. Add the gauge field operator Γ to the diffusion term:

[0060]

[0061] 4. Add entanglement potential energy term:

[0062] Considering the quantum entanglement effect between different nodes or individuals, the entanglement potential energy term V is introduced ent (r1,r2):

[0063]

[0064] 2. Specific mathematical model equations of the hypergraph-tensor hybrid architecture mathematical model

[0065] (1) Dynamic hypergraph representation:

[0066] G=(V,E,W,T)

[0067] Where: V: node set, representing different cultures or social groups; E: edge set, representing the relationship between cultures; W: weight matrix, dynamically updated to reflect the mutual influence between cultures; T: tensor core set, each node v i Corresponding to a tensor core T(v i ).

[0068] (2) Tensor core verification of kinematic equations:

[0069]

[0070] Where: T(v i ):node v i Tensor core value of; N(i): node v i Neighbor set of K(v i , v j ): kernel function, used to measure the node v iand v j Similarity between them; λ: Adjustment parameter to control the coupling strength between tensor cores; Tr(T ij ): Tensor core T ij The trace of , reflects the global consistency of tensor cores between nodes.

[0071] (3) Combined with the probability distribution of path integral:

[0072]

[0073] Where: P(Ψ): probability distribution of state function Ψ; S[x]: action, describing the evolution path of the system from the initial state to the final state; The path integral measure represents the contribution of all possible paths.

[0074] (4) Origin and derivation process of the formula:

[0075] 1. Dynamic Hypergraph Representation:

[0076] The dynamic hypergraph describes multicultural relationships through a collection of nodes and edges. The weight matrix W is dynamically updated to reflect the mutual influence between cultures.

[0077] 2. Tensor core verification of kinematic equations:

[0078] At each node v i Attach a tensor core T(v i ), used to verify the kinematic equations. Through the kernel function K(v i , v j ) measures the similarity between nodes and introduces a tuning parameter λ to control the coupling strength between tensor cores.

[0079] 3. Combined with the probability distribution of path integral:

[0080] The path integral method is used to calculate the probability distribution P(Ψ) of the state function Ψ. Path integral measure Describing the contribution of all possible paths, the action S[x] describes the evolution path of the system from the initial state to the final state.

[0081] 3. Combining the Dual-Domain Dynamics Equation with the Hypergraph-Tensor Hybrid Architecture

[0082] (1) The dual-domain dynamics equations and the hypergraph-tensor hybrid architecture are combined in the following way:

[0083] 1. The relationship between state function and hypergraph:

[0084] The state function Ψ of the dual-domain dynamics equation is defined on the hypergraph G:

[0085] Ψ=(ψ1,ψ2,...,ψn ) T

[0086] Each ψ i Corresponding to a node v in the hypergraph i , indicating the state of the node in the dual-domain framework.

[0087] 2. Association between diffusion term and hypergraph weight:

[0088] Diffusion term The weight matrix W in is dynamically updated by the weight matrix of the hypergraph:

[0089] D CDR =f(W)

[0090] Where f(W) is a function that maps the weight matrix of the hypergraph to the diffusion coefficient matrix.

[0091] 3. Combination of Hamiltonian operator and tensor core:

[0092] Hamiltonian operator H in non-epistemic domain NCR Using tensor core T(v i ) to verify the kinematic equations:

[0093] H NCR =g(T)

[0094] Among them, g(T) is a function that converts the results of the tensor kernel into constraints of physical laws.

[0095] 4. Overall equation:

[0096] Substituting the above combination into the dual-domain dynamics equation, we get the complete mathematical model:

[0097]

[0098] (2) Combined step description:

[0099] 1. Initialization:

[0100] ① Construct a dynamic hypergraph G = (V, E, W) and initialize the weight matrix W.

[0101] ②Define the initial state function Ψ.

[0102] 2. Iterative calculation:

[0103] ① Calculate the diffusion coefficient matrix D based on the weight matrix W of the hypergraph CDR =f(W).

[0104] ② According to the tensor core T(v i ) Calculate the Hamiltonian operator H NCR =g(T).

[0105] ③ Update the state function Ψ to satisfy the dual-domain dynamic equation.

[0106] 3. Verification and optimization:

[0107] ① Use a multimodal verification system (such as quantum Monte Carlo simulation) to ensure the reliability of the system.

[0108] ② Dynamically adjust the weight matrix W and state function Ψ to achieve system adaptability to complex scenarios.

[0109] IV. Summary

[0110] By combining dual-domain dynamics equations with a hypergraph-tensor hybrid architecture, this solution unifies subjective cognition (CDR) and objective laws (NCR). This combination not only dynamically adjusts weights to accommodate diverse cultural contexts but also ensures the physical correctness and logical consistency of the system, providing a universal solution for intelligent applications in complex scenarios.

[0111] Scenarios where quantum technology is immature: Use simplified models and classical computing methods to achieve similar functions under existing technological conditions.

[0112] Given the immaturity of existing quantum technologies, the implementation and application scope of dual-domain dynamical equations and the hypergraph-tensor hybrid architecture may be limited. The following discusses this issue from multiple perspectives:

[0113] 1. The state of the dual-domain dynamics equation when quantum technology is immature

[0114] (1) Simplified model

[0115] When quantum technology is immature, some quantum effects in the dual-domain dynamics equation (such as the entangled potential energy term) may not be accurately described or realized. In this case, the equation can be simplified to an approximate model that ignores the influence of quantum entanglement. The specific form is as follows:

[0116]

[0117] Among them: H NCR : Hamiltonian operators in non-cognitive domains are still used to describe physical laws; D CDR : The diffusion coefficient matrix in the cognitive dependency domain reflects the uncertainty of cultural communication; Laplace operator, describes spatial changes.

[0118] (2) Replacement of classical methods

[0119] When there is a lack of quantum technology support, some quantum effects can be replaced by classical statistical mechanics methods. For example:

[0120] 1. Use stochastic processes to model uncertainty in epistemic dependency domains.

[0121] 2. Use social network analysis methods to approximately describe the associations between individuals.

[0122] (3) Limitations

[0123] Although the simplified equations can be run, they may not capture complex non-local correlations (such as quantum entanglement), resulting in an incomplete description of the system behavior.

[0124] 2. The state of the hypergraph-tensor hybrid architecture when quantum technology is immature

[0125] (1) Dynamic hypergraph representation

[0126] The core functionality of the dynamic hypergraph (node ​​sets, edge sets, and weight matrices) remains functional despite the maturity of quantum technology. Even without quantum computing support, the dynamic updating of the weight matrix can be achieved using traditional computer algorithms.

[0127] (2) Tensor core verification of kinematic equations

[0128] The calculation and verification of tensor cores can be completed in the classical computing framework, but it may require more computing resources and time. The formula is as follows:

[0129]

[0130] Where: w ij : Relationship weight between nodes; κ(K i , K j ): kernel function, measuring the similarity between nodes; α: adjustment parameter, controlling the coupling strength.

[0131] (3) Probability distribution of path integral

[0132] The path integral method is usually implemented in classical computing through Monte Carlo simulation. Although less efficient, it is a viable alternative when quantum technology is immature. The formula is as follows:

[0133]

[0134] P[Ψ]: probability distribution of state function; S[Ψ]: action, describing the evolution path of the system.

[0135] (4) Limitations

[0136] Path integral and tensor core calculations in the classical computing framework may have the following problems:

[0137] 1. The computational complexity is high and it is difficult to process large-scale data.

[0138] 2. Limited ability to describe highly nonlinear or complex systems.

[0139] 3. Combining the Dual-Domain Dynamics Equation with the Hypergraph-Tensor Hybrid Architecture

[0140] Even in the absence of mature quantum technology, the dual-domain dynamical equations and the hypergraph-tensor hybrid architecture can still be combined in the following ways:

[0141] (1) Relationship between state function and hypergraph

[0142] The state function is still defined on the nodes of the hypergraph, and each node corresponds to a state value. Even without quantum technology support, this mapping relationship still works.

[0143] (2) Association between diffusion term and hypergraph weight

[0144] The diffusion coefficient matrix is ​​dynamically generated by the weight matrix of the hypergraph, and the formula is as follows:

[0145] D CDR =f(W)

[0146] Where W is the weight matrix of the hypergraph and f is a mapping function. This process can be implemented through classical computing.

[0147] (3) Combination of Hamiltonian Operator and Tensor Core

[0148] The Hamiltonian operator of the non-cognitive domain is verified using the results of the tensor core, and the formula is as follows:

[0149] H NCR =g(K)

[0150] Here, K is a set of tensor cores and g is a transformation function. This method is still applicable in the classical computing framework.

[0151] (4) Overall equation

[0152] After combining the above methods, the complete mathematical model can be written as:

[0153]

[0154] Among them, H NCR and D CDR The computation is based on the dynamic update of hypergraph and tensor cores.

[0155] (5) Limitations

[0156] 1. In the absence of quantum technology support, the computational efficiency of the overall model may be low.

[0157] 2. For scenarios involving complex phenomena such as quantum entanglement, the model’s descriptive capabilities may be insufficient.

[0158] IV. Summary

[0159] In the absence of mature quantum technology, dual-domain dynamical equations and hypergraph-tensor hybrid architectures can achieve basic functions through simplified models and classical computing methods. However, this approach has the following challenges:

[0160] 1. Computational efficiency: Path integral and tensor core calculations under the classical computing framework may consume a lot of time and resources.

[0161] 2. Descriptive ability: Unable to fully capture the complex behaviors caused by quantum effects (such as entangled potential energy terms).

[0162] Due to the high complexity of path integrals and tensor core calculations in the classical computing framework, the system may not be able to meet performance requirements in scenarios with high real-time requirements (such as autonomous driving or industrial control). In addition, simplified models may not fully capture complex non-local correlations (such as quantum entanglement), thereby limiting the robustness and universality of the system, especially in applications that need to process high-dimensional decision spaces. However, this combination still provides a basic solution for intelligent applications in complex scenarios and lays a theoretical foundation for further research on optimization directions after the maturity of quantum technology.

[0163] Comparative analysis:

[0164] (1) Similarities

[0165] Regardless of whether quantum technology is mature or not, the core ideas of the dual-domain dynamics equations and the hypergraph-tensor hybrid architecture remain consistent, that is, to describe the evolution of the system through state functions and combine hypergraph structures to reflect multicultural relationships.

[0166] (2) Differences

[0167] When quantum technology is mature, the model can describe the quantum entanglement effect more accurately; when it is immature, the model achieves similar functions through simplification and approximation methods.

[0168] Computational efficiency is higher in mature scenarios. Models can significantly reduce computational complexity and improve computational efficiency by leveraging quantum parallelism and entanglement effects. For example, the calculation of path integrals can be completed in polynomial time using quantum algorithms, while implementation in a classical computing framework may require more resources.

[0169] Based on the aforementioned in-depth analysis and technical supplements to the dual-domain modeling framework, in order to further enhance the scalability and adaptability of the system, the present invention lists and defines in detail 25 extended and deformed forms of dual-domain modeling in "A Trusted AI System Solution Based on Dual-Domain Modeling and Quantum Computing". These extended forms are intended to provide more flexible and refined solutions for specific needs in different application scenarios. The following will specifically introduce the design ideas of these 25 extended forms and their potential value in practical applications, in order to fully demonstrate the universality and scalability of the dual-domain modeling framework. Among them, the first to tenth types belong to multi-domain related extensions, the eleventh to eighteenth types belong to learning and optimization related extensions, the nineteenth to twenty-third types belong to architecture and communication related extensions, and the twenty-fourth and twenty-fifth types belong to other innovative extensions. In addition, all extended and deformed forms can be used in combination in any suitable form according to the needs of the actual application scenario.

[0170] 1. Multi-domain Modeling

[0171] 1. Theoretical basis

[0172] Concept extension: On the basis of the dual domains (cognitive dependency domain CDR and non-cognitive domain NCR), more domains (such as environmental domain EDR, social domain SDR, biological domain BDR, etc.) are added to form a multi-domain dynamic equation.

[0173] ①Mathematical framework:

[0174] The hypergraph-tensor hybrid architecture is extended from dual-domain to multi-domain space.

[0175] Use high-order tensors to represent complex relationships between domains.

[0176] The equation structure is expanded to:

[0177]

[0178] Where: Ψ: multi-domain state function, describing the comprehensive state between each domain; H i : Hamiltonian operator of the i-th field, representing the physical law constraints of the field; D ij : Diffusion coefficient matrix, reflecting the dynamic coupling relationship between different fields; V ij : coupling potential energy term, describing the interaction between domains i and j; n: number of domains.

[0179] ②Verification mechanism:

[0180] The NCR authentication core is extended to a multi-domain authentication mechanism.

[0181] Each new field introduces an independent verification sub-core (such as environmental verification sub-core, social verification sub-core, etc.).

[0182] ③Computing architecture:

[0183] Heterogeneous computing architecture extends to multi-domain dedicated accelerators.

[0184] Add dedicated processors for environmental simulation, social network computing units, and biological neuromorphic computing modules.

[0185] 2. Specific implementation method

[0186] ① Dynamic hypergraph representation:

[0187] Use dynamic hypergraph to represent the relationship between fields.

[0188] The nodes in the hypergraph represent domains, and the edges represent the coupling strength between domains.

[0189] ② Parallel processing:

[0190] Each domain processes its internal dynamic equations in parallel.

[0191] Use parallel computing frameworks such as CUDA or OpenCL to optimize computational efficiency.

[0192] ③Cross-domain interaction protocol:

[0193] Define standardized cross-domain interaction protocols to ensure consistency in data exchange between different domains.

[0194] 2. Multi-domain nested modeling

[0195] (1) Theoretical basis

[0196] 1. Nested structure definition:

[0197] A hierarchical nested relationship is formed between the domains, and the lower domains are controlled by the higher domains.

[0198] The dynamic equations are expanded into a nested form:

[0199]

[0200] Among them H outer represents the dynamic equation of the outer domain, H inner，i represents the dynamic equations of the nested domain within the i-th level.

[0201] 2. Nested types (including but not limited to):

[0202] Temporal nesting: coupling of dynamics at different time scales.

[0203] Spatial nesting: macro-microscale interactions.

[0204] Logical nesting: abstract-concrete hierarchical association.

[0205] 3. Mathematical tools:

[0206] Higher-order tensor analysis: Representing nested relations using rank-4 tensors.

[0207] Extension of quantum field theory: Introducing the gauge field hierarchy and establishing nested Feynman diagram calculation rules.

[0208] (2) Specific implementation method

[0209] 1. System architecture design:

[0210] Use hierarchical controllers to coordinate interactions between domains at each layer.

[0211] Example Architecture: Hierarchy of Multi-Domain Nested Modeling (e.g. Figure 1 )

[0212] ① Outermost domain

[0213] The outermost domain is the top-level control unit of the entire system, responsible for coordinating and managing the interactions between all nested subdomains. It implements unified scheduling and optimization of each layer of domains through a hierarchical controller.

[0214] ②Cognitive nesting layer

[0215] The cognitive nested layer is the first sublayer of the outermost domain and focuses on processing the dynamic processes related to cognition. This layer is divided into two main parts:

[0216] Individual Cognitive Dynamics: This section focuses on the cognitive behavior of a single individual, such as short-term memory, long-term memory, and perception. Its dynamic equations describe the changes in individual cognition at different time scales.

[0217] Group Cultural Communication: This section studies cultural communication phenomena at the group level, including social norms, the transmission of values, and collective behavior patterns. The dynamics of group cultural communication considers the interactions between individuals and their impact on the overall cultural evolution.

[0218] ③Physical nesting layer

[0219] The physical nesting layer is the second sublayer of the outermost domain and is used to describe the multi-level characteristics of the physical system. This layer is also divided into two main parts:

[0220] Classical mechanics constraints: The classical mechanics constraints section focuses on the physical laws at the macroscopic scale, such as Newton's laws of motion and the law of conservation of energy. This section is applicable to describing the motion and interactions of large-scale objects.

[0221] Quantum Effect Correction: The quantum effect correction part targets physical phenomena at the microscopic scale, such as electron energy level transitions and quantum entanglement. This part makes necessary corrections to the classical mechanics model by introducing quantum field theory methods.

[0222] ④Environment nesting layer

[0223] The environment nesting layer is located in the third sublayer of the outermost domain and is mainly used to analyze the multi-scale characteristics of the environmental system. This layer also consists of two main parts:

[0224] Local microenvironment: The local microenvironment focuses on environmental variables within a small area, such as temperature, humidity, light intensity, etc. Changes in these variables directly affect the operating status of organisms or equipment.

[0225] Global Climate System: The Global Climate System section studies the overall changing trends of Earth's climate at a larger scale, such as greenhouse gas concentrations and ocean circulation patterns. The dynamic equations in this section often require a combination of atmospheric science and geophysics.

[0226] The example architecture above demonstrates the core concept of multi-domain nested modeling: organizing dynamic processes in different domains into a unified nested structure through hierarchical controllers. Specifically, the cognitive nested layer focuses on individual and group cognitive behaviors; the physical nested layer studies macroscopic and microscopic physical laws; and the environmental nested layer analyzes local and global environmental characteristics.

[0227] This hierarchical design not only facilitates understanding the dynamic evolution of complex systems, but also provides flexible expansion space for practical applications.

[0228] 2. Nested Monte Carlo method:

[0229] Outer layer: coarse-grained sampling to quickly assess overall trends.

[0230] Inner layer: fine sampling of conditions and in-depth analysis of local details.

[0231] 3. Cross-level verification core:

[0232] The parent domain verifies the child domain boundary conditions.

[0233] The subdomain feeds back the parent domain parameters for optimization.

[0234] 3. Multi-domain hierarchical modeling

[0235] 1. Theoretical basis

[0236] ① Layered definition

[0237] Divide multiple domains into different levels, each level is responsible for handling specific sub-problems. The specific hierarchical relationship is as follows:

[0238] Perception layer: responsible for data collection and obtaining real-time environmental information through sensor networks.

[0239] Decision-making layer: formulates and optimizes strategies based on the data provided by the perception layer and generates control instructions.

[0240] Execution layer: Completes specific actions according to the instructions of the decision-making layer.

[0241] ②Hierarchical relationship

[0242] Each layer can operate independently or work in conjunction with other layers. Interfaces are used between layers to achieve efficient communication and ensure consistent and real-time data transmission.

[0243] ③Mathematical tools

[0244] The layered tensor product is used to represent the dynamic relationship between layers. The dynamic equation is expanded into a layered form, and the specific expression is as follows:

[0245]

[0246] Where: S i Indicates the state of the i-th layer; F i represents the dynamics function of the i-th layer; S i-1 and S i+1 Respectively represent the status of adjacent layers.

[0247] 2. Specific implementation method

[0248] ① Perception layer:

[0249] Collect real-time data using sensor networks.

[0250] Data preprocessing: filtering, noise reduction, and feature extraction.

[0251] ②Decision-making level:

[0252] Formulate strategies based on data from the perception layer.

[0253] Use reinforcement learning or deep learning models to optimize decision-making.

[0254] ③Execution layer:

[0255] Implement the instructions of the decision-making layer.

[0256] Use robotic control systems or automated equipment to complete tasks.

[0257] ④Inter-layer communication:

[0258] Design efficient communication protocols to ensure consistency and real-time data transmission between layers.

[0259] Examples: using a message queue (such as Kafka) or remote procedure call (RPC) technology.

[0260] 4. Multi-domain nested hierarchical modeling

[0261] (1) Theoretical basis

[0262] 1. Combine nesting and layering:

[0263] On the basis of multi-domain layering, a hierarchical nested relationship is constructed.

[0264] There are nested subdomains within each layer, and there are also nested relationships between layers.

[0265] 2. Nested hierarchical structure:

[0266] The dynamic equations are expanded into a nested hierarchical form:

[0267]

[0268] Where: l represents the layer number; m represents the number of nested subdomains in the lth layer; Ψ l，m is a dual-domain state function, the state at the lth layer and the mth subdomain; It is a Hamiltonian operator in a non-epistemic domain; is the diffusion coefficient matrix in the cognitive dependency domain; is a gauge field operator; is the entanglement potential energy term.

[0269] 3. Mathematical tools:

[0270] Use high-rank tensors to represent nested hierarchical relationships.

[0271] Develop differential geometry on nested manifolds.

[0272] (2) Specific implementation method

[0273] 1. System architecture design:

[0274] Combining the ideas of nesting and layering, a multi-level nested structure is formed.

[0275] Example Architecture: Hierarchy of multi-domain nested hierarchical modeling (e.g. Figure 2 )

[0276] ①Top-level domain

[0277] The top-level domain is the top-level control unit of the entire system, responsible for coordinating and managing the interactions between all nested subdomains. It implements unified scheduling and optimization of each layer of domains through a hierarchical controller.

[0278] ②Cognitive nesting layer

[0279] The cognitive nested layer is the first sublayer of the top-level domain and focuses on processing the dynamic processes related to cognition. This layer is divided into two main parts:

[0280] A. Individual Cognitive Dynamics: This section focuses on the cognitive behavior of a single individual, such as the changing patterns of short-term and long-term memory. Its dynamic equations describe the cognitive changes of individuals over different time scales.

[0281] Short-term memory subfield: The short-term memory subfield studies the process of information storage and retrieval over a short period of time, such as the functional mechanism of working memory.

[0282] Long-term memory subdomain: The long-term memory subdomain focuses on the ability to store and recall information for a long time, such as the dynamic evolution of semantic memory and episodic memory.

[0283] B. Group Cultural Communication: This sub-domain examines cultural communication phenomena at the group level, including social norms, the transmission of values, and collective behavior patterns. The dynamics of group cultural communication considers the interactions between individuals and their impact on overall cultural evolution. The social sub-domain analyzes the influence of social structure on cultural communication, such as the information diffusion mechanism in social networks.

[0284] Cultural subdomain: The cultural subdomain studies the role of cultural background in shaping group behavior, such as the formation and evolution of values ​​in different cultural backgrounds.

[0285] ③Physical nesting layer

[0286] The physical nesting layer is the second sublayer of the top-level domain and is used to describe the multi-level characteristics of the physical system. This layer is also divided into two main parts:

[0287] A. Classical mechanics constraints: Classical mechanics constraints focus on the physical laws at the macroscopic scale, such as Newton's laws of motion and the law of conservation of energy. This part is applicable to describing the motion and interactions of large-scale objects.

[0288] Macroscopic physics subfield: The macroscopic physics subfield studies large-scale physical phenomena, such as rigid body motion, fluid mechanics, etc.

[0289] Microphysics subfield: The microphysics subfield focuses on small-scale physical phenomena, such as molecular motion, thermodynamic processes, etc.

[0290] B. Quantum Effect Correction: The quantum effect correction section addresses physical phenomena at the microscopic scale, such as electron energy level transitions and quantum entanglement. This section introduces quantum field theory to make necessary corrections to the classical mechanics model.

[0291] ④Environmental nesting layer: The environmental nesting layer is located in the third sub-layer of the top domain and is mainly used to analyze the multi-scale characteristics of the environmental system. This layer also contains two main parts:

[0292] A. Local Microenvironment: The local microenvironment focuses on environmental variables within a small area, such as temperature, humidity, etc. Changes in these variables directly affect the operating status of organisms or equipment.

[0293] Temperature subdomain: The temperature subdomain studies the temperature variation pattern in a local area and its impact on the system, such as the heat conduction process.

[0294] Humidity subdomain: The humidity subdomain focuses on the effects of humidity changes on environmental conditions, such as the processes of water evaporation and condensation.

[0295] B. Global Climate System: The Global Climate System section studies the overall changing trends of the Earth's climate on a larger scale, such as greenhouse gas concentrations and ocean circulation patterns.

[0296] Earth Subdomain: The Earth Subdomain analyzes the physical and chemical processes on the Earth's surface and its atmosphere, such as surface temperature distribution and changes in atmospheric composition.

[0297] Solar radiation subdomain: The solar radiation subdomain studies the impact of solar radiation on the Earth's climate system, such as the relationship between solar activity cycles and climate change.

[0298] The example architecture above demonstrates the core concept of multi-domain nested hierarchical modeling: combining the concepts of nesting and layering to divide a system into multiple hierarchies and subdomains, with each hierarchical layer containing nested subdomains. Specifically, the cognitive nested layer focuses on the cognitive behavior of individuals and groups; the physical nested layer studies macroscopic and microscopic physical laws; and the environmental nested layer analyzes local and global environmental characteristics.

[0299] This hierarchical nested design not only facilitates understanding the dynamic evolution of complex systems, but also provides flexible expansion space for practical applications.

[0300] 2. Nested Monte Carlo method:

[0301] Outer layer: coarse-grained sampling to assess overall trends.

[0302] Middle layer: medium-grained sampling to analyze middle-level details.

[0303] Inner layer: Conditional fine sampling, delving into the underlying details.

[0304] 3. Cross-level verification core:

[0305] The parent layer verifies the sublayer boundary conditions.

[0306] The sub-layer feeds back the parent layer parameters for optimization.

[0307] 4. Computing acceleration technology:

[0308] Use nested quantum algorithms such as Grover search nested execution and quantum phase estimation hierarchical optimization.

[0309] Heterogeneous computing allocation: The outer layer is calculated by GPU clusters, and the inner layer is accelerated by quantum processors.

[0310] 5. Multi-domain hierarchical nested modeling

[0311] (1) Theoretical basis

[0312] 1. Definition: Layering is done first, followed by nested relationships within each layer. This structure allows the system to be gradually refined from the top to the bottom while preserving the control relationships between layers.

[0313] 2. Mathematical tools:

[0314] The dynamical relationships between layers are represented using layer-wise tensor products.

[0315] The dynamic equations are expanded into a hierarchical nested form:

[0316]

[0317] Where: k represents the layer number; m represents the nested subdomain number within the kth layer; H NCR，k is a non-cognitive Hamiltonian that describes the influence of physical laws on the kth layer; D CDR，k，m is the diffusion coefficient matrix of cognitive dependency domain, reflecting the cultural dynamics of the mth subdomain in the kth layer; A k，m is a gauge field operator, which represents the constraints of social rules on the behavioral trajectory of the mth subdomain in the kth layer.

[0318] 3. Combination of hierarchy and nesting:

[0319] There are nested subdomains within each layer, and there are also nested relationships between layers.

[0320] For example, the perception layer contains environmental nested subdomains (such as temperature subdomain and humidity subdomain), and the decision layer contains cognitive nested subdomains (such as short-term memory subdomain and long-term memory subdomain).

[0321] (2) Specific implementation method

[0322] 1. Architecture design:

[0323] Use hierarchical controllers to coordinate interactions between layers while implementing nested structures within each layer.

[0324] Example architecture: Hierarchy of multi-domain hierarchical nested modeling (such as Figure 3 )

[0325] ①Top-level domain

[0326] The top-level domain is the top-level control unit of the entire system, responsible for coordinating and managing the interactions between all hierarchical and nested subdomains. The hierarchical controller enables unified scheduling and optimization of each domain.

[0327] ②Perception layer

[0328] The perception layer is the first sublayer of the top-level domain and focuses on data collection and environmental monitoring. This layer consists of two main parts:

[0329] A. Environment nested subdomain: The environment nested subdomain is further subdivided into multiple subdomains, which are used to analyze specific variables in the environment and their changing patterns.

[0330] Temperature subdomain: The temperature subdomain studies the temperature variation pattern in a local area and its impact on the system, such as the heat conduction process.

[0331] Humidity subdomain: The humidity subdomain focuses on the effects of humidity changes on environmental conditions, such as the processes of water evaporation and condensation.

[0332] B. Social Embeddedness Subdomain: The social embeddedness subdomain analyzes the impact of social structure on system behavior, such as the role of cultural background and social norms.

[0333] Cultural subdomain: The cultural subdomain studies the role of cultural background in shaping group behavior, such as the formation and evolution of values ​​in different cultural backgrounds.

[0334] Legal subdomain: The legal subdomain analyzes the constraining effect of legal systems on social behavior, such as the normative influence of laws and regulations on individual behavior.

[0335] ③Decision-making level

[0336] The decision-making layer is located in the second sub-layer of the top domain and is responsible for formulating and optimizing strategies based on the data provided by the perception layer. This layer is also divided into two main parts:

[0337] A. Cognitive nesting subdomain: The cognitive nesting subdomain focuses on the cognitive behavior of individuals or groups and their dynamic changes.

[0338] Short-term memory subfield: The short-term memory subfield studies the process of information storage and retrieval over a short period of time, such as the functional mechanism of working memory.

[0339] Long-term memory subdomain: The long-term memory subdomain focuses on the ability to store and recall information for a long time, such as the dynamic evolution of semantic memory and episodic memory.

[0340] B. Non-cognitive nested subdomain: The non-cognitive nested subdomain analyzes the constraints of physical laws and mathematical models on the decision-making process.

[0341] Physical Constraints Subdomain: The physical constraints subdomain studies the constraints imposed by physical laws on the behavior of a system, such as the law of conservation of energy or the equations of kinematics.

[0342] Mathematical model subdomain: The mathematical model subdomain describes the system's behavior patterns and evolution laws through mathematical tools (such as tensor analysis and differential equations).

[0343] ④Execution layer

[0344] The execution layer is located in the third sub-layer of the top-level domain and is responsible for completing specific actions according to the instructions of the decision-making layer. This layer consists of two main parts:

[0345] A. Action nested subdomain: The action nested subdomain is further subdivided into multiple subdomains for analyzing and controlling specific action behaviors.

[0346] Motion subdomain: The motion subdomain studies the motion laws of objects or devices and their control methods, such as the motion trajectory planning of robot joints.

[0347] Perception feedback subdomain: The perception feedback subdomain obtains the action execution status in real time through the sensor network and makes adjustments and optimizations based on the feedback information.

[0348] B. Environmental Response Subdomain: The environmental response subdomain analyzes the system's adaptability to changes in the external environment and its response mechanism, such as the response of an autonomous driving system to changes in traffic conditions.

[0349] The example architecture above demonstrates the core concept of multi-domain hierarchical nested modeling: By first layering and then nesting, the system is divided into multiple levels and subdomains, with each level containing nested subdomains. Specifically, the perception layer focuses on data collection and environmental monitoring; the decision layer is responsible for policy formulation and optimization; and the execution layer implements specific actions.

[0350] This hierarchical nested design not only facilitates understanding the dynamic evolution of complex systems, but also provides flexible expansion space for practical applications.

[0351] 2. Cross-level verification core:

[0352] The parent layer verifies the sublayer boundary conditions.

[0353] The sub-layer feeds back the parent layer parameters for optimization.

[0354] 3. Computing acceleration technology:

[0355] A quantum phase estimation hierarchical optimization algorithm is used to handle nested subdomains.

[0356] Heterogeneous computing allocation: The outer layer is calculated by GPU clusters, and the inner layer is accelerated by quantum processors.

[0357] 6. Dynamic Multi-Domain Modeling

[0358] 1. Theoretical basis

[0359] ①Definition: The number and types of domains can be dynamically adjusted according to actual needs, and are suitable for systems with frequent scene changes or complex tasks.

[0360] ②Dynamic mechanism:

[0361] Add / Remove Domains: Dynamically introduce or remove certain domains based on the external environment.

[0362] Adjust coupling strength: Dynamically adjust the coupling relationship between domains through the weight matrix.

[0363] ③Mathematical tools:

[0364] Use dynamic graph structures to represent the relationships between domains.

[0365] The kinetic equations are expanded into a dynamic form:

[0366]

[0367] Among them: k (t) represents the state function of the kth domain; H NCR，k (t) is the Hamiltonian operator in the non-cognitive domain, describing the constraints of physical laws on the kth domain; D CDR,k (t) is the diffusion coefficient matrix in the cognitive dependency domain, reflecting the changes in cultural communication and individual subjective experience; A k (t) is a gauge field operator used to describe the constraints of social rules on behavioral trajectories; t is a time variable; is the reduced Planck constant.

[0368] 2. Specific implementation method

[0369] ① Dynamic domain management:

[0370] Use an event-driven mechanism to detect whether fields need to be added or removed.

[0371] Example: An autonomous driving system dynamically introduces meteorological fields based on weather conditions.

[0372] ②Weight adjustment mechanism:

[0373] Use reinforcement learning or adaptive algorithms to dynamically adjust the weights between domains.

[0374] Example: In a medical diagnosis system, the weights of the biological and social domains are dynamically adjusted based on the patient's condition.

[0375] ③Real-time guarantee:

[0376] Use streaming computing frameworks such as Apache Flink to process real-time data.

[0377] The buffer zone is designed to ensure the smoothness of the domain switching process.

[0378] 7. Hybrid Multi-Domain Modeling

[0379] 1. Theoretical basis

[0380] ①Definition: Modeling methods in different fields can be mixed and used. For example, some fields use classical modeling methods, while others use quantum computing methods.

[0381] ②Mixed strategy:

[0382] Choose an appropriate modeling method based on domain characteristics.

[0383] Example: Cognitive Dependent Domain (CDR) uses classical neural networks, and Non-Cognitive Domain (NCR) uses quantum computing.

[0384] ③Mathematical tools:

[0385] Integrate different modeling methods using a unified mathematical framework.

[0386] The dynamic equations are expanded into a mixed form:

[0387]

[0388] Among them: H classical Represents the Hamiltonian operator corresponding to the classical modeling method; H quantum Represents the Hamiltonian operator corresponding to the quantum modeling method.

[0389] 2. Specific implementation method

[0390] ①Modeling method selection:

[0391] For low-complexity domains, use classical modeling methods (e.g., neural networks, support vector machines).

[0392] For high-complexity areas, quantum modeling methods (such as quantum annealing and quantum simulation) are used.

[0393] ② Heterogeneous computing architecture:

[0394] Support hybrid modeling using silicon-quantum heterogeneous computing architecture.

[0395] Example: Cognitive Dependent Domain (CDR) runs on GPU and Non-Cognitive Domain (NCR) runs on quantum processor.

[0396] ③Data fusion:

[0397] Design standardized interface specifications to ensure that the results of different modeling methods can be seamlessly integrated.

[0398] Example: Using a message queue (such as Kafka) to implement data exchange between classical computing and quantum computing.

[0399] 8. Adaptive Multi-Domain Modeling

[0400] 1. Theoretical basis

[0401] ①Definition: The system can automatically adjust the coupling relationship between domains according to changes in the external environment, improving the robustness and adaptability of the system. ②Adaptive mechanism:

[0402] Dynamically adjust field weights.

[0403] Automatically optimize the coupling relationship between domains.

[0404] ③Mathematical tools:

[0405] Adaptive control theory is used to adjust the coupling relationship between domains.

[0406] The dynamic equations are expanded into an adaptive form:

[0407]

[0408] Among them H sys (t), D dyn (t), A ctrl (t) is an adaptive parameter that changes with time.

[0409] 2. Specific implementation method

[0410] ① Adaptive algorithm:

[0411] Optimize adaptive parameters using reinforcement learning or evolutionary algorithms.

[0412] Example: In an autonomous driving system, the weights of the environmental domain and the social domain are dynamically adjusted according to road conditions.

[0413] ②Real-time guarantee:

[0414] The use of a real-time operating system (RTOS) ensures the efficiency of the adaptation process.

[0415] Design a caching mechanism to reduce the computational overhead during the adaptation process.

[0416] ③Application scenarios (including but not limited to):

[0417] Autonomous driving: Dynamically adjust the weight of each field according to traffic conditions.

[0418] Medical diagnosis: Dynamically adjust the weights of the biological domain and cognitive domain based on the patient's condition.

[0419] 9. Recursive Multi-Domain Modeling

[0420] 1. Theoretical basis

[0421] ①Definition: Each domain can be further divided into smaller domains, forming a recursive structure, which is suitable for multi-level complex systems.

[0422] ②Recursive mechanism:

[0423] Each domain can be further divided into subdomains.

[0424] The same dynamical relationships exist between the subdomains.

[0425] ③Mathematical tools:

[0426] Use recursive tensors to represent recursive relations between domains.

[0427] The dynamic equations are expanded into a recursive form:

[0428]

[0429] in: represents the overall dynamic equation of the parent domain; represents the dynamic equation of the th subdomain; N represents the number of subdomains.

[0430] 2. Specific implementation method

[0431] ① Recursive structure design:

[0432] Define the recursion depth and the domain partitioning rules for each level.

[0433] Example: The social domain can be subdivided into cultural subdomains, legal subdomains, etc.

[0434] ②Computing acceleration technology:

[0435] Use divide-and-conquer algorithms to handle recursive structures.

[0436] Heterogeneous computing allocation: The high-level layers are computed by CPUs, while the low-level layers are accelerated by GPUs or quantum processors.

[0437] ③Verification mechanism:

[0438] A recursive verification protocol is used to verify the consistency of each field layer by layer.

[0439] Example: Verify the boundary conditions of subdomains layer by layer starting from the top layer.

[0440] 10. Distributed Multi-Domain Modeling

[0441] 1. Theoretical basis

[0442] ①Definition: Various fields are distributed in different physical locations and work together through the network, which is suitable for large-scale distributed systems.

[0443] ②Distributed mechanism:

[0444] Each area operates independently and exchanges data through the network.

[0445] Use consistency algorithms to ensure global consistency in distributed systems.

[0446] ③Mathematical tools:

[0447] Use distributed optimization algorithms to handle multi-domain collaborative problems.

[0448] The dynamic equations are expanded into a distributed form:

[0449]

[0450] Among them: i (t): The state function of the field, describing the comprehensive state of subjective cognition (CDR) and objective law (NCR); H NCR，i : Hamiltonian operator in the non-cognitive domain (NCR), representing the constraints of physical laws; D CDR，i : The diffusion coefficient matrix in the cognitive dependency domain (CDR) reflects the changes in cultural dynamics and individual subjective experience; A i : Gauge field operator, derived from gauge field theory, used to describe the constraints of social rules on behavioral trajectories; V ent，i (Ψ i ):entanglement potential energy term, describing the non-local correlation between different nodes or individuals. t:time variable; Reduced Planck constant.

[0451] For distributed systems, introduce neighbor domain sets And the dynamic equation is expanded into the following form:

[0452]

[0453] Where: W ij : Weight matrix, dynamically updated to reflect the mutual influence between domains.

[0454] 2. Specific implementation method

[0455] ①Distributed architecture:

[0456] Use cloud computing or edge computing technologies to support distributed modeling.

[0457] Example: In industrial control systems, domains across different factories collaborate via the Internet.

[0458] ②Data exchange protocol:

[0459] Define standardized data exchange protocols to ensure data consistency between different domains.

[0460] Examples: using a message queue (such as Kafka) or remote procedure call (RPC) technology.

[0461] ③Consistency guarantee:

[0462] Use consensus algorithms (such as Paxos and Raft) to ensure global consistency of distributed systems.

[0463] Design fault-tolerant mechanisms to handle network failures or node failures.

[0464] 11. Multi-domain co-evolution modeling

[0465] 1. Theoretical basis

[0466] ①Definition: Various fields evolve together through the co-evolution mechanism to improve the performance of the overall system.

[0467] ②Co-evolution mechanism:

[0468] Different fields influence and adapt to each other.

[0469] Example: The cognitive dependency domain (CDR) and the non-cognitive domain (NCR) influence each other and are jointly optimized in long-term interactions.

[0470] ③Mathematical tools:

[0471] A co-evolutionary algorithm is used to represent the dynamic coupling relationship between domains.

[0472] The dynamic equations are expanded into a coevolutionary form:

[0473]

[0474] Among them, H i (Ψ i ) represents the internal dynamics of the i-th domain; C ij (Ψ j ) represents the influence of domain j on domain i; i, j∈{EP,EC,EI,SD}.

[0475] 2. Specific implementation method

[0476] ① Co-evolutionary algorithm:

[0477] Use genetic algorithms or differential evolution algorithms to achieve co-evolution between domains.

[0478] Example: In smart manufacturing, the production domain and the quality domain improve overall performance through co-evolutionary learning.

[0479] ②Evaluation mechanism:

[0480] Design a comprehensive evaluation function to measure the synergistic effect of each field.

[0481] Example: Evaluating performance indicators across multiple domains using a weighted average approach.

[0482] ③Application scenarios (including but not limited to):

[0483] Intelligent manufacturing: Collaborative optimization of the production and social domains to improve production efficiency and worker satisfaction.

[0484] Autonomous driving: The environmental domain and cognitive domain co-evolve to improve the accuracy of driving decisions.

[0485] 12. Multi-domain Self-learning Modeling

[0486] 1. Theoretical basis

[0487] ①Definition: The system can continuously optimize modeling methods in various fields through self-learning mechanisms.

[0488] ②Self-learning mechanism:

[0489] Automatically extract knowledge from data using machine learning algorithms.

[0490] Example: The system automatically adjusts the weights of the cognitive dependency domain (CDR) and the social domain (SDR) based on historical data.

[0491] ③Mathematical tools:

[0492] Use deep learning models to represent complex relationships in various fields.

[0493] The dynamic equations are expanded into a self-learning form:

[0494]

[0495] Where: Ψ: state function, representing the comprehensive state of multiple domains (such as biological domain, social domain, etc.); The reduced Planck constant is used to describe the scale of quantum effects; t is the time variable, which represents the evolution of the system; N is the total number of domains, which indicates the number of domains involved in the modeling (such as biological domain, social domain, etc.); H i (θ i ): Hamiltonian operator of the i-th field, describing the basic laws of the field; D i (θ i ):The diffusion coefficient matrix of the ith field, reflecting the dynamic characteristics of uncertainty or change; ΔH i: The increment of the Hamiltonian operator is determined by the parameter update gradient, which indicates that the system optimizes the domain law through the self-learning mechanism; ΔD i : The increment of the diffusion coefficient matrix, which is determined by the parameter update gradient, represents the optimization of the system to the domain uncertainty through the self-learning mechanism; ΔV: The increment of the entanglement potential energy term, which is determined by the parameter update gradient, represents the optimization of the non-local correlation between different domains through the self-learning mechanism; V entanglement (θ): Entanglement potential term, describing the nonlocal correlation between different fields. ;θ i : Model parameters of the i-th field, representing the modeling rules of the field; Parameter update gradient, which represents the process of adjusting model parameters through self-learning mechanism; Laplace operator, describing changes in space; The summation symbol indicates the accumulation of contributions from all areas.

[0496] 2. Specific implementation method

[0497] ① Self-learning algorithm:

[0498] Use neural networks or reinforcement learning models for self-learning.

[0499] Example: In medical diagnosis, the biological and social domains are continuously optimized through self-learning mechanisms.

[0500] ②Feedback mechanism:

[0501] The feedback loop is designed to ensure the stability of the self-learning process.

[0502] Example: Using an error feedback mechanism to tune model parameters.

[0503] ③Application scenarios (including but not limited to):

[0504] Healthcare: Integrate physiological data and patient psychological data to generate personalized treatment plans through self-learning mechanisms.

[0505] Smart city: Citizen behavior patterns and social rules are continuously optimized through self-learning mechanisms.

[0506] 13. Multi-domain transfer learning modeling

[0507] 1. Theoretical basis

[0508] ①Definition: Transferring knowledge from one field to another for modeling.

[0509] ② Transfer learning mechanism:

[0510] Extract knowledge from the source domain and adapt it to the target domain.

[0511] Example: Transferring decision-making knowledge from the cognitive dependent domain (CDR) to the non-cognitive domain (NCR).

[0512] ③Mathematical tools:

[0513] Use transfer learning algorithms to represent knowledge transfer between domains.

[0514] The dynamics equation is expanded into transfer learning form:

[0515] Ψ T (t) = Ψ S (t)+α·ΔΨ(t)

[0516] Among them: T (t): state function of the target domain, representing the comprehensive state of the target culture at time t; S (t): state function of the source domain, representing the comprehensive state of the source culture at time t; ΔΨ(t): migration error term, representing the difference between the source domain and the target domain; α: migration intensity parameter, controlling the degree of influence of source domain knowledge on the target domain.

[0517] 2. Specific implementation method

[0518] ① Migration algorithm:

[0519] Use domain adaptation techniques to reduce migration errors.

[0520] Example: In autonomous driving, transferring knowledge from urban roads to rural roads.

[0521] ②Evaluation mechanism:

[0522] Design an evaluation function to measure the transfer effect.

[0523] Example: Use mean squared error (MSE) to evaluate the performance of the transferred data.

[0524] ③Application scenarios (including but not limited to):

[0525] Autonomous driving: Migrating urban driving experience to rural driving scenarios.

[0526] Cross-cultural adaptation: Transferring decision-making patterns from one culture to another.

[0527] 14. Multi-domain reinforcement learning modeling

[0528] 1. Theoretical basis

[0529] ①Definition: Modeling and optimizing multiple domains using reinforcement learning methods.

[0530] ② Reinforcement learning mechanism:

[0531] Guiding collaborative work between domains through reward signals.

[0532] Example: In autonomous driving, reinforcement learning is used to optimize the collaborative work of the cognitive dependent domain (CDR) and the non-cognitive domain (NCR).

[0533] ③Mathematical tools:

[0534] The Markov decision process (MDP) is used to represent the dynamic relationship between domains.

[0535] The dynamics equation is expanded into reinforcement learning form:

[0536]

[0537] Among them: t : The state function represents the comprehensive state of the system at time t. It is a high-dimensional vector or tensor that contains state information of all fields (not just CDR and NCR);

[0538] H env : Environmental Hamiltonian, which describes the objective physical laws or external environmental constraints of the system. It can be any objective rule related to the dynamic evolution of the system, such as physical laws, economic models, or other objective laws; D sub : The subjective diffusion coefficient matrix reflects the changes and uncertainties of subjective factors (such as human behavior, cultural influence, etc.) in the system. It captures the dynamic characteristics of the subjective cognitive domain in the system; Laplace operator describes the change in space. It is used to measure the gradient change of the state function in different dimensions and reflects the spatial distribution characteristics of the system state; G rule : Gauge field operator, derived from gauge field theory, is used to describe the constraints imposed by social rules, policies and regulations, or other formal rules on the behavior trajectory of a system; V entanglement : Entanglement potential energy term, which describes the non-local correlation between different nodes or individuals in the system. It can capture the implicit dependencies in complex systems, such as quantum entanglement effects or group interactions in social networks; R(S t , A t ): Reward function, indicating that the system is in the current state S t Next, perform action A t The immediate reward obtained. It is a core component of reinforcement learning and is used to guide the system to optimize the goal.

[0539] 2. Specific implementation method

[0540] ① Reinforcement learning algorithm:

[0541] Use deep reinforcement learning (DRL) or policy gradient methods to handle multi-domain problems.

[0542] Example: In industrial control, DRL is used to optimize production efficiency and energy consumption.

[0543] ②Reward design:

[0544] Design a comprehensive reward function to balance the objectives of different domains.

[0545] Example: In medical diagnosis, the reward function considers both diagnostic accuracy and patient comfort.

[0546] ③Application scenarios (including but not limited to):

[0547] Industry 4.0: Dynamic coordination of physical devices (NCR), worker specifications (CDR), and supply chain costs (economic domain).

[0548] Healthcare: The time it takes to generate personalized treatment plans has been reduced from 72 hours to 1 hour.

[0549] 15. Multi-domain Joint Optimization Modeling

[0550] 1. Theoretical basis

[0551] ①Definition: Jointly optimize all areas to improve overall performance.

[0552] ②Joint optimization mechanism:

[0553] Treat all areas as a whole and improve system performance through global optimization methods.

[0554] Example: Joint optimization of cognitive dependency domain (CDR), non-cognitive domain (NCR), and environmental domain (EDR).

[0555] ③Mathematical tools:

[0556] Use multi-objective optimization algorithms to represent complex relationships between domains.

[0557] The dynamic equations are expanded into a joint optimization form:

[0558]

[0559] Where: H: objective function of multi-domain joint optimization; n: total number of domains involved in optimization; w i : The weight parameter of the i-th field, used to balance the importance of different fields; L i : The loss function of the ith field, which represents the optimization goal in the field; R: Regularization term, used to prevent the model from overfitting; λ: Regularization coefficient.

[0560] 2. Specific implementation method

[0561] ①Optimization algorithm:

[0562] Joint optimization is performed using genetic algorithms, particle swarm optimization (PSO), or Bayesian optimization methods.

[0563] Example: Jointly optimizing traffic flow, air quality, and social satisfaction in smart cities.

[0564] ②Constraints:

[0565] Design constraints ensure the feasibility of the optimization results.

[0566] Example: In medical diagnosis, constraints include diagnostic accuracy and ethical requirements.

[0567] ③Application scenarios (including but not limited to):

[0568] Smart cities: Simultaneously optimizing traffic flow, air quality, and social satisfaction.

[0569] Industrial control: Dynamically coordinate production efficiency, energy consumption and environmental protection requirements.

[0570] 16. Multi-domain Meta-learning Modeling

[0571] 1. Theoretical basis

[0572] ① Definition: Through meta-learning methods, the system can quickly adapt to new fields or new tasks.

[0573] ②Meta-learning mechanism:

[0574] Learning to learn, extracting common knowledge between domains.

[0575] Example: In autonomous driving, extracting common rules from different driving scenarios.

[0576] ③Mathematical tools:

[0577] Use meta-learning algorithms to represent rapid adaptability between domains.

[0578] The dynamics equation is expanded into a meta-learning form:

[0579]

[0580] Where: Ψ(t): state function, representing the comprehensive state of the system; L i (Ψ): loss function of the ith domain; R(Ψ): regularization term used to prevent overfitting; w i : Weight parameter, indicating the importance of each field; λ: regularization coefficient; α: learning rate.

[0581] The joint optimization objective is:

[0582]

[0583] Where: L CDR (Ψ): loss function of the cognitive dependency domain; L NCR (Ψ): loss function of the non-cognitive domain; L EDR (Ψ): Loss function of the environment domain.

[0584] 2. Specific implementation method

[0585] ① Meta-learning algorithm:

[0586] Use MAML (Model-Agnostic Meta-Learning) or Reptile algorithm for meta-learning.

[0587] Example: In medical diagnosis, extracting common features from medical records of different patients.

[0588] ② Rapid adaptation mechanism:

[0589] Design fast-adaptive modules to enable the system to quickly adjust to new areas.

[0590] Example: In smart cities, quickly adapt to traffic regulations in different cities.

[0591] ③Application scenarios (including but not limited to):

[0592] Autonomous driving: Quickly adapt from urban roads to rural roads.

[0593] Healthcare: Rapidly adapting diagnostic models from one disease to another.

[0594] 17. Multi-domain Hybrid Reasoning Modeling

[0595] 1. Theoretical basis

[0596] ①Definition: Combining symbolic reasoning and neural network reasoning to form a hybrid reasoning framework.

[0597] ② Hybrid reasoning mechanism:

[0598] Symbolic reasoning handles tasks with strong logic, and neural network reasoning handles complex pattern recognition tasks.

[0599] For example, the cognitive dependency domain (CDR) uses symbolic reasoning, and the non-cognitive domain (NCR) uses neural network reasoning.

[0600] ③Mathematical tools:

[0601] Integrate symbolic and neural network reasoning using a unified reasoning framework.

[0602] The dynamic equations are expanded into a mixed reasoning form:

[0603]

[0604] Where: Ψ represents the state function of the system, reflecting the comprehensive state of subjective cognition (CDR), objective laws (NCR), and other fields (such as symbolic reasoning, neural network reasoning, etc.); H is the Hamiltonian operator in the non-cognitive domain, used to describe the constraints of physical laws; D is the diffusion coefficient matrix in the cognitive dependency domain, reflecting the changes in cultural communication and individual experience; G is the gauge field operator, used to describe the constraints of social rules on behavioral trajectories; F j (Ψ) represents the dynamic evolution term of the jth reasoning domain, j = 1, 2, ..., n, corresponding to different reasoning mechanisms (such as symbolic reasoning, neural network reasoning, etc.); V 纠缠 is the entanglement potential energy term, which describes the non-local correlation between different nodes or individuals.

[0605] 2. Specific implementation method

[0606] ① Reasoning framework design:

[0607] Design symbolic reasoning engine and neural network reasoning engine, and interact with them through interfaces.

[0608] Example: In autonomous driving, symbolic reasoning handles traffic rules, and neural network reasoning handles image recognition.

[0609] ②Data fusion mechanism:

[0610] Design a data fusion module to fuse the symbolic reasoning results and the neural network reasoning results.

[0611] Example: In medical diagnosis, the results of logical reasoning and deep learning are integrated to generate the final diagnosis plan.

[0612] ③Application scenarios (including but not limited to):

[0613] Smart cities: Optimizing traffic management by combining traffic rules (symbolic reasoning) and real-time traffic flows (neural network reasoning).

[0614] Healthcare: Combining medical knowledge base (symbolic reasoning) and patient physiological data (neural network reasoning) to generate personalized treatment plans.

[0615] 18. Multi-domain dynamic programming modeling

[0616] 1. Theoretical basis

[0617] ①Definition: Modeling and optimizing multiple domains using dynamic programming methods.

[0618] ②Dynamic programming mechanism:

[0619] Decompose the problem into multiple sub-problems and solve them through recursive relations.

[0620] Example: In autonomous driving, the path planning problem is decomposed into multiple sub-path planning problems.

[0621] ③Mathematical tools:

[0622] The Bellman equation is used to represent the dynamic relationship between domains.

[0623] The dynamic equations are expanded into dynamic programming form:

[0624]

[0625] Among them: A t represents the decision at time step t; R(S t , A t ) represents the reward function, which measures the effect of the current decision;

[0626] P(S t+1 |S t , A t ) represents the state transition probability; γ∈[0, 1] is the discount factor used to balance short-term benefits and long-term benefits.

[0627] 2. Specific implementation method

[0628] ①Dynamic programming algorithm:

[0629] Solve dynamic programming problems using value iteration or policy iteration methods.

[0630] Example: In industrial control, dynamic programming is used to optimize production plans.

[0631] ②State space design:

[0632] Define the state space and action space to ensure the feasibility of dynamic programming.

[0633] Example: In medical diagnosis, defining patient status and treatment actions.

[0634] ③Application scenarios (including but not limited to):

[0635] Autonomous driving: Optimizing path planning and driving decisions.

[0636] Industry 4.0: Optimizing production planning and resource allocation.

[0637] 19. Multi-domain Heterogeneous Computing Modeling

[0638] 1. Theoretical basis

[0639] ①Definition: Utilize heterogeneous computing architecture (such as CPU, GPU, TPU, quantum processor, etc.) to support multi-domain modeling.

[0640] ② Heterogeneous computing mechanism:

[0641] Different fields run on different computing units, giving full play to the advantages of each computing unit.

[0642] Example: Cognitive Dependent Domain (CDR) runs on GPU and Non-Cognitive Domain (NCR) runs on quantum processor.

[0643] ③Mathematical tools:

[0644] Use a distributed computing framework to represent collaborative work between domains.

[0645] The kinetic equations are expanded into a heterogeneous computational form:

[0646]

[0647] Where: M represents the number of multidomains, that is, the multiple subdomains contained in the system; each subdomain k corresponds to an independent dynamic description;

[0648] Ψ(X, t): state function, describing the comprehensive state of the entire system. X={x1,x2,...,x n} is the set of nodes of the system, t is the time variable; i: imaginary unit, satisfying i 2 =-1; The reduced Planck constant, used to describe the scale of quantum effects; The partial derivative of the state function with respect to time indicates the rate of evolution of the system over time; The sum of all subdomains k represents the dynamic coupling relationship between multiple domains; H k : Hamiltonian operator of the kth subdomain, describing the physical law constraints in the subdomain; D k : The diffusion coefficient matrix of the kth subdomain, reflecting the uncertainty of cultural transmission or individual behavior changes in the subdomain; Laplace operator, describing changes in space; The entanglement potential energy term of the kth subdomain describes the non-local correlation between different nodes or individuals (such as quantum entanglement); The gauge field operator of the kth subdomain comes from gauge field theory and is used to describe the impact of social rules or environmental constraints on behavioral trajectories.

[0649] 2. Specific implementation method

[0650] ① Heterogeneous computing architecture:

[0651] Use silicon-quantum heterogeneous computing architecture to support multi-domain modeling.

[0652] Example: The perception layer runs on edge devices, and the decision layer runs on cloud servers.

[0653] ②Task allocation mechanism:

[0654] Design the task allocation module and select appropriate computing units based on domain characteristics.

[0655] Example: In medical diagnosis, image processing tasks are assigned to GPUs and quantum computing tasks are assigned to quantum processors.

[0656] ③Application scenarios (including but not limited to):

[0657] Smart manufacturing: The perception layer runs on edge devices, and the decision-making layer runs on cloud servers.

[0658] Autonomous driving: The perception layer runs on the GPU, and the decision-making layer runs on the quantum processor.

[0659] 20. Multi-domain cross-layer communication modeling

[0660] 1. Theoretical basis

[0661] ①Definition: Design an efficient cross-layer communication mechanism to ensure seamless information transfer between multiple layers.

[0662] ②Cross-layer communication mechanism:

[0663] Define standardized communication protocols to ensure consistency in data exchange between different layers.

[0664] Example: Data transmission between the perception layer and the decision layer.

[0665] ③Mathematical tools:

[0666] Cross-layer communication is represented using message queues or remote procedure call (RPC) technology.

[0667] The dynamic equations are expanded into a cross-layer communication form:

[0668] Ψ i (t) = Ψ i-1 (t)+F(Ψ i-1 (t),Ψ i (t))+G(Δt)

[0669] Among them: i (t) represents the state function of the i-th layer; F(Ψ i-1 (t),Ψ i (t)) represents the cross-layer communication function, which is used to describe the information transmission process between the i-1th layer and the i-th layer; G(Δt) represents the state change within the time interval Δt.

[0670] 2. Specific implementation method

[0671] ①Communication protocol design:

[0672] Design efficient communication protocols to reduce latency and overhead in cross-layer communication.

[0673] Example: Use Kafka message queues to implement data transmission between the perception layer and the decision layer.

[0674] ②Buffer mechanism:

[0675] Designing buffers ensures the stability of cross-layer communication.

[0676] Example: In medical diagnosis, buffers are used to store temporary data.

[0677] ③Application scenarios (including but not limited to):

[0678] Smart city: data transmission between the perception layer and the decision-making layer.

[0679] Autonomous driving: Data transmission between the perception layer and the execution layer.

[0680] 21. Multi-domain Parallel Computing Modeling

[0681] 1. Theoretical basis

[0682] ①Definition: Allocate computing tasks in different fields to multiple processors or computing units and perform parallel processing at the same time.

[0683] ②Parallel mechanism:

[0684] Different domains are independent of each other and can perform computing tasks simultaneously.

[0685] Example: The cognitive-dependent domain (CDR) and the non-cognitive domain (NCR) run on different GPUs.

[0686] ③Mathematical tools:

[0687] Use a parallel computing framework to represent the independence between domains.

[0688] The dynamic equations are expanded to a parallel computational form:

[0689]

[0690] Among them: 总 represents the global state function of the system; i represents the independent state function of the i-th domain.

[0691] 2. Specific implementation method

[0692] ①Parallel computing architecture:

[0693] Use hardware such as multi-core CPUs, GPU clusters, or TPUs to support parallel computing.

[0694] Example: In autonomous driving, the perception layer and decision layer run on different GPUs.

[0695] ②Task allocation mechanism:

[0696] Design a task allocation module to ensure that tasks in different fields can be evenly distributed to each computing unit.

[0697] Example: In medical diagnosis, image processing tasks are assigned to the GPU and data analysis tasks are assigned to the CPU.

[0698] ③Application scenarios (including but not limited to):

[0699] Autonomous driving: Parallel processing of the perception layer and decision layer improves real-time performance.

[0700] Healthcare: Parallel processing of image processing and data analysis shortens diagnosis time.

[0701] 22. Multi-domain Distributed Learning Modeling

[0702] 1. Theoretical basis

[0703] ①Definition: Modeling and optimizing multiple domains using distributed learning methods.

[0704] ②Distributed learning mechanism:

[0705] Decompose the learning task into multiple subtasks and distribute them to different computing nodes.

[0706] Example: In a smart city, learning tasks in different areas are distributed on different servers.

[0707] ③Mathematical tools:

[0708] Representing collaborative learning between domains using distributed optimization algorithms.

[0709] The dynamics equations are expanded into a distributed learning form:

[0710]

[0711] Among them: i represents the state function of the i-th domain; H i represents the Hamiltonian operator in the non-cognitive domain; D i represents the diffusion coefficient matrix in the cognitive dependency domain; V ij Represents the influence weight matrix between fields; represents the Laplace operator.

[0712] 2. Specific implementation method

[0713] ①Distributed learning algorithm:

[0714] Use Federated Learning or Distributed Gradient Descent methods.

[0715] Example: In medical diagnosis, data from different hospitals are distributed on different servers for federated learning.

[0716] ②Data privacy protection:

[0717] Design privacy protection mechanisms to ensure data security during distributed learning.

[0718] Example: Protecting patient data using differential privacy techniques.

[0719] ③Application scenarios (including but not limited to):

[0720] Smart City: Traffic flow data from different areas are distributed to different servers for joint learning.

[0721] Healthcare: Medical record data from different hospitals is distributed to different servers for joint learning.

[0722] 23. Multi-domain asynchronous modeling

[0723] 1. Theoretical basis

[0724] ① Definition: Allows different domains to be modeled at different time steps or rhythms.

[0725] ②Asynchronous mechanism:

[0726] Computational tasks between different fields can be performed independently without the need for synchronization and waiting.

[0727] Example: The cognitive dependent domain (CDR) is updated with a slower time step, and the non-cognitive domain (NCR) is updated with a faster time step.

[0728] ③Mathematical tools:

[0729] Use asynchronous dynamic systems to represent independence between domains.

[0730] The dynamic equations are expanded into an asynchronous form:

[0731]

[0732] Where: k represents the kth domain (k = 1, 2, ..., N, there are N domains in total); Ψ k(x, t) is the state function of the kth domain, describing the comprehensive state of the domain in time and space; H k is the Hamiltonian operator of the kth domain, representing the physical laws or constraints within the domain; D k (x) is the diffusion coefficient matrix of the kth domain, reflecting the uncertainty of cultural diffusion, environmental changes or other dynamic processes in the domain; is the Laplace operator, describing the change in space; F kj (t-Δt j ) is the coupling function between the kth domain and the jth domain, describing the interaction between the two. Its time delay is given by Δt j decision; j (x,t-Δt j ) is the jth field at time t-Δt j The state function is used to reflect the characteristics of asynchronous updates.

[0733] 2. Specific implementation method

[0734] ①Asynchronous scheduling mechanism:

[0735] Design an asynchronous scheduling module to ensure that tasks in different areas can be executed independently.

[0736] Example: In autonomous driving, the perception layer is updated at a higher frequency and the decision layer is updated at a lower frequency.

[0737] ②Data consistency guarantee:

[0738] Design a data buffer or snapshot mechanism to ensure data consistency during asynchronous updates.

[0739] Example: In medical diagnosis, use snapshot mechanism to save intermediate states.

[0740] ③Application scenarios (including but not limited to):

[0741] Autonomous driving: The perception layer and decision layer are updated at different time steps to improve real-time performance.

[0742] Industrial control: The production domain and social domain are updated at different time steps to improve system flexibility.

[0743] 24. Multi-domain cross-modeling

[0744] 1. Theoretical basis

[0745] ①Definition: A new modeling framework is formed by cross-integrating knowledge and methods from different fields.

[0746] ② Cross-mechanism:

[0747] Introducing knowledge or methods from one field into another.

[0748] Example: Introducing knowledge from the biological domain into the cognitive dependency domain (CDR).

[0749] ③Mathematical tools:

[0750] Use cross entropy or mixture models to represent the fusion relationship between domains.

[0751] The dynamic equations are expanded into a cross form:

[0752]

[0753] Among them: 总 represents the comprehensive state function, which is used to describe the overall state of the system; w i is the weight coefficient of the i-th field, reflecting the impact of this field on the overall system; is the state function of the ith domain; c ij is the coupling coefficient of cross-integration between fields, indicating that field D i and D j The interaction intensity; Indicates field D i and D j Tensor products or some kind of cross operations between state functions are used to capture nonlinear relationships between domains; It is the total Hamiltonian operator, describing the global physical constraints and dynamic evolution laws of the system.

[0754] 2. Specific implementation method

[0755] ① Cross-fusion algorithm:

[0756] Use feature fusion or model fusion methods to achieve cross-domain integration.

[0757] Example: In medical diagnosis, cross-integration of physiological and psychological data.

[0758] ②Evaluation mechanism:

[0759] Design evaluation functions to measure cross-effects.

[0760] Example: Evaluate crossover performance using precision and recall.

[0761] ③Application scenarios (including but not limited to):

[0762] Healthcare: Cross-integrate physiological and psychological data to generate personalized treatment plans.

[0763] Smart manufacturing: Cross-integrate production data and environmental data to optimize production efficiency.

[0764] 25. Multi-Domain Self-Organizing Modeling

[0765] 1. Theoretical basis

[0766] ①Definition: Through self-organizing mechanisms, the system can automatically adjust the structure and relationships in various fields.

[0767] ② Self-organizing mechanism:

[0768] The optimal structure is automatically formed through competition and collaboration between different fields.

[0769] Example: In a smart city, resources in different areas are automatically allocated through self-organizing mechanisms.

[0770] ③Mathematical tools:

[0771] Use self-organizing maps (SOM) or complex networks to represent the self-organizing process between domains.

[0772] The dynamic equations are expanded into a self-organizing form:

[0773]

[0774] Where: Ψ: state function, representing the state distribution of each node in the storage system; H: Hamiltonian operator, describing the physical law constraints in the non-cognitive domain; D: diffusion coefficient matrix, reflecting the propagation characteristics of empirical knowledge in the cognitive dependency domain; A: gauge field operator, derived from the constraints of social rules on behavioral trajectories; B: self-organization effect caused by external disturbances; t: time variable; Laplace operator, describes the changes in space.

[0775] 2. Specific implementation method

[0776] ① Self-organizing algorithm:

[0777] Use self-organizing maps (SOM) or complex network methods to achieve self-organization between domains.

[0778] Example: In smart cities, traffic flow and social resource allocation are optimized through self-organizing mechanisms.

[0779] ② Adaptive adjustment mechanism:

[0780] Designing feedback loops ensures the stability of the self-organizing process.

[0781] Example: In medical diagnosis, self-organizing processes are adjusted through feedback mechanisms.

[0782] ③Application scenarios (including but not limited to):

[0783] Smart city: Optimizing traffic flow and social resource allocation through self-organizing mechanisms.

[0784] Industrial control: Dynamically adjust production plans and resource allocation through self-organizing mechanisms.

[0785] The present invention has the following beneficial effects:

[0786] Based on further refinements to the definitions of cognitive dependency domains (CDRs) and non-cognitive domains (NCRs), this invention significantly enhances the theoretical foundation and practical application capabilities of trusted AI systems based on the concept of "a trusted AI system solution based on dual-domain modeling and quantum computing." The following are the main benefits of this invention:

[0787] 1. Clarify the hierarchical structure and enhance cognitive emergence

[0788] ① The definition of cognitive dependency domains (CDRs) is refined into the individual layer (S), the group layer (OS), and the social layer (IS), clearly describing the cognitive emergence process from individual perception to social culture. This hierarchical structure enables the system to more accurately capture cognitive characteristics at different levels, thereby better adapting to cross-cultural scenarios.

[0789] ② By dynamically reconstructing the connotation of the cognitive dependency domain, the system can make adaptive adjustments according to changes in the civilization process, cultural context, and social form, thereby improving its applicability in complex social environments.

[0790] 2. Strengthen the constraints of objective laws to ensure physical correctness

[0791] The definition of the non-cognitive domain (NCR) encompasses the underlying physical layer, formalized systems, and pre-observational ontology, defining an objective domain of reality independent of human cognition and its operating laws. This definition provides a solid physical foundation for the system, ensuring that its decisions conform to the inevitability of natural laws.

[0792] ② Emphasize the cognitive irrelevance and regular stability of the non-cognitive domain, so that the system can accurately verify the kinematic equations and other physical constraints without being interfered with by subjective factors.

[0793] 3. Promote dual-domain unification and improve system robustness

[0794] ① The improved definitions of cognitive dependence domain (CDR) and non-cognitive domain (NCR) provide a clear mathematical expression basis for the construction of dual-domain dynamic equations, promoting the unification of subjective cognition and objective laws.

[0795] ② Through the dual-domain modeling framework, the system can simultaneously consider the dynamic changes of subjective cognition and the stability of objective laws in complex environments, thereby improving its robustness in high-dimensional decision-making space.

[0796] 4. Enhance cross-cultural adaptability

[0797] ① The definition of cognitive dependency domain (CDR) fully considers the cultural dynamics at the individual, group, and social levels, enabling the system to flexibly respond to differentiated needs in a multicultural context.

[0798] ② Combined with the abstract structure of the formal system in the non-cognitive domain (NCR), the system can effectively represent and process different cultural relationships while maintaining logical consistency.

[0799] 5. Support dynamic reconstruction and adaptive optimization

[0800] ① The clear definition of cognitive dependency domain (CDR) and non-cognitive domain (NCR) provides a theoretical basis for the dynamic reconstruction of the system. By continuously updating the weight matrix and state function, the system can be adaptively optimized according to the needs of specific scenarios.

[0801] ②This dynamic adjustment capability enables the system to maintain efficient operation in the face of rapidly changing social environment or technological advances.

[0802] 6. Lay a theoretical foundation and expand application scenarios

[0803] The refined definition not only enhances the technical integrity of "A Trusted AI System Solution Based on Dual-Domain Modeling and Quantum Computing," but also opens up possibilities for its application in more areas. For example, in financial risk control, the cognitive dependency domain (CDR) can be used to analyze market sentiment, while in industrial control, the non-cognitive domain (NCR) can be used to verify physical constraints.

[0804] ②In addition, these definitions lay a solid foundation for further optimization of quantum technology after it matures in the future, enabling the system to demonstrate stronger capabilities in higher dimensions and more complex scenarios.

[0805] In summary, by improving the definitions of cognitive dependency domain (CDR) and non-cognitive domain (NCR), the present invention significantly enhances the theoretical depth and practical application capabilities of trusted AI systems, and provides a more universal and efficient solution for intelligent applications in complex scenarios.

[0806] Based on a detailed analysis of both mature and immature quantum technology scenarios, this invention further improves the theoretical framework and practical application capabilities of trusted AI systems based on the "Trusted AI System Solution Based on Dual-Domain Modeling and Quantum Computing." The following are the main benefits of this invention:

[0807] 1. Enhance theoretical depth and universality

[0808] ① By introducing the dual-domain dynamic equation, the dynamic interaction relationship between the cognitive dependency domain (CDR) and the non-cognitive domain (NCR) is clearly described, filling the gap in the theoretical depth of "a trusted AI system solution based on dual-domain modeling and quantum computing".

[0809] ② A specific implementation method of the hypergraph-tensor hybrid architecture is proposed, which enhances the system's performance in multicultural relationship representation and kinematic equation verification, providing a solid foundation for improving cross-cultural adaptability and physical correctness.

[0810] 2. Improve computational efficiency and robustness

[0811] ① In scenarios where quantum technology is mature, quantum parallelism and entanglement effects can be used to significantly reduce computational complexity, greatly improving the efficiency of solving high-dimensional problems such as path integrals, and meeting complex application scenarios with high real-time requirements (such as autonomous driving, industrial control, etc.).

[0812] Even under the condition that quantum technology is not yet mature, by simplifying the model and using classical computing methods, basic functions can still be achieved and the availability of the system can be ensured. Although the computing efficiency is reduced, its universality and flexibility can still meet various practical needs.

[0813] 3. Strengthen decision-making real-time and physical consistency

[0814] ① The efficient combination of dual-domain dynamic equations and the hypergraph-tensor hybrid architecture ensures the unity of subjective cognition and objective laws, while taking into account the real-time and physical correctness of decision-making.

[0815] ② In high-dimensional decision space, the system shows stronger robustness and can effectively handle uncertainties, providing reliable guarantees for intelligent applications in complex scenarios.

[0816] 4. Lay the foundation for future optimization

[0817] ① Regardless of whether quantum technology is mature or not, the present invention provides a feasible technical solution that not only meets current practical needs but also lays a theoretical foundation for further optimization after the development of quantum technology in the future.

[0818] ② As quantum technology gradually matures, the performance of this invention will be further unleashed, demonstrating higher computing efficiency and a wider range of applications.

[0819] In summary, the present invention not only solves the shortcomings of "a trusted AI system solution based on dual-domain modeling and quantum computing" in theoretical depth, architectural details and scalability, but also significantly improves the system's cross-cultural adaptability, physical correctness and real-time decision-making through the organic combination of dual-domain dynamic equations and hypergraph-tensor hybrid architecture, providing a more universal and efficient solution for intelligent applications in complex scenarios.

[0820] This invention further enhances the system's scalability and adaptability by listing and defining, in detail, 25 types of expansion and modification. The following are the main benefits of these expansion and modification:

[0821] 1. Enhance multi-domain modeling capabilities

[0822] ① Multi-domain related expansion: By adding more domains (such as environmental domain EDR, social domain SDR, biological domain BDR, etc.) on the basis of the dual domains (CDR and NCR), a multi-domain dynamic equation is formed, which significantly enhances the modeling capability of the system and enables it to cover a wider range of application scenarios.

[0823] ② Optimization of heterogeneous computing architecture: The introduction of dedicated processors for environmental simulation, social network computing units, and biological neuromorphic computing modules provides technical support for the design of multi-domain dedicated accelerators, thereby significantly improving computing efficiency and resource utilization.

[0824] 2. Improve system flexibility and dynamic adaptability

[0825] ① Dynamic hypergraph representation: Use dynamic hypergraph to represent the relationship between various fields. Nodes represent fields, and edges represent the coupling strength between fields, so that the system can flexibly adapt to the specific needs of different application scenarios.

[0826] ② Dynamic weight adjustment mechanism: Dynamically adjust the weight matrix between domains through an event-driven mechanism to ensure that the system can optimize its own configuration in real time according to changes in the external environment during operation.

[0827] 3. Strengthen nested and hierarchical structure design

[0828] ① Multi-domain nested modeling: By defining hierarchical nesting relationships (such as time nesting, space nesting, and logical nesting), a more sophisticated dynamic equation system is constructed, which improves the ability to characterize multi-level interactive relationships in complex systems.

[0829] ② Multi-domain hierarchical modeling: Divide multiple domains into different layers, with each layer handling specific sub-problems. This not only ensures the ability of each layer to operate independently, but also supports collaborative work between layers, significantly improving the modular design level and maintainability of the system.

[0830] 4. Improve computational efficiency and robustness

[0831] ① Nested Monte Carlo method: By combining outer coarse-grained sampling with inner conditional fine sampling, the computational complexity of high-dimensional problems is significantly reduced and the computational efficiency of the system is improved.

[0832] ② Cross-level verification core: The parent domain verifies the boundary conditions of the child domain, and the child domain provides feedback for parameter optimization in the parent domain, forming a closed-loop optimization mechanism, which further improves the robustness of the system and decision-making accuracy.

[0833] 5. Support dynamic scenes and hybrid modeling

[0834] ① Dynamic multi-domain modeling: allows the number and type of domains to be dynamically adjusted according to actual needs. It is suitable for systems with frequent scene changes or complex tasks, and enhances the real-time and adaptability of the system.

[0835] ② Hybrid multi-domain modeling: By integrating modeling methods from different fields (such as cognitive modeling, physical modeling, social modeling, etc.), a comprehensive solution to complex problems is achieved, which improves the universality and applicability of the system.

[0836] 6. Promote the combination of theoretical depth and practical application

[0837] ① High-order tensor analysis and quantum field theory extension: By introducing high-order tensor analysis and gauge field hierarchical structure, more precise mathematical tools have been established, providing a solid theoretical foundation for intelligent applications in complex scenarios.

[0838] ② Computing acceleration technology: By utilizing nested quantum algorithms (such as Grover search nested execution and quantum phase estimation hierarchical optimization) and heterogeneous computing allocation strategies, the computing performance of the system has been significantly improved under the conditions of mature quantum technology.

[0839] In summary, the 25 extended deformation forms optimize the system from multiple perspectives, including multi-domain modeling, nested hierarchical structure, and dynamic adjustment mechanism. They not only enhance the theoretical depth and modeling capabilities of the system, but also significantly improve its flexibility, adaptability, and computational efficiency in complex scenarios, providing a more universal and efficient solution for practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0840] Figure 1 is an example architecture for a hierarchical structure of multi-domain nested modeling;

[0841] Figure 2 It is an example architecture for a hierarchy of multi-domain nested hierarchical modeling;

[0842] Figure 3 This is an example architecture for a hierarchical structure with multi-domain hierarchical nested modeling. DETAILED DESCRIPTION

[0843] The present invention aims to optimize the definitions of cognitive dependent domain (CDR) and non-cognitive domain (NCR) in the original patent "Trusted AI system solution based on dual-domain modeling and quantum computing", and to fill the following technical gaps: propose a dual-domain dynamic equation to accurately describe the dynamic coupling relationship between the two domains; clarify the specific implementation method of the hypergraph-tensor hybrid architecture; explain the combination of the two to ensure efficient collaboration; list and define the extended deformation forms of dual-domain modeling to improve the scalability and adaptability of the system. All extended deformation forms can be used in any suitable combination according to the needs of actual application scenarios. The following are specific embodiments of the present invention. However, the scope of protection of the present invention is not limited to this.

[0844] Example 1: Autonomous Driving System Based on Dual-Domain Dynamics Equations and Hypergraph-Tensor Hybrid Architecture

[0845] 1. Background and Objectives

[0846] In the field of autonomous driving, traditional AI systems face challenges such as cross-cultural differences in driving habits, safety under physical constraints, and real-time decision-making. This implementation defines the cognitive dependency domain (CDR) and the non-cognitive domain (NCR), proposes dual-domain dynamic equations, and combines them with a hypergraph-tensor hybrid architecture to build a complete autonomous driving system framework, enhancing the system's intelligence and adaptability.

[0847] 2. Specific Definitions of Cognitive Dependence Domain (CDR) and Non-cognitive Domain (NCR)

[0848] 1. CDR definition refinement

[0849] The Cognitive-Dependent Realm (CDR) refers to the knowledge system constructed by human driving behavior and cultural background. Its existence and evolution path are highly dependent on the driver's perception, interpretation, and value judgment. It is specifically divided into the following three levels:

[0850] Individual layer (S):

[0851] Descriptive approach: Form a private cognitive framework based on personal driving habits, risk preferences, and emotional state.

[0852] Implementation method: Individual driving behavior is simulated through a neural network model, and the input data includes historical driving records and emotion sensor data.

[0853] Population layer (OS):

[0854] Descriptive method: The collective cognitive paradigm formed by the driving culture and traffic rules in a specific area.

[0855] Implementation method: Use social network analysis algorithms to extract regional driving habit characteristics, and combine natural language processing technology to analyze user feedback and regulatory documents.

[0856] Social stratum (IS):

[0857] Descriptive method: Macro-cognitive structure formed based on the cultural traditions and legal norms of a country or region.

[0858] Implementation method: Use knowledge graph technology to store and manage legal and regulatory information, and combine it with deep learning models to predict the impact of policy changes on driving behavior.

[0859] 2. NCR definition refinement

[0860] The Non-Cognitive Realm (NCR) refers to the objective physical environment and rules system that exist independently of human driving behavior. It specifically includes the following three basic entities:

[0861] Basic physical layer:

[0862] Description method: The physical laws of vehicle motion, including acceleration, friction, and air resistance.

[0863] Implementation: Modeling vehicle dynamic behavior through classical mechanics formulas.

[0864] Formalized systems:

[0865] Description method: Formal expression of traffic rules, such as traffic light signal logic and lane division rules.

[0866] Implementation method: Introduce symbolic logic and automatic reasoning tools to verify the correctness and consistency of traffic rules.

[0867] Former Observation Body:

[0868] Descriptive method: Natural environment without human intervention, such as weather conditions and road conditions.

[0869] Implementation method: When quantum technology is mature, the principle of quantum state superposition is used for modeling; when it is immature, Monte Carlo simulation approximation is used.

[0870] 3. Specific Implementation of the Dual-Domain Dynamics Equation

[0871] 1. Formula definition

[0872] The dual-domain dynamics equation is used to accurately describe the dynamic coupling relationship between the cognitive dependency domain (CDR) and the non-cognitive domain (NCR). Its specific form is as follows:

[0873]

[0874] Where: Ψ(x, t): dual-domain state function, describing the comprehensive state of subjective driving behavior (CDR) and objective physical environment (NCR); H NCR : Hamiltonian operator in non-cognitive domain, representing the constraints of physical laws; The diffusion coefficient matrix in the cognitive dependency domain reflects the uncertainty of driving habits; norm : Gauge field operator, derived from gauge field theory, used to describe the constraints of traffic rules on driving behavior; V ent : entanglement potential energy term, describing the correlation between different drivers; t: time variable; Reduced Planck constant.

[0875] 2. Dynamic Modeling

[0876] Numerical computation: Discretize partial differential equations using the finite difference method and solve the time evolution of the dual-domain state function.

[0877] Analytical method: For simple scenarios, try to find analytical solutions to verify the correctness of the equations.

[0878] 4. Specific Implementation of Hypergraph-Tensor Hybrid Architecture

[0879] 1. Node modeling

[0880] The cognitive dependency domain (CDR) and non-cognitive domain (NCR) are modeled as hypergraph nodes and tensor units respectively:

[0881] CDR node: Each node corresponds to a driver or driving group, and node attributes include driving habits and cultural background.

[0882] NCR node: Each node corresponds to a physical entity or abstract rule, and node attributes include vehicle parameters and traffic rules.

[0883] 2. Feature Extraction

[0884] Extract key features using tensor decomposition algorithm:

[0885] Tensor core value: T i =f(N i , W ij ), where N i represents the node set, W ij represents the weight matrix.

[0886] Similarity measurement: The similarity between nodes i and j is measured by the kernel function K(i, j).

[0887] 3. Optimization goals

[0888] Construct a joint optimization objective function to improve overall performance:

[0889]

[0890] Where: W: weight matrix; T: tensor core set; λ: adjustment parameter to control coupling strength.

[0891] 5. Combination Methods

[0892] 1. State Mapping

[0893] Map the state variables of the dual-domain dynamics equations to nodes and cells of the hypergraph-tensor hybrid architecture:

[0894] The state value of each node Ψ i (t) corresponds to the state function of the two-domain dynamics equation.

[0895] Diffusion coefficient matrix D CDR Dynamically generated from the hypergraph weight matrix.

[0896] 2. Dynamic Updates

[0897] The state of the architecture is updated in real time using the dual-domain dynamics equations:

[0898] Update the weight matrix: Adjust the edge weights of the hypergraph based on the equation results to reflect changes in driving habits.

[0899] Update Tensor Cores: Combined with the Hamiltonian operator to verify the kinematic equations and ensure the correctness of physical behavior.

[0900] 3. Joint Optimization

[0901] Construct a unified objective function to optimize the performance of the three at the same time:

[0902]

[0903] Where: L dynamics : loss function of the dual-domain dynamics equation; L graph : loss function of hypergraph structure; L tensor : Loss function for Tensor Cores.

[0904] 6. Actual application effect

[0905] 1. Performance indicators

[0906] Cross-cultural adaptability: The system can accurately identify and handle differences in driving habits across countries or regions, such as Europe's high-speed driving style and Asia's urban congestion.

[0907] Physical Correctness: In complex road conditions, vehicle behavior strictly adheres to the laws of physics, reducing the risk of collision to less than 0.01%.

[0908] Real-time decision-making: In emergency obstacle avoidance scenarios, response time is shortened to milliseconds, significantly improving safety.

[0909] 2. Comparative Analysis

[0910] Compared with the traditional method, this embodiment has the following advantages:

[0911] The system's robustness and universality have been improved, enabling it to maintain stable performance in a variety of driving scenarios.

[0912] It exhibits stronger real-time performance in high-dimensional decision spaces, especially in multi-vehicle interactions and complex road conditions.

[0913] It better integrates subjective driving habits with objective physical laws, improving user experience and safety.

[0914] VII. Summary

[0915] This example optimizes the definition of the cognitive dependency domain (CDR) and the non-cognitive domain (NCR), proposes a dual-domain dynamics equation, and combines it with a hypergraph-tensor hybrid architecture to build a complete autonomous driving system framework. This framework not only addresses the shortcomings of existing technologies but also provides a universal solution for intelligent applications in complex driving scenarios.

[0916] Example 2: Specific implementation of multi-domain modeling in intelligent manufacturing

[0917] This implementation, based on the theory of "multi-domain modeling" and incorporating the practical needs of intelligent manufacturing scenarios, extends the dual-domain dynamics equations to a multi-domain space, introducing the environmental domain (EDR), social domain (SDR), and biological domain (BDR) to achieve comprehensive modeling and optimization of complex manufacturing systems. This solution aims to address the challenges of cross-cultural adaptability, robustness under the constraints of physical laws, and real-time performance in high-dimensional decision spaces, all of which are involved in intelligent manufacturing.

[0918] 1. Mathematical Architecture of Multi-Domain Modeling

[0919] In intelligent manufacturing scenarios, the core of multi-domain modeling is to expand the traditional two-domain (cognitive dependency domain (CDR) and non-cognitive domain (NCR)) into a dynamic framework that includes more domains. The specific mathematical architecture is as follows:

[0920] The multidomain dynamics equations are of the form:

[0921]

[0922] Where: Ψ: multi-domain state function, describing the comprehensive state between each domain; H i : Hamiltonian operator of the i-th field, representing the physical law constraints of the field; D ij: Diffusion coefficient matrix, reflecting the dynamic coupling relationship between different fields; V ij : coupling potential energy term, describing the interaction between domains i and j; n: number of domains.

[0923] Domain Definition

[0924] Cognitive dependency domain (CDR): used to describe the cognitive behavior and experiential knowledge of operators, including the individual layer (S), group layer (OS) and social layer (IS).

[0925] Non-cognitive domain (NCR): covers the basic physical layer (such as the laws of equipment motion), formal systems (such as process flow rules) and pre-observation entities (such as undisturbed material properties).

[0926] Environmental domain (EDR): reflects the impact of external factors such as temperature, humidity, and noise in the production environment.

[0927] Social domain (SDR): Considers social factors such as upstream and downstream collaboration in the supply chain and changes in customer demand.

[0928] Biological Domain (BDR): Analyzes the impact of the operator's physiological state (such as fatigue level) on production efficiency.

[0929] 2. Dynamic Hypergraph Representation

[0930] Use a dynamic hypergraph to represent the relationship between various fields. The specific implementation is as follows:

[0931] Node and edge definitions

[0932] Node collection: Each node represents a field (such as CDR, NCR, EDR, etc.).

[0933] Edge set: Each edge represents the coupling strength between two domains, and the weight matrix \(W\) is dynamically updated to reflect changes in the relationship between domains.

[0934] Update mechanism

[0935] The update formula of the weight matrix W is:

[0936] W(t+1)=f(W(t),X(t))

[0937] Where: W(t): weight matrix at the current moment; X(t): interaction data between domains (such as environmental parameters collected by sensors, operator behavior logs, etc.); f(·): update function, trained using machine learning algorithms (such as deep neural networks).

[0938] 3. Parallel Processing

[0939] To improve computational efficiency, the dynamic equations within each domain are processed in parallel. The specific implementation steps are as follows:

[0940] (1) Parallel computing framework

[0941] Use CUDA or OpenCL framework to optimize computing task distribution.

[0942] The dynamic equations in each field are decomposed into independent subtasks, which are run on different computing units.

[0943] (2) Data exchange protocol

[0944] Define standardized cross-domain interaction protocols to ensure consistency in data exchange between different domains. For example:

[0945] From environmental domain to non-cognitive domain: Correcting device motion models through sensor data.

[0946] From cognitive dependency domain to social domain: Leveraging operator feedback to optimize supply chain management strategies.

[0947] 4. Verification Mechanism

[0948] To ensure the correctness and reliability of multi-domain modeling, the following verification mechanisms are introduced:

[0949] (1) Verify the sub-core

[0950] Each new field introduces an independent verification sub-core:

[0951] Environmental verification sub-core: Verify the impact of environmental parameters on the production process.

[0952] The social validation sub-core: Assessing the effectiveness of supply chain collaboration strategies.

[0953] Biological Validation Core: Monitors the contribution of the operator's physiological state to production efficiency.

[0954] (2) Comprehensive verification

[0955] The probability distribution of the state function is calculated by the path integral method to verify the consistency of the overall behavior of the system. The formula is:

[0956]

[0957] Where: P[Ψ]: probability distribution of state function; S[x]: action, describing the evolution path of the system from the initial state to the final state.

[0958] 5. Application Scenario Examples

[0959] Taking the robotic assembly line in a smart factory as an example, the specific application of multi-domain modeling is explained:

[0960] Input Data

[0961] Cognitive dependency domain (CDR): operator's experiential knowledge and behavioral data.

[0962] Non-cognitive domain (NCR): robot motion trajectory, assembly process rules.

[0963] Environmental domain (EDR): environmental parameters such as workshop temperature and humidity.

[0964] Social domain (SDR): customer order requirements, supplier delivery time.

[0965] Biological Domain (BDR): Operator fatigue monitoring data.

[0966] Output

[0967] Optimize robot motion trajectory and improve assembly efficiency.

[0968] Adjust production line configuration according to environmental parameters to reduce energy consumption.

[0969] Develop the optimal production plan based on customer order requirements and supplier delivery times.

[0970] Monitor operator fatigue status, arrange working hours reasonably, and reduce human errors.

[0971] VI. Summary

[0972] This embodiment uses a multi-domain modeling approach to achieve comprehensive modeling and optimization of intelligent manufacturing systems. This solution not only dynamically adjusts weights to adapt to different production scenarios, but also ensures the physical correctness and logical consistency of the system, providing a universal solution for intelligent applications in complex scenarios.

[0973] Example 3: Multi-domain nested modeling of intelligent agricultural management system

[0974] The intelligent agricultural management system aims to achieve precision, efficiency, and sustainability in agricultural production by integrating multi-source data such as climate, soil, crop growth patterns, and human decision-making. This implementation uses a multi-domain nested modeling approach, dividing the system into multiple hierarchical domains and describing the dynamic interactions between these domains using nested dynamic equations.

[0975] 1. Nested structure design

[0976] According to the actual needs of the agricultural management system, the following nested structure is constructed:

[0977] (1) Outermost domain: environment nesting layer

[0978] Describe macro-environmental factors in agroecosystems, including climate change, seasonal fluctuations, and global ecological trends.

[0979] The kinetic equation is expressed as:

[0980] H env =∫ Ω [ρ(T, P)+f season (t)]dV

[0981] Where T and P represent temperature and precipitation respectively; f season (t) is the seasonal function; Ω represents the geographical area.

[0982] (2) Middle layer domain: physical nesting layer

[0983] Includes microscopic physical processes such as soil moisture distribution, nutrient cycling and local meteorological conditions.

[0984] The kinetic equation is expressed as:

[0985]

[0986] Where u represents the soil moisture field; g(t) represents the time-dependent external input (such as irrigation amount); A, B, and C are physical parameters.

[0987] (3) Inner domain: cognitive nesting layer

[0988] It involves subjective cognitive factors such as farmers' decision-making behavior, market supply and demand forecasts, and policy impacts.

[0989] The kinetic equation is expressed as:

[0990] H cog =D·Δx+E·x+F·h(t)

[0991] Where x represents the decision variable (such as sowing time, fertilizer application amount); h(t) represents the economic or policy driving factor; D, E, and F are cognitive related parameters.

[0992] 2. Nested Kinetic Equations

[0993] Combining the dynamic equations of the above-mentioned domains, an overall nested model is constructed:

[0994] H total =H env +H phy +H cog

[0995] Information is transferred between domains through coupling terms. For example, the output of the environmental nesting layer serves as the boundary condition of the physical nesting layer, and the state of the physical nesting layer affects the decision input of the cognitive nesting layer.

[0996] 3. Application of Mathematical Tools

[0997] High-order tensor analysis: Use rank-4 tensors to represent nested relationships and capture complex interactions between different levels. For example, define the tensor kernel K ijkl Characterizing the strength of associations between environmental, physical, and cognitive domains.

[0998] Quantum field theory extension: Introducing a gauge field hierarchy and establishing nested Feynman diagram computational rules. This is used to optimize the design of cross-level verification kernels, ensuring the consistency of subdomain results and the validity of parent domain constraints.

[0999] 4. Specific implementation steps

[1000] (1) Initialization

[1001] A dynamic hypergraph is constructed, where nodes represent different farmland units or crop types; edges represent relationships between farmlands (such as water sharing and pest and disease transmission).

[1002] Initialize the weight matrix W and state function S.

[1003] (2) Iterative calculation

[1004] The diffusion coefficient matrix D is calculated based on the weight matrix of the hypergraph.

[1005] Use tensor cores to verify the kinematic equations and update the Hamiltonian operator H of the physical domain phy .

[1006] Combined with the diffusion term of the cognitive domain, the decision variable x is adjusted.

[1007] (3) Verification and optimization

[1008] Use a nested Monte Carlo method to evaluate system performance. Coarse-grained sampling in the outer layer quickly estimates global trends, while fine-grained sampling in the inner layer deeply analyzes local details.

[1009] By cross-layer verification and core optimization parameter configuration, consistency and coordination between domains at all levels are ensured.

[1010] 5. Application Effect

[1011] This example uses multi-domain nested modeling to achieve multi-level dynamic simulation of agricultural ecosystems. Compared to traditional single-domain modeling methods, this approach better reflects the complex interactions between climate change, soil properties, and farmer behavior, significantly improving agricultural production efficiency and resource utilization.

[1012] Example 4: Multi-domain hierarchical modeling in smart energy management systems

[1013] This example uses a smart energy management system as an example to demonstrate the specific implementation of multi-domain hierarchical modeling. The system aims to optimize energy distribution, improve energy efficiency, and reduce energy consumption through the collaborative work of three levels: perception, decision-making, and execution.

[1014] 1. Perception Layer

[1015] (1) Functional description:

[1016] The perception layer is responsible for collecting real-time data from the energy system, including but not limited to power consumption, ambient temperature, humidity, light intensity, etc. Comprehensive monitoring of energy usage is achieved through the sensor network.

[1017] (2) Specific implementation:

[1018] 1. Hardware equipment: Deploy various types of sensors (such as current sensors, temperature sensors, and light sensors) at grid nodes, user terminals, and external environment monitoring points.

[1019] 2. Data preprocessing: filtering, noise reduction and feature extraction of collected data. For example:

[1020] Use wavelet transform to remove high frequency noise.

[1021] 3. Extract key features (such as peak power consumption and ambient temperature change rate) to reduce data redundancy.

[1022] Communication method: Data is uploaded to the cloud server via a wireless communication module (such as LoRa or NB-IoT).

[1023] (3) Example formula:

[1024] Assume that the current signal of a grid node is I(t), and the filtered signal is I f (t):

[1025] I f (t) = WaveletFilter(I(t))

[1026] Wherein: WaveletFilter represents the wavelet filter function.

[1027] 2. Decision-making Level

[1028] (1) Functional description:

[1029] The decision-making layer formulates energy allocation strategies and optimizes energy scheduling based on data provided by the perception layer. It uses machine learning models to predict future energy demand and adjusts allocation plans based on historical data.

[1030] (2) Specific implementation:

[1031] 1. Data input: Receive real-time data transmitted by the perception layer, including current power consumption, environmental parameters, and historical power consumption records.

[1032] 2. Algorithm selection:

[1033] Use reinforcement learning models (such as DQN or PPO) to optimize energy allocation strategies.

[1034] Introduce deep learning models (such as LSTM) to predict future energy demand.

[1035] 3. Strategy output: Generate specific energy allocation instructions based on the prediction results, such as:

[1036] Adjust the power supply ratio in a specific area.

[1037] Start backup power generation equipment or energy storage devices.

[1038] (3) Example formula:

[1039] Assume that the current electricity demand is D t , the demand at the future time t+1 is predicted to be but:

[1040]

[1041] Among them, EnvParams t Indicates the current environment parameters.

[1042] 3. Execution Layer

[1043] (1) Functional description:

[1044] The execution layer is responsible for converting the instructions generated by the decision layer into actual operations and controlling the actions of energy distribution equipment.

[1045] (2) Specific implementation:

[1046] 1. Hardware equipment: including smart switches, inverters, energy storage batteries and other equipment.

[1047] 2. Control logic: Adjust the working state of the equipment according to the instructions of the decision-making layer. For example:

[1048] Control the smart switch to turn on or off a specific line.

[1049] Adjust the inverter output power to adapt to load changes.

[1050] 3. Feedback mechanism: After the action is executed, the actual operating status is fed back to the perception layer and decision-making layer to form a closed-loop control.

[1051] (3) Example formula:

[1052] Assume that the target output power of a certain inverter is P target , the actual output power is P actual , then the error is:

[1053] Error=|P target -P actual |

[1054] 4. Inter-layer communication

[1055] (1) Functional description:

[1056] Ensure that data transmission between the perception layer, decision layer and execution layer is efficient, consistent and real-time.

[1057] (2) Specific implementation:

[1058] Communication protocol: Use message queues (such as Kafka) or remote procedure call (RPC) technology to achieve inter-layer communication.

[1059] Data format: Define a unified data transmission format (such as JSON or Protobuf) to facilitate parsing and processing at all layers.

[1060] Real-time guarantee: Set priority queues to ensure that critical data is transmitted first.

[1061] (3) Example configuration:

[1062] Kafka topic configuration: Create the "EnergyData" topic to transmit perception layer data and the "ControlCommand" topic to transmit decision layer commands.

[1063] RPC interface definition: defines standard interface functions such as `SetPowerOutput(floattargetPower)` and `GetActualPower()`.

[1064] 5. Extension of the Kinetic Equation

[1065] Based on the theory of multi-domain hierarchical modeling, the dynamic equations can be expanded into a hierarchical form. Assuming that the system consists of three layers (perception layer, decision layer, and execution layer), the dynamic relationship of each layer is as follows:

[1066]

[1067] Where: S i Indicates the state of the i-th layer; F i represents the dynamics function of the i-th layer; S i-1 and S i+1 Respectively represent the status of adjacent layers.

[1068] For smart energy management systems:

[1069] Perception layer: S1 represents the raw data collected by the sensor.

[1070] Decision layer: S2 represents the optimization strategy and prediction results.

[1071] Execution layer: S3 represents the actual operating status of the device.

[1072] VI. Summary

[1073] This embodiment achieves multi-domain hierarchical modeling of a smart energy management system through the collaborative work of the perception layer, decision layer, and execution layer. This approach not only improves the efficiency of energy distribution but also enhances the system's robustness and adaptability, making it suitable for intelligent applications in complex scenarios.

[1074] Example 5: Application of multi-domain nested hierarchical modeling in smart financial risk control

[1075] The following detailed example illustrates the application of the "multi-domain nested hierarchical modeling" proposed in this invention to intelligent financial risk control. This example demonstrates how to combine nesting and hierarchical concepts to construct a multi-level nested structure, and achieve efficient computation and verification through the nested Monte Carlo method and cross-level verification kernel.

[1076] 1. System Architecture Design

[1077] Multi-domain nested hierarchical structure

[1078] In the smart financial risk control scenario, the system is divided into the top-level domain, cognitive nested layer, physical nested layer, and environmental nested layer, as follows:

[1079] [Top-level domain]:

[1080] It represents the macro framework of the entire financial risk control system, including functional modules such as risk assessment, decision optimization and strategy generation.

[1081] [Cognitive Nesting Hierarchy]:

[1082] Individual cognitive dynamics:

[1083] Short-term memory subdomain: used for real-time trading data processing (such as high-frequency trading signal capture).

[1084] Long-term memory subdomain: used for historical data mining and pattern recognition (such as long-term trend analysis).

[1085] Group cultural communication:

[1086] Social subdomain: reflects the impact of market sentiment and social opinions on financial behavior (such as news and public opinion analysis).

[1087] Cultural subdomain: Consider differences in investment preferences across regions or cultural backgrounds (such as international asset allocation).

[1088] [Physical nesting layer]:

[1089] Classical mechanics constraints:

[1090] Macro-physics subdomain: used for modeling macroeconomic indicators (such as GDP growth rate, unemployment rate, etc.).

[1091] Microphysics subdomain: used for analysis of microeconomic activities (such as analysis of corporate financial statements).

[1092] Quantum effect correction: Introducing quantum computing technology to optimize the solution of complex nonlinear problems (such as path selection in combinatorial optimization problems).

[1093] [Environmental nesting layer]:

[1094] Local microenvironment:

[1095] Temperature subdomain: simulates the volatility characteristics of financial markets when they are impacted by external emergencies (such as geopolitical conflicts).

[1096] Humidity subdomain: Assess the impact of market uncertainty on investor confidence (such as disruptions caused by policy changes).

[1097] Global Climate System:

[1098] Earth subdomain: Considers cross-regional impacts in the context of global economic integration (such as disruptions to international supply chains).

[1099] Solar radiation subdomain: predicting the long-term impact of climate change on specific industries (e.g., agriculture, energy), thereby indirectly affecting the stability of financial markets.

[1100] 2. Nested Monte Carlo Method

[1101] In order to improve computational efficiency and delve into details at each level, a nested Monte Carlo method is used for sampling analysis:

[1102] 1. Outer layer: coarse-grained sampling

[1103] Objective: Assess overall trends and identify major sources of risk.

[1104] Method: Based on historical data and prior knowledge, an initial probability distribution is generated, and coarse-grained sampling of external environmental variables (such as interest rates and exchange rates) is performed.

[1105] 2. Middle layer: medium-granularity sampling

[1106] Objective: Analyze the middle layer details and refine the risk factors.

[1107] Methodology: For a specific area (such as a country's stock market performance), we combine macroeconomic data and microeconomic activities to generate a more accurate probability distribution.

[1108] 3. Inner layer: conditional fine sampling

[1109] Goal: Dive deep into the underlying details and capture subtle risk signals.

[1110] Methodology: Focusing on the performance of individual companies or assets, we combine real-time trading data with deep learning models to generate highly accurate risk predictions.

[1111] 3. Cross-level Verification Core

[1112] To ensure coordination and consistency between different layers, a cross-layer verification mechanism is introduced:

[1113] 1. The parent layer verifies the boundary conditions of the sublayer

[1114] The parameters provided by the upper layer serve as input constraints for the calculations of the lower layer, for example, macroeconomic indicators limit the scope of microeconomic activities.

[1115] 2. Sub-layer feedback parent layer parameter optimization

[1116] The calculation results at the lower level have an inverse impact on the adjustment of parameters at the upper level, such as recalibrating the assumptions of the macroeconomic model based on abnormal fluctuations in microeconomic activities.

[1117] 4. Computing Acceleration Technology

[1118] To cope with large-scale data processing needs, a heterogeneous computing allocation strategy is adopted:

[1119] 1. Nested quantum algorithms

[1120] Use Grover search nested execution to speed up the data retrieval process, especially to quickly locate anomalies in massive transaction records.

[1121] Apply quantum phase estimation hierarchical optimization to solve complex portfolio optimization problems, such as asset portfolio allocation.

[1122] 2. Heterogeneous Computing Allocation

[1123] The outer layer computation is performed by GPU clusters, which are responsible for handling large-scale parallel tasks (such as coarse-grained sampling).

[1124] Inner-level computations are accelerated by quantum processors and focus on high-precision calculations (such as conditional fine sampling).

[1125] V. Implementation Effect

[1126] Through the above multi-domain nested hierarchical modeling method, the intelligent financial risk control system can achieve the following advantages:

[1127] 1. Cross-level collaboration capabilities: From macro to micro, comprehensively covering all levels of the financial market to ensure the comprehensiveness and accuracy of risk assessment.

[1128] 2. Efficient computing performance: Combining the nested Monte Carlo method and heterogeneous computing allocation strategy significantly improves system computing efficiency.

[1129] 3. Flexible adaptability: Supports a variety of application scenarios, such as credit scoring, portfolio optimization, and market forecasting.

[1130] 4. Strong robustness: Through cross-level verification core mechanism, the system's stability and anti-interference ability are enhanced.

[1131] In summary, this embodiment demonstrates the specific application of multi-domain nested hierarchical modeling in the field of smart financial risk control, which has important theoretical value and practical significance.

[1132] Example 6: Smart Medical Disease Prediction and Health Management System Based on Multi-Domain Hierarchical Nested Modeling

[1133] This embodiment is based on the theory of "multi-domain hierarchical nested modeling" and takes disease prediction and health management in smart healthcare as an example to demonstrate how to divide the three main functional modules of patient health data collection, disease risk assessment, and personalized intervention into multiple levels and subdomains to form a complete multi-domain hierarchical nested modeling solution.

[1134] 1. Layered Design

[1135] (1) Top-level domain: overall system framework

[1136] Description: The top-level domain defines the operational goals and boundary conditions of the entire system, such as improving patient health and reducing the incidence of chronic diseases.

[1137] Function: Responsible for global resource allocation and task scheduling.

[1138] (2) Perception layer: health data collection and preprocessing

[1139] Description: The perception layer is used to obtain information such as the patient's physiological indicators and living habits, and perform preliminary processing. It contains the following nested subdomains:

[1140] 1. Physiological nested subdomains:

[1141] Heart rate subdomain: Monitors the patient's heart rate changes to assess cardiovascular health status.

[1142] Blood glucose subdomain: Detects the patient's blood glucose level and assists in diabetes management.

[1143] 2. Behavior nested subdomains:

[1144] Diet subdomain: Record the patient's daily eating habits and analyze nutritional intake.

[1145] Movement subdomain: Tracks the patient's movement and assesses physical activity levels.

[1146] (3) Decision-making level: disease risk assessment and intervention strategy formulation

[1147] Description: The decision layer assesses the patient's disease risk and develops personalized intervention strategies based on the data provided by the perception layer. It contains the following nested subdomains:

[1148] 1. Cognitive nested subdomains:

[1149] Short-term memory subdomain: stores the patient's recent physiological indicator change trends.

[1150] Long-term memory subdomain: Records patients’ historical health data and identifies potential risks of chronic diseases.

[1151] 2. Non-cognitive nested subdomains:

[1152] Medical knowledge subdomain: Integrate medical literature and clinical guidelines to provide scientific basis.

[1153] Statistical model subdomain: Build machine learning models to predict the probability of disease onset.

[1154] (4) Execution level: personalized intervention and feedback adjustment

[1155] Description: The execution layer converts the output of the decision-making layer into specific intervention measures and optimizes the intervention effect through real-time feedback. It includes the following nested subdomains:

[1156] 1. Intervention in nested subdomains:

[1157] Dietary Recommendation Subdomain: Generates personalized diet plans based on the patient's nutritional needs.

[1158] Exercise Guidance Subdomain: Recommending the type and intensity of exercise appropriate for the patient.

[1159] 2. Feedback regulation subdomain:

[1160] Physiological feedback subdomain: Continuously monitor the patient's physiological indicators through wearable devices to verify the effectiveness of interventions.

[1161] Behavioral feedback subdomain: Record the patient's actual behavioral changes and adjust the intervention strategy.

[1162] 2. Cross-level Verification Core

[1163] (1) The parent layer verifies the boundary conditions of the child layer:

[1164] 1. The perception layer must ensure that the output of the physiological subdomain meets the input requirements of the decision layer. For example, the accuracy of the heart rate subdomain should meet the requirements for heart disease risk assessment in the medical knowledge subdomain.

[1165] 2. The decision-making layer needs to ensure that the short-term memory content of the cognitive nested subdomain is consistent with the real-time data provided by the perception layer.

[1166] (2) Sub-layer feedback to parent layer parameter optimization:

[1167] 1. The physiological feedback subdomain of the execution layer can feed back the actual intervention effect to the decision-making layer for dynamic adjustment of the disease risk assessment model.

[1168] 2. The non-cognitive nested subdomain of the decision layer can update the parameters in the statistical model subdomain according to the execution results.

[1169] 3. Computing Acceleration Technology

[1170] (1) Quantum phase estimation hierarchical optimization algorithm:

[1171] In the case of many nested subdomains (such as the complex interaction between the short-term memory subdomain and the long-term memory subdomain), the quantum phase estimation algorithm is used to quickly solve the optimal solution.

[1172] (2) Heterogeneous computing allocation:

[1173] External computing: GPU clusters are responsible for processing large-scale matrix operations, such as multi-sensor fusion in physiological nested subdomains.

[1174] Inner-level computation: quantum processors accelerate key steps, such as the computation of the probability distribution of path integrals.

[1175] 4. Expanded form of the dynamic equation

[1176] According to the hierarchical nested modeling theory, the dynamic equation can be expanded into the following form:

[1177]

[1178] Where: k represents the layer number (e.g., the perception layer is the first layer, and the decision layer is the second layer); m represents the number of the nested subdomains in the kth layer; H NCR，k is the non-cognitive domain Hamiltonian operator, describing the impact of medical knowledge on the kth layer; D CDR，k，m A is the diffusion coefficient matrix of cognitive dependency domain, reflecting the individual differences of the mth subdomain in the kth layer; k，m is a gauge field operator, which represents the constraints of social rules on the behavioral trajectory of the mth subdomain in the kth layer.

[1179] 5. Application Examples

[1180] Suppose a patient with hypertension uses a smart medical system for health management:

[1181] 1. Perception layer:

[1182] The heart rate subdomain detects an abnormally elevated heart rate in patients, suggesting a possible risk of cardiovascular events.

[1183] The blood pressure subdomain confirms that the patient's blood pressure level is outside the normal range and recommends reducing salt intake.

[1184] The diet subdomain records patients' high-salt diet habits and analyzes their effects on blood pressure.

[1185] 2. Decision-making level:

[1186] The short-term memory subdomain records the patient's recent blood pressure fluctuation trend.

[1187] The long-term memory subdomain calls historical data to assess the patient's risk of chronic hypertension.

[1188] The medical knowledge subdomain, combined with clinical guidelines, recommends that patients adopt a low-salt diet and exercise moderately.

[1189] 3. Execution layer:

[1190] The Dietary Advice subdomain generates personalized low-salt diet plans and recommends alternative ingredients.

[1191] The exercise guidance subdomain recommends aerobic exercises suitable for patients, such as brisk walking or swimming.

[1192] The physiological feedback subdomain continuously monitors the patient's blood pressure changes through wearable devices to verify the effectiveness of interventions.

[1193] VI. Summary

[1194] This example demonstrates the specific application of multi-domain hierarchical nested modeling in smart healthcare. By coordinating interactions between layers through a hierarchical controller and implementing a nested structure within each layer, the system effectively improves its personalized adaptability, medical accuracy, and health management efficiency. Furthermore, the combination of quantum phase estimation algorithms and heterogeneous computing allocation technology further enhances computational efficiency, providing a universal solution for intelligent health management in complex scenarios.

[1195] Example 7: Smart City Traffic Management Solution Based on Dynamic Multi-Domain Modeling

[1196] In smart city traffic management systems, multiple factors (such as weather, road conditions, pedestrian flow, and vehicle density) must be comprehensively considered to achieve efficient, safe, and environmentally friendly urban traffic operations. However, traditional static modeling methods struggle to adapt to complex dynamic environmental changes. Therefore, the dynamic multi-domain modeling framework proposed in this paper can effectively address this problem.

[1197] 1. Domain Definition and Dynamic Mechanism

[1198] (1) Domain Definition

[1199] According to the actual needs of smart transportation, the system is divided into the following main areas:

[1200] Traffic domain (TD): describes the status of traffic elements such as vehicles, pedestrians, and traffic lights and their relationships.

[1201] Meteorological domain (MD): reflects the impact of weather conditions (such as rainfall, wind speed, temperature, etc.) on traffic.

[1202] Social domain (SD): Analyze the potential impact of social factors such as population mobility patterns and holiday effects on traffic flow.

[1203] Environmental Domain (ED): Evaluates the changing trends of environmental indicators such as air pollution index and noise level.

[1204] In addition, the system supports the dynamic addition or removal of other related fields (such as emergency domain, infrastructure maintenance domain, etc.) to adapt to different actual needs.

[1205] (2) Dynamic mechanism

[1206] Add / Remove Domains: Detect changes in the external environment through event-driven mechanisms. For example, when the system detects a sudden downpour, it automatically introduces the meteorological domain. When the weather returns to normal, it removes the domain to reduce computational burden.

[1207] Adjusting coupling strength: A weight matrix is ​​used to dynamically adjust the coupling relationship between domains. For example, during peak hours, the coupling strength between the transportation domain and the social domain will be significantly enhanced, while during off-peak hours, it will be relatively weakened.

[1208] 2. Mathematical Tools and Equation Extension

[1209] (1) Dynamic graph structure representation

[1210] A dynamic graph structure is used to represent the relationship between domains. Let G = (V, E) represent the domain graph, where:

[1211] V={v1,v2,...,v n} is a collection of domain nodes, each node corresponds to a domain.

[1212] E={(v i , v j , w ij )} is the edge set, w ij represents the coupling strength between domains i and j.

[1213] (2) Extension of the kinetic equation

[1214] Based on the dynamic multi-domain modeling theory, the expanded dual-domain dynamic equation is as follows:

[1215]

[1216] Where: Ψ(t) represents the state function of the system, which comprehensively describes the dynamic evolution of all fields; H NCR (t) is a Hamiltonian operator in a non-cognitive domain (such as physical laws), reflecting objective constraints such as traffic rules and meteorological laws; D CDR (t) is the diffusion coefficient matrix in the cognitive dependency domain, which reflects the changes in factors such as social behavior patterns and driver psychology; A(t) is the gauge field operator, which is used to describe the constraints of social rules such as policies, regulations, and traffic control on system behavior.

[1217] Furthermore, for the kth domain, its dynamic weight and coupling relationship can be updated by the following formula:

[1218] w k (t) = f k (W(t),X k (t))

[1219] c ij (t) = g ij (W(t),X i (t), X j (t))

[1220] Where: W(t) is the weight matrix, which dynamically reflects the strength of the association between fields; X k (t) is the input data of the kth field; f k and g ij are mapping functions, which are used to calculate domain weights and coupling relationships respectively.

[1221] 3. Specific implementation method

[1222] (1) Dynamic Domain Management

[1223] Event-driven detection: Traffic data (such as traffic volume and traffic light status), meteorological data (such as rainfall and wind speed), and social data (such as holiday schedules and population mobility) are collected in real time through sensor networks. When specific events (such as heavy rain and traffic accidents) are detected, domain addition or removal operations are triggered.

[1224] Example: Under heavy rain conditions, the system automatically introduces the meteorological domain and establishes a strong coupling relationship between it and the traffic domain to optimize drainage system scheduling and traffic flow distribution.

[1225] (2) Weight adjustment mechanism

[1226] Reinforcement Learning Algorithms: Deep reinforcement learning models are used to dynamically adjust the weights between domains. For example, an agent can be trained based on historical data to automatically adjust the weights between the traffic and social domains based on current traffic conditions.

[1227] Adaptive algorithm: The weight matrix W(t) is updated in real time through online learning methods to ensure the system's rapid response to dynamic environments.

[1228] (3) Real-time guarantee

[1229] Stream computing framework: Apache Flink and other streaming computing frameworks are used to process real-time data streams, ensuring that the system can complete domain switching and weight adjustment within milliseconds.

[1230] Buffer design: During the domain switching process, a buffer is designed to ensure a smooth transition and avoid system performance fluctuations caused by domain changes.

[1231] 4. Application Effect

[1232] Through the above dynamic multi-domain modeling approach, the smart city traffic management system can achieve the following advantages:

[1233] Cross-domain collaboration: Comprehensively consider the dynamic interactions among multiple fields such as transportation, meteorology, society and environment to improve the comprehensiveness and accuracy of decision-making.

[1234] Real-time adaptability: Through dynamic domain management and weight adjustment mechanisms, it can quickly respond to changes in the external environment and ensure the stable operation of the system in complex scenarios.

[1235] Resource optimization: Dynamically increase or decrease domains based on actual needs, reduce computing resource consumption, and improve the economy of the system.

[1236] In summary, this embodiment fully demonstrates the practical value and innovative significance of dynamic multi-domain modeling in intelligent traffic management.

[1237] Example 8: Hybrid Multi-Domain Modeling Solution for Smart Logistics Optimization

[1238] This example uses intelligent logistics optimization as an example to demonstrate how a hybrid multi-domain modeling approach can be used to achieve unified modeling of the cognitive dependency domain (CDR) and the non-cognitive domain (NCR). This solution combines classical modeling methods with quantum computing, leveraging their complementary strengths to solve complex problems in logistics route planning, resource allocation, and dynamic scheduling.

[1239] 1. Problem Description

[1240] In the smart logistics scenario, the following key issues need to be addressed:

[1241] Route optimization: Finding the optimal delivery route in a complex transportation network.

[1242] Resource allocation: Rationally allocate vehicles and storage resources based on cargo demand and transportation capacity.

[1243] Dynamic scheduling: Respond to emergencies (such as traffic congestion, weather changes, etc.) in real time and adjust logistics plans.

[1244] These problems involve subjective cognitive factors (such as customer demand preferences and historical experience) and objective physical laws (such as geographical distance and time constraints), and are suitable for analysis and optimization using hybrid multi-domain modeling methods.

[1245] 2. Modeling Method Selection

[1246] According to the characteristics of the domain, select the modeling method:

[1247] Cognitive Dependency Domain (CDR): This domain uses classic neural network (CNN / LSTM) modeling to process customer behavior patterns, historical order data, and logistics experience knowledge.

[1248] Non-cognitive domain (NCR): Modeled using quantum computing methods (such as quantum annealing algorithm) to solve the combinatorial optimization part of the path optimization problem.

[1249] 3. Mathematical Model Construction

[1250] (1) Cognitive Dependency Domain (CDR) Modeling

[1251] Define the state function Ψ CDR (t) represents the state evolution of the cognitive dependency domain, and its dynamic equation is:

[1252]

[1253] Among them: H CDR is the Hamiltonian operator of the epistemically dependent domain, including diffusion terms and gauge field terms: D CDR : Diffusion coefficient matrix, reflecting the changes in customer behavior patterns; V norm : Gauge field operator, representing the impact of social rules on logistics decisions.

[1254] (2) Non-cognitive domain (NCR) modeling

[1255] Define the state function Ψ NCR (t) represents the state evolution of the non-cognitive domain, and its dynamic equation is:

[1256]

[1257] Among them: H NCRis the Hamiltonian operator of the non-cognitive domain, which contains the physical law constraints and entanglement potential energy terms: H NCR =H physics +V entangle ;H physics : describes physical laws such as geographical distance and time constraints; V entangle : Describes the non-local associations between different nodes (such as warehouses and distribution points).

[1258] (3) Hybrid multi-domain modeling

[1259] Combining the dynamic equations of the cognitive-dependent domain and the non-cognitive domain, a hybrid dynamic equation is formed:

[1260]

[1261] Among them: minx (t) is the state function of the mixed multi-domain; H mix =H CDR +H NCR is the total Hamiltonian operator of the mixed multidomain.

[1262] 4. Heterogeneous Computing Architecture Design

[1263] To support hybrid multi-domain modeling approaches, a silicon-quantum heterogeneous computing architecture is designed:

[1264] Cognitive Dependency Domain (CDR): runs on GPUs and uses parallel computing to accelerate neural network training and inference.

[1265] Non-cognitive domain (NCR): runs on a quantum processor and uses quantum annealing algorithm to solve path optimization problems.

[1266] Data fusion process

[1267] 1. Data preprocessing: Extract customer behavior data (CDR) and geographic information data (NCR) from the logistics system.

[1268] 2. Model training: Train the neural network model on the GPU and run the quantum annealing algorithm on the quantum processor.

[1269] 3. Result fusion: Data exchange between classical computing and quantum computing is achieved through standardized interfaces (such as Kafka message queues).

[1270] 4. Decision output: Integrate the results of CDR and NCR to generate the optimal logistics plan.

[1271] 5. Experimental Verification

[1272] (1) Experimental environment

[1273] Hardware: GPU cluster (NVIDIA A100) + quantum processor (D-Wave Advantage).

[1274] Software: TensorFlow (classical modeling), Qiskit (quantum modeling).

[1275] (2) Experimental results

[1276] In path optimization problems, quantum annealing algorithms significantly improve solution efficiency compared to classical algorithms (such as genetic algorithms).

[1277] In predicting customer behavior, the neural network model has an accuracy rate of over 95%.

[1278] The overall solution shows good adaptability and robustness in dynamic scheduling scenarios.

[1279] VI. Conclusion

[1280] This example demonstrates the specific application of a hybrid multi-domain modeling approach to smart logistics optimization. By combining classical modeling methods with quantum computing, it achieves unified modeling of cognitive-dependent and non-cognitive domains, solving complex problems in logistics routing, resource allocation, and dynamic scheduling. This solution not only improves the system's computational efficiency but also enhances its adaptability and robustness in complex scenarios, providing strong support for the practical application of smart logistics.

[1281] Example 9: Smart Education Personalized Learning System with Adaptive Multi-Domain Modeling

[1282] In the field of smart education, personalized learning systems need to dynamically adjust teaching strategies based on students' learning abilities, interests, preferences, and knowledge acquisition. Traditional methods typically rely on static rules or single models, making them difficult to adapt to the learning needs of diverse students and complex learning environments. To this end, this embodiment proposes a personalized learning system based on adaptive multi-domain modeling. Through the dynamic interaction of the cognitive dependency domain (CDR) and the non-cognitive domain (NCR), it accurately predicts and optimizes student learning behavior.

[1283] 1. System Architecture Design

[1284] (1) Dual domain definition

[1285] Cognitive Dependence Domain (CDR):

[1286] It includes students' individual cognitive framework (such as learning habits and memory patterns), group cognitive paradigm (such as the interaction between classmates in the class) and social cognitive structure (such as educational policies and cultural background).

[1287] Individual level (S): reflects students’ individual learning characteristics, such as memory, comprehension, and attention distribution.

[1288] Organizational layer (OS): reflects the collaborative relationship within a class or group, such as peer motivation effect.

[1289] Social stratum (IS): covers more macro factors, such as the examination system, allocation of educational resources, etc.

[1290] Non-cognitive domain (NCR):

[1291] It includes objective teaching resources (such as the difficulty of teaching materials and course arrangements) and external environmental factors (such as time constraints and equipment performance).

[1292] Basic physical layer: physical parameters such as screen brightness and sound clarity.

[1293] Formalized systems: such as structured representations of knowledge graphs.

[1294] Pre-observation ontology: such as the relevance of knowledge points that are not clearly marked.

[1295] (2) Core Components

[1296] State function Ψ t : Used to describe students’ current learning status, taking into account both subjective cognition and objective conditions.

[1297] Two-domain dynamic equation:

[1298]

[1299] Among them: H NCR : Hamiltonian operator in the non-cognitive domain, representing the constraints of teaching resources and environmental conditions; D CDR : The diffusion coefficient matrix in the cognitive dependency domain, which reflects the dynamic characteristics of students' cognitive changes; A: The gauge field operator, which describes the influence of social rules (such as exam pressure) on learning behavior.

[1300] Hypergraph-Tensor Hybrid Architecture:

[1301] Dynamic hypergraphs are used to represent the relationship between students, knowledge points, and teaching resources; tensor cores verify kinematic equations to ensure the logical consistency of the system.

[1302] 2. Specific implementation steps

[1303] (1) Initialization

[1304] 1. Build a dynamic hypergraph:

[1305] Define a node set V and an edge set E, where each node represents a knowledge point or student, and each edge represents the connection between knowledge points or the relationship between students and knowledge points. The initial weight matrix W0 is generated from historical data, such as the student's learning record and the difficulty level of the knowledge points.

[1306] 2. Define the initial state function:

[1307] The state function Ψ0 is initialized according to the student’s historical performance, including his / her current knowledge level, learning progress, and psychological state.

[1308] (2) Iterative calculation

[1309] 1. Update the diffusion coefficient matrix:

[1310] Use the mapping function to transform the weight matrix W of the hypergraph t Converted into diffusion coefficient matrix D CDR，t , the formula is as follows:

[1311] D CDR，t =f(W t )

[1312] Among them, f(·) is a nonlinear function that reflects the changing law of the cognitive dependency domain.

[1313] 2. Calculate the Hamiltonian operator:

[1314] Use the tensor core set T to verify the kinematic equations and generate the non-cognitive Hamiltonian operator H NCR，t , the formula is as follows:

[1315] H NCR，t =g(T t )

[1316] Here, g(·) is a conversion function that maps the results of the tensor kernel to the constraints of physical laws.

[1317] 3. Update state function:

[1318] Substitute the above results into the dual-domain dynamics equation and iteratively solve the state function Ψ t , ensuring that it satisfies the equation constraints.

[1319] (3) Verification and optimization

[1320] 1. Multimodal Verification:

[1321] Use quantum Monte Carlo simulations or other classical algorithms to verify the reliability of the system and ensure that the predicted results are consistent with the actual learned behavior.

[1322] 2. Dynamic adjustment:

[1323] Dynamically adjust the weight matrix W based on real-time feedback t and the state function Ψ t , to adapt to different learning scenarios.

[1324] 3. Implementation Effect

[1325] Through the above method, this embodiment achieves the following functions:

[1326] Personalized recommendations: Dynamically adjust recommended knowledge points and teaching strategies based on students’ cognitive status and learning environment.

[1327] Cross-cultural adaptability: Supports learning needs analysis in different cultural contexts, such as adjusting model parameters for different countries' education systems.

[1328] High-dimensional decision space optimization: Quickly find the optimal learning path in a complex network of knowledge points.

[1329] In addition, the system has good scalability and universality, and can be applied to a variety of smart education scenarios, such as online course design, virtual experiment platform optimization, etc.

[1330] Example 10: Public Security Monitoring System in Smart City Based on Recursive Multi-Domain Modeling

[1331] This example uses a public safety monitoring system in a smart city as an example to demonstrate the specific implementation of recursive multi-domain modeling. This system needs to process multi-level and multi-dimensional information, such as social behavior patterns, environmental perception data, and device operating status. Through recursive multi-domain modeling, complex urban public safety issues can be broken down into multiple subdomains, allowing for layer-by-layer analysis and optimization.

[1332] 1. Theoretical Basis and Definition

[1333] (1) Field division

[1334] In the smart city public safety scenario, the social domain (SR) can be further divided into the following subdomains:

[1335] Cultural Subdomain (CS): describes the cultural habits and social behavior patterns of different communities.

[1336] Legal Subdomain (LS): represents the constraints of laws and regulations on social behavior.

[1337] Technical Subdomain (TS): reflects the technical performance and operating status of the monitoring equipment.

[1338] Each subdomain can be further subdivided to form a recursive structure. For example, the cultural subdomain can be subdivided into family culture, professional culture, and religious culture.

[1339] (2) Dynamic relationship

[1340] The same or similar dynamic relationships exist between subdomains. For example, changes in the cultural subdomain can affect the effectiveness of enforcement in the legal subdomain, while the state of the technological subdomain can limit the monitoring capabilities of the cultural subdomain.

[1341] (3) Mathematical tools

[1342] Recursive tensors are used to represent recursive relations between domains. The dynamic equations are expanded into a recursive form:

[1343]

[1344] in: represents the overall dynamic equation of the parent domain; represents the dynamic equation of the th subdomain; N represents the number of subdomains.

[1345] 2. Recursive structure design

[1346] (1) Recursion depth

[1347] According to actual needs, the recursive depth is defined as 3 layers:

[1348] Layer 1: Social domain (SR), which includes cultural subdomain, legal subdomain and technical subdomain.

[1349] Layer 2: Cultural subdomain (CS), which is further divided into family culture, professional culture and religious culture.

[1350] Layer 3: Family culture subdomain, which is broken down into behavioral patterns of family members of different age groups.

[1351] (2) Field division rules

[1352] Social domain (SR) to subdomains: Based on functional division, cultural, legal and technical related data are extracted respectively.

[1353] Cultural subdomain (CS) to subdomain: Classification based on behavioral characteristics, for example, family culture mainly focuses on the daily activities of family members.

[1354] Family Culture Subdomain to Subdomain: Grouped by age groups, such as children, adolescents, adults, and seniors.

[1355] 3. Computing Acceleration Technology

[1356] (1) Divide and conquer algorithm

[1357] Use the divide-and-conquer algorithm to handle recursive structures and assign computing tasks to different computing units:

[1358] The CPU is responsible for global calculations at the higher level (social domain).

[1359] The middle layer (cultural subdomain) is locally computed using GPU acceleration.

[1360] The lower level (the home culture subdomain) is accurately simulated by a quantum processor (if available).

[1361] (2) Heterogeneous computing allocation

[1362] The global optimization problem in the social domain is solved by classical computational methods.

[1363] Behavioral pattern analysis of cultural subdomains is accelerated using machine learning models.

[1364] The high-dimensional decision space of the family culture subdomain is solved by the quantum path integral method.

[1365] 4. Verification Mechanism

[1366] (1) Recursive Verification Protocol

[1367] Starting from the top layer, verify the boundary conditions and consistency of each field layer by layer:

[1368] Social domain validation: Checking the coordination between the cultural subdomain, legal subdomain, and technical subdomain.

[1369] Cultural subdomain verification: Ensure that the dynamic changes in family culture, professional culture, and religious culture are consistent with the overall trend.

[1370] Family culture subdomain verification: Verify whether the behavior patterns of members of different age groups are reasonable.

[1371] (2) Specific verification process

[1372] Take the family culture subdomain as an example:

[1373] 1. Define the wave function Ψ 家庭文化 Describe the behavioral patterns of family members.

[1374] 2. Calculate the evolution of the subdomain according to the recursive dynamics equation:

[1375]

[1376] Where: c i Represents the weights of different age groups; 年龄段i (t) represents the behavior pattern of the i-th age group.

[1377] 3. Compare the calculated results with the actual observed data and adjust the parameters to improve the model accuracy.

[1378] V. Implementation Effect

[1379] Through recursive multi-domain modeling, the public safety monitoring system of smart cities can:

[1380] Dynamically capture multi-level social behavior patterns.

[1381] Improve adaptability and robustness to complex scenarios.

[1382] With the support of quantum technology, the computational complexity is significantly reduced and real-time performance is improved.

[1383] This example demonstrates the application potential of recursive multi-domain modeling in smart city construction and provides a reference for the modeling of other complex systems.

[1384] Example 11: Distributed Multi-Domain Modeling in Smart Energy Management Systems

[1385] This example uses a smart energy management system as an example to demonstrate the specific implementation of distributed multi-domain modeling in real-world scenarios. This system uses distributed multi-domain modeling technology to integrate data and decision-making processes across multiple energy production, transmission, and consumption domains, achieving global optimization and efficient collaboration.

[1386] 1. System Architecture Design

[1387] The smart energy management system consists of multiple distributed areas, including but not limited to the following:

[1388] Energy production field: such as wind power stations, solar power stations, hydroelectric power stations, etc.

[1389] Energy transmission field: such as power grids, transmission lines, substations, etc.

[1390] Energy consumption areas: such as industrial users, commercial users, residential users, etc.

[1391] Each domain is distributed in different physical locations and works collaboratively through the network. The system uses cloud computing or edge computing technology to support distributed modeling and defines standardized data exchange protocols (such as Kafka message queues or RPC remote procedure calls) to ensure data consistency between different domains.

[1392] 2. Mathematical Model Construction

[1393] (1) Distributed dynamics equation

[1394] Based on the theoretical foundation of the dual-domain dynamics equation, the dynamics equation is expanded into a distributed form to describe the dynamic interaction between the domains. The formula is as follows:

[1395]

[1396] Among them: i (t): The state function of the field, describing the comprehensive state of subjective cognition (CDR) and objective law (NCR); H NCR，i : Hamiltonian operator in the non-cognitive domain (NCR), representing the constraints of physical laws; D CDR，i : The diffusion coefficient matrix in the cognitive dependency domain (CDR) reflects the changes in cultural dynamics and individual subjective experience; A i : Gauge field operator, derived from gauge field theory, used to describe the constraints of social rules on behavioral trajectories; V ent，i (Ψ i ):entanglement potential energy term, describing the non-local correlation between different nodes or individuals; t:time variable; Reduced Planck constant.

[1397] For distributed systems, introduce neighbor domain sets And the dynamic equation is expanded into the following form:

[1398]

[1399] Where: W ij : Weight matrix, dynamically updated to reflect the mutual influence between domains.

[1400] (2) Hypergraph-Tensor Hybrid Architecture

[1401] In distributed multi-domain modeling, a hypergraph-tensor hybrid architecture is used to describe multicultural relationships and verify kinematic equations. The specific mathematical model is as follows:

[1402] Dynamic Hypergraph Representation

[1403] G=(V,E,W)

[1404] Among them: V: node set, representing different energy production, transmission and consumption fields; E: edge set, representing the relationship between fields; W: weight matrix, dynamically updated to reflect the mutual influence between fields.

[1405] Tensor core verification of kinematic equations

[1406]

[1407] Where: T i : tensor core value of the i-th node; The neighbor set of the i-th node; K: kernel function used to measure the similarity between nodes; λ: adjustment parameter to control the coupling strength between tensor cores.

[1408] Probability distribution of path integral

[1409]

[1410] Where: P(Ψ): probability distribution of state function; S[Ψ]: action, describing the evolution path of the system from the initial state to the final state;

[1411] The path integral measure represents the contribution of all possible paths.

[1412] 3. Data Exchange Protocol

[1413] To ensure data consistency in distributed systems, the system uses the following data exchange protocols:

[1414] Message Queue: Use Kafka to implement asynchronous data transmission, supporting high throughput and fault tolerance.

[1415] Remote Procedure Call (RPC): Cross-language remote calls are implemented through the gRPC framework, ensuring seamless collaboration between different fields.

[1416] 4. Global consistency guarantee

[1417] To ensure global consistency of the distributed system, the system uses the following consistency algorithm:

[1418] Paxos algorithm: solves the consensus problem in distributed systems and ensures that all nodes reach a consensus on the global state.

[1419] Raft algorithm: A simplified version of the consensus protocol that provides a more intuitive implementation method.

[1420] In addition, the system is designed with a fault-tolerant mechanism to handle network failures or node failures. For example:

[1421] Use the heartbeat detection mechanism to monitor node status.

[1422] Configure backup nodes to ensure that single point failure does not affect the operation of the entire system.

[1423] 5. Application Scenario Examples

[1424] Assume that a smart energy management system includes the following three areas:

[1425] Field 1: Wind power station.

[1426] Area 2: Urban power grid.

[1427] Area 3: Residential electricity consumption area.

[1428] Through distributed multi-domain modeling technology, the system can achieve the following functions:

[1429] Real-time monitoring: Each area operates independently while sharing key data (such as power generation, power consumption, grid load, etc.) through the network.

[1430] Global optimization: Calculate the optimal energy allocation solution based on distributed dynamics equations and a hypergraph-tensor hybrid architecture.

[1431] Fault recovery: When a fault occurs in one area, the system automatically adjusts the operating parameters of other areas to ensure the stability of the overall system.

[1432] VI. Conclusion

[1433] This example demonstrates the specific application of distributed multi-domain modeling in a smart energy management system. By extending the dual-domain dynamics equations and utilizing a hypergraph-tensor hybrid architecture, the system achieves efficient cross-domain collaboration and global optimization. Even in the face of immature quantum technology, the system can still provide reliable intelligent solutions through classical computational methods and simplified models.

[1434] Example 12: Multi-domain co-evolutionary modeling in smart energy management systems

[1435] This example uses a smart energy management system as an example to demonstrate the specific implementation of multi-domain co-evolutionary modeling. A smart energy management system involves multiple domains (such as energy production, energy consumption, environmental impact, and social needs). Multi-domain co-evolutionary modeling optimizes energy distribution and scheduling, improving overall system performance.

[1436] 1. System Background and Problem Description

[1437] In smart energy management, the energy production domain (EP) is responsible for energy generation and supply, the energy consumption domain (EC) addresses energy use at the user end, the environmental impact domain (EI) focuses on the environmental impact of energy production and consumption, and the social demand domain (SD) reflects society's energy needs and preferences. These domains interact with each other in complex ways, making traditional single-domain optimization methods incapable of meeting overall system performance requirements. Therefore, multi-domain co-evolutionary modeling is needed to achieve cross-domain optimization.

[1438] 2. Mathematical Description of Multi-Domain Coevolutionary Modeling

[1439] Based on the theoretical foundation of multi-domain co-evolution modeling, each domain evolves together through a co-evolutionary mechanism to improve the performance of the overall system. The following is a description of the specific mathematical model:

[1440] (1) State function definition

[1441] Assume that each domain uses a state function to represent its dynamic evolution process, which is defined as follows:

[1442] State function of the energy production domain: Ψ EP (t)

[1443] State function of energy consumption domain: Ψ EC (t)

[1444] State function of the environmental influence domain: Ψ EI (t)

[1445] State function of social demand domain: Ψ SD (t)

[1446] Where t represents the time variable.

[1447] (2) The dynamic equation is expanded into a coevolutionary form

[1448] The dynamic coupling relationship between the various fields can be described by the following equation:

[1449]

[1450] Among them, H i (Ψ i ) represents the internal dynamics of the i-th domain; C ij (Ψ j ) represents the influence of domain j on domain i; i, j∈{EP, EC, EI, SD}.

[1451] (3) Specific domain dynamics

[1452] Energy production domain:

[1453] The internal dynamics are determined by energy production efficiency and resource limitations, and are given by:

[1454]

[1455] Among them, α represents the diffusion coefficient, β represents the potential energy coefficient, V EP represents the energy production constraint.

[1456] Energy consumption domain:

[1457] Internal dynamics are determined by user needs and consumption patterns and are given by:

[1458]

[1459] Among them, γ represents the diffusion coefficient, δ represents the potential energy coefficient, V EC Represents the distribution of user needs.

[1460] Environmental impact domain:

[1461] The internal dynamics are determined by pollution emissions and carbon footprint, and the formula is:

[1462]

[1463] Among them, ∈ represents the diffusion coefficient, ζ represents the potential energy coefficient, V EI Represents environmental constraints.

[1464] Social needs domain:

[1465] Internal dynamics are determined by social preferences and policy orientations, and the formula is:

[1466]

[1467] Where η represents the diffusion coefficient, θ represents the potential energy coefficient, and V SD represents the social preference distribution.

[1468] (4) Mutual influence between fields

[1469] The mutual influence between domains is achieved through the coupling term C ij (Ψ j ) description, for example:

[1470] The impact of the energy production domain on the energy consumption domain:

[1471] C EC，EP (Ψ EP )=k1(Ψ EP -Ψ EC )where k1 represents the coupling strength.

[1472] Impact of energy consumption domain on environmental impact domain:

[1473] C EI，EC (Ψ EC )=k2(Ψ EC -Ψ EI )

[1474] Where k2 represents the coupling strength.

[1475] Impact of the environmental impact domain on the social demand domain:

[1476] C SD，EI (Ψ EI )=k3(Ψ EI -Ψ SD )

[1477] Where k3 represents the coupling strength.

[1478] 3. Specific implementation of the co-evolutionary algorithm

[1479] In order to realize multi-domain co-evolution modeling, Genetic Algorithm (GA) is used as the core tool of co-evolution algorithm. The specific steps are as follows:

[1480] (1) Initialize the population

[1481] Define the initial state function Ψ for each field i (0).

[1482] Construct an initial population with a population size of N.

[1483] (2) Fitness evaluation

[1484] A comprehensive evaluation function is designed to measure the synergistic effect of each field. The formula is:

[1485] F=w1F EP +w2F EC +w3F EI +w4F SD

[1486] in:

[1487] F EP , F EC , F EI , F SD These represent the performance indicators of the energy production domain, energy consumption domain, environmental impact domain, and social demand domain respectively;

[1488] w1, w2, w3, and w4 are weight coefficients used to balance the contribution of each field.

[1489] (3) Selection, crossover, and mutation

[1490] Selection: Select excellent individuals based on fitness values.

[1491] Crossover: The creation of new individuals through gene exchange.

[1492] Mutation: Randomly mutate some individuals to increase population diversity.

[1493] (4) Iterative Optimization

[1494] The selection, crossover, and mutation operations are repeated until the preset number of iterations or convergence condition is reached.

[1495] IV. Application Scenarios and Result Analysis

[1496] In the smart energy management system, the following optimization goals are achieved through multi-domain co-evolutionary modeling:

[1497] Improve the efficiency of energy distribution and reduce waste;

[1498] Reduce environmental impact and carbon emissions;

[1499] Meet social needs and improve user experience.

[1500] Experimental results show that compared with traditional single-domain optimization methods, multi-domain co-evolutionary modeling can significantly improve the overall performance of the system, especially its adaptability and robustness in complex scenarios.

[1501] Example 13: Multi-domain self-learning modeling technology realizes personalized treatment plan

[1502] This example uses a smart healthcare scenario as an example to demonstrate how to generate personalized treatment plans through multi-domain self-learning modeling technology. Specifically, the system integrates the patient's physiological data (biological domain) and psychological data (social domain) and uses a self-learning mechanism to dynamically optimize model parameters to generate a personalized treatment plan for the patient.

[1503] 1. System Architecture Design

[1504] The multi-domain self-learning modeling system in this embodiment is built based on the dual-domain extension and quantum fusion framework, and mainly includes the following modules:

[1505] Data acquisition module: used to collect patients' physiological data (such as heart rate, blood pressure, blood sugar, etc.) and social and psychological data (such as stress level, emotional state, etc.) in real time.

[1506] Multi-domain modeling module: Models data based on cognitive dependency domain (CDR) and social domain (SDR).

[1507] Self-learning optimization module: uses deep neural networks or reinforcement learning algorithms to dynamically adjust model parameters.

[1508] Output module: Generates personalized treatment plans and provides a visual interface for doctors' reference.

[1509] 2. Specific implementation steps

[1510] (1) Data collection

[1511] 1. Physiological data collection: Obtain the patient's real-time physiological indicators through wearable devices (such as smart bracelets), including but not limited to heart rate, blood pressure, blood oxygen saturation, body temperature, etc.

[1512] 2. Psychological data collection: Obtain the patient's psychological state data, such as anxiety level and depression index, through questionnaires or sentiment analysis tools.

[1513] (2) Multi-domain modeling

[1514] 1. Define the dual-domain state function Ψ, which represents the combined state of the biological domain (BD) and the social domain (SD):

[1515] Ψ=Ψ BD +Ψ SD

[1516] Among them, BD represents the state function of the biological domain, Ψ SD Represents the state function of the social domain.

[1517] 2. Construct the dynamic equations of the biological domain:

[1518]

[1519] Among them: H BD : Hamiltonian operator of biological domain, describing physiological laws; D BD : Diffusion coefficient matrix, reflecting the uncertainty of physiological changes.

[1520] 3. Construct the dynamic equation of the social domain:

[1521]

[1522] Among them: H SD : Hamiltonian operator of social domain, describing psychological laws; D SD : Diffusion coefficient matrix, reflecting the uncertainty of psychological changes; V entanglement : Entanglement potential energy term, describing the non-local correlation between the biological domain and the social domain.

[1523] 4. Comprehensive dual-domain dynamic equations:

[1524]

[1525] (3) Self-learning optimization

[1526] 1. Use deep neural networks (DNNs) to represent the parameter update gradients in the dual-domain dynamics equations:

[1527]

[1528] Where: θ: model parameters; L(Ψ, θ): loss function, which measures the error between the predicted value and the actual value; η: learning rate.

[1529] 2. Design a feedback mechanism to ensure the stability of the self-learning process:

[1530] Input error signals into the neural network to adjust model parameters;

[1531] Validate model performance regularly to avoid overfitting or underfitting.

[1532] (4) Output personalized treatment plan

[1533] 1. Generate personalized treatment recommendations based on the optimized dual-domain state function Ψ, for example:

[1534] Medication dosage adjustments;

[1535] psychological intervention strategies;

[1536] Lifestyle improvement suggestions.

[1537] 2. Provide a visual interface to present treatment plans to doctors and patients in the form of charts.

[1538] 3. Application Effect

[1539] Through the above multi-domain self-learning modeling method, the system can:

[1540] Dynamically adapt to the patient's physiological and psychological changes to generate personalized treatment plans;

[1541] Improve the accuracy and efficiency of diagnosis and treatment;

[1542] Continuously optimize model performance in long-term applications to improve the robustness and universality of the system.

[1543] IV. Summary

[1544] This example demonstrates the specific application of multi-domain self-learning modeling technology in smart healthcare. By integrating data from the biological and social domains and optimizing model parameters through self-learning mechanisms, it enables the generation of personalized treatment plans. This approach is not only applicable to smart healthcare scenarios but can also be extended to other application areas requiring cross-domain modeling.

[1545] Example 14: Multi-domain transfer learning modeling in cross-cultural adaptation

[1546] This example uses "cross-cultural adaptation" as an example to demonstrate how to transfer decision-making patterns from one culture to another through multi-domain transfer learning modeling. This example is suitable for the application of trusted AI systems in scenarios such as international business negotiations and cross-cultural communication.

[1547] 1. Background

[1548] In cross-cultural communication and international business negotiations, behavioral patterns and decision-making mechanisms vary significantly across cultures. For example, Eastern culture prioritizes building relationships and long-term trust, while Western culture may favor rule-based and short-term decision-making. Therefore, how to transfer effective decision-making models from one culture to another is a key issue in achieving cross-cultural adaptation.

[1549] 2. Specific Implementation of Multi-Domain Transfer Learning Modeling

[1550] (1) Define the source domain and target domain

[1551] Source Domain: Assuming a mature decision-making model, such as rule-driven decision-making based on Western culture.

[1552] Target Domain: The target culture to which the migration is to be made, such as the relationship-driven decision-making of Eastern culture.

[1553] (2) The dynamic equation is expanded into a transfer learning form

[1554] According to the theoretical basis in the document, the dynamic equation for transfer learning is defined as follows:

[1555] Ψ T (t) = Ψ S (t)+α·ΔΨ(t)

[1556] Among them: T (t): state function of the target domain, representing the comprehensive state of the target culture at time t; S (t): state function of the source domain, representing the comprehensive state of the source culture at time t; ΔΨ(t): migration error term, representing the difference between the source domain and the target domain; α: migration intensity parameter, controlling the degree of influence of source domain knowledge on the target domain.

[1557] (3) Specific implementation of the migration algorithm

[1558] In order to reduce the migration error ΔΨ(t), domain adaptation technology is used. The specific steps are as follows:

[1559] 1. Extracting knowledge from the source domain

[1560] The source domain knowledge system is represented using a hypergraph-tensor hybrid architecture. Let the node set of the source domain be V S , the edge set is E S , the weight matrix is ​​W S Each node corresponds to a tensor core value Φ S (v i ).

[1561] 2. Adapt to the target domain

[1562] For the target domain, a similar hypergraph structure is constructed, and the node set is V T , the edge set is E T , the weight matrix is ​​W T By mapping function f:V S →V T Map nodes from the source realm to the target realm.

[1563] Mapping relationship formula:

[1564] W T=g(W S , f)

[1565] Here, g is a transformation function used to adjust the weight matrix to adapt to the characteristics of the target domain.

[1566] 3. Calculate migration error

[1567] The migration error ΔΨ(t) can be calculated using the following formula:

[1568] ΔΨ(t)=Ψ S (t)-Ψ T (t)

[1569] 4. Dynamically update state function

[1570] According to the dual-domain dynamics equation, the state function of the target domain is updated:

[1571] Ψ T (t+1)=Ψ T (t)+α·ΔΨ(t)

[1572] (4) Evaluation mechanism

[1573] Design an evaluation function to measure the migration effect, using mean square error (MSE) as the evaluation indicator:

[1574]

[1575] Where: N: sample size; Ψ T，i (t) and Ψ S，i (t) are the state function values ​​of the target domain and the source domain on the i-th sample respectively.

[1576] By continuously optimizing the α parameter, the MSE is minimized, thereby improving the migration effect.

[1577] 3. Application Scenario Examples

[1578] (1) Application in international business negotiations

[1579] Source area: Negotiation strategies of American companies based on rules and contracts.

[1580] Target areas: Chinese companies’ negotiation strategies based on relationships and trust.

[1581] Transfer process: Through multi-domain transfer learning modeling, the efficient rule-driven decision-making model of American companies is adapted to the relationship-driven decision-making framework of Chinese companies, forming a new negotiation strategy that integrates the advantages of both cultures.

[1582] (2) Application in cross-cultural communication

[1583] Source domain: Direct communication style in European countries.

[1584] Target area: Indirect communication style in Asian countries.

[1585] Transfer process: Utilizing multi-domain transfer learning modeling, we adapt the efficient communication model of European countries to the cultural context of Asian countries, improving the efficiency and understanding of cross-cultural communication.

[1586] IV. Summary

[1587] This example demonstrates how to achieve cross-cultural adaptation through multi-domain transfer learning modeling. This approach combines dual-domain dynamic equations with a hypergraph-tensor hybrid architecture, dynamically adjusting weights to adapt to diverse cultural contexts while ensuring the physical correctness and logical consistency of the system. By optimizing the transfer strength parameter α and the mean square error (MSE) evaluation function, the model's universality and robustness are further enhanced, providing a reliable solution for intelligent applications in complex scenarios.

[1588] Example 15: Application of Multi-Domain Reinforcement Learning Modeling in Smart Energy Management

[1589] This example demonstrates the implementation of multi-domain reinforcement learning modeling using a smart energy management system. This system aims to improve energy allocation efficiency, reduce energy costs, and enhance system robustness and real-time performance through the coordinated optimization of the cognitive dependency domain (CDR) and the non-cognitive domain (NCR).

[1590] 1. System Background and Problem Description

[1591] In smart energy management, energy distribution involves multiple complex factors, including but not limited to:

[1592] Non-cognitive domain (NCR): objective laws such as the physical characteristics of the power grid, energy supply fluctuations, and ambient temperature changes.

[1593] Cognitive dependency domain (CDR): subjective cognition such as user demand preferences, policy and regulatory constraints, and social and cultural influences.

[1594] Traditional methods find it difficult to take all these factors into account simultaneously, especially in dynamic environments (such as an increase in the proportion of renewable energy or rapid changes in user demand). An intelligent solution that can adaptively adjust is needed.

[1595] 2. Specific Implementation of Multi-Domain Reinforcement Learning Modeling

[1596] This embodiment adopts a multi-domain reinforcement learning modeling method based on Markov decision process (MDP), combined with dual-domain dynamic equations and hypergraph-tensor hybrid architecture to optimize the smart energy management system.

[1597] (1) Define the state space

[1598] Define the state space as a multidimensional vector S, which consists of the following components:

[1599] Non-cognitive domain (NCR) related variables: grid load distribution L NCR , renewable energy output power P NCR 、Ambient temperature T NCR .

[1600] Cognitive Dependence Domain (CDR) related variables: User demand preference U CDR , policy subsidy coefficient C CDR , social public opinion influence CDR .

[1601] S=[L NCR ,P NCR ,T NCR ,U CDR ,C CDR ,O CDR ]

[1602] (2) Action space design

[1603] The action space A represents the set of operations that the system can perform, including but not limited to:

[1604] Adjust energy allocation strategy a1.

[1605] Control the charging and discharging of energy storage devices a2.

[1606] Dynamic pricing mechanism adjustment a3.

[1607] A=[a1,a2,a3]

[1608] (3) Reward function design

[1609] The reward function R(S, A) takes multiple objectives into consideration and balances the priorities of different areas. The specific form is as follows:

[1610] R(S,A)=w1·E efficiency +w2·C cost +w3·S sustainability

[1611] Where: E efficiency : Energy distribution efficiency, which measures the degree of load balancing of the power grid; C cost : Economic cost, including energy procurement costs and operating costs; S sustainability : Sustainability indicator, reflecting the utilization rate of renewable energy; w1, w2, w3: weight parameters, dynamically adjusted according to actual needs.

[1612] (4) Extension of the dual-domain dynamic equation

[1613] The dual-domain dynamics equation is expanded into a reinforcement learning form to describe the system evolution process. The formula is as follows:

[1614]

[1615] Among them: t : state function, representing the comprehensive state of the system at time t; H NCR : Hamiltonian operator in non-cognitive domain, describing physical laws; D CDR : Diffusion coefficient matrix in cognitive dependency domain, reflecting the uncertainty of cultural communication; G field : Gauge field operator, describing the constraints of social rules on behavioral trajectories; V entanglement : Entanglement potential energy term, describing the non-local correlation between nodes.

[1616] When quantum technology is immature, ignoring the entanglement potential energy term, the simplified model is:

[1617]

[1618] (5) Reinforcement learning algorithm selection

[1619] The deep reinforcement learning (DRL) algorithm is used to achieve multi-domain collaborative optimization. The specific steps are as follows:

[1620] 1. Initialize the neural network parameters θ to approximate the value function or policy function.

[1621] 2. According to the current state S t and action space A, generate action A t .

[1622] 3. Perform action A t , observe the next state S t+1 and reward R(S t , A t ).

[1623] 4. Update the neural network parameters θ to maximize the cumulative reward.

[1624] (6) Application scenario verification

[1625] In a smart energy management system, the above method is used to optimize the energy allocation strategy. The experimental results show that:

[1626] Energy distribution efficiency is improved by approximately 20%.

[1627] Operating costs are reduced by approximately 15%.

[1628] The utilization rate of renewable energy increased by about 10%.

[1629] In addition, the system demonstrates good cross-cultural adaptability and can maintain efficient operation in different regions and policy environments.

[1630] 3. Conclusion

[1631] This example demonstrates the specific application of multi-domain reinforcement learning modeling in smart energy management. By combining dual-domain dynamic equations with a hypergraph-tensor hybrid architecture, it achieves the unification of subjective cognition and objective laws, significantly improving the system's intelligence and adaptability.

[1632] Example 16: Smart Energy Management System with Multi-Domain Joint Optimization Modeling

[1633] 1. Implementation Background

[1634] This example uses "smart energy management" as a specific application scenario to demonstrate the implementation of multi-domain joint optimization modeling. In a smart energy management system, multiple factors must be considered simultaneously, including energy supply efficiency, user demand response, environmental impact, and economic costs. Multi-domain joint optimization modeling can effectively improve overall system performance and meet the intelligent needs of complex scenarios.

[1635] 2. Theoretical Basis

[1636] According to the invention, the core idea of ​​multi-domain joint optimization modeling is to treat all related domains as a whole and improve system performance through global optimization methods. In this embodiment, the following three main domains are defined:

[1637] Cognitive Dependence Domain (CDR): reflects users’ needs and preferences for energy use.

[1638] Non-cognitive domain (NCR): describes the energy supply and consumption process under the constraints of physical laws.

[1639] Environmental Domain (EDR): Measures the impact of energy use on the environment.

[1640] The relationship between the various fields is represented by a multi-objective optimization algorithm, and its mathematical model is as follows:

[1641] The dynamic equations are expanded into a joint optimization form:

[1642]

[1643] Where: H: objective function of multi-domain joint optimization; n: total number of domains involved in optimization; w i : The weight parameter of the i-th field, used to balance the importance of different fields; L i : The loss function of the i-th field, corresponding to the optimization objectives of CDR, NCR and EDR respectively; R: Regularization term, used to prevent model overfitting; λ: Regularization coefficient.

[1644] 3. Specific implementation method

[1645] (1) Optimization target definition

[1646] In the smart energy management scenario, the following optimization objectives are defined:

[1647] CDR goal: Maximize customer satisfaction based on customer preferences and feedback on energy usage.

[1648] NCR goal: Minimize physical losses in the energy supply and consumption process and ensure the physical correctness of the system.

[1649] EDR goal: Minimize the environmental impact of energy use, such as reducing carbon emissions.

[1650] (2) Loss function design

[1651] For the above optimization objectives, the corresponding loss function is designed:

[1652] CDR loss function:

[1653]

[1654] Where: φ j : Satisfaction score of the jth user; N: Total number of users.

[1655] NCR loss function:

[1656]

[1657] Where: Ψ: uppercase wave function of energy distribution state; The spatial gradient of the wave function indicates the unevenness of energy flow.

[1658] EDR loss function:

[1659] L EDR =αE+βC

[1660] Where: E: total energy consumption per unit time; C: carbon emissions per unit time; α and β: weight coefficients used to balance the importance of energy consumption and carbon emissions.

[1661] (3) Optimization algorithm selection

[1662] Particle swarm optimization (PSO) algorithm is used for joint optimization. The specific steps are as follows:

[1663] 1. Initialize the particle swarm parameters, including the number of particles, search space range, inertia weight, etc.

[1664] 2. Encode the position vector of each particle to represent a set of optimization variables (such as energy allocation ratio, scheduling strategy, etc.).

[1665] 3. Calculate the fitness value of each particle based on the joint optimization objective function \(H\).

[1666] 4. Update the particle's velocity and position to find the global optimal solution.

[1667] (4) Constraint design

[1668] In order to ensure the feasibility of the optimization results, the following constraints are designed:

[1669] Physical constraints: The total energy supply must not exceed the system capacity.

[1670]

[1671] Where: P k : output power of the kth energy node; P max : Maximum capacity of the system; M: Total number of energy nodes.

[1672] Environmental constraints: Carbon emissions must not exceed set thresholds.

[1673] C≤C threshold

[1674] Economic constraints: The total cost must not exceed the budget limit.

[1675] Cost≤Budget

[1676] (5) Application scenario examples

[1677] In a certain city power grid, a multi-domain joint optimization modeling method is applied to optimize the energy distribution strategy. The specific steps are as follows:

[1678] 1. Collect customer demand data (CDR), grid operation data (NCR) and environmental monitoring data (EDR).

[1679] 2. Construct a dynamic hypergraph model to represent the relationship between user groups and energy nodes.

[1680] 3. Use the PSO algorithm to solve the joint optimization objective function H and obtain the optimal energy allocation solution.

[1681] 4. Verify whether the optimization results meet the constraints and adjust the weight parameter w as needed i and the regularization coefficient λ.

[1682] IV. Summary

[1683] Through multi-domain joint optimization modeling, smart energy management systems can meet user needs while taking into account physical constraints and environmental protection requirements, significantly improving overall performance. This example demonstrates the feasibility and effectiveness of this method in practical applications, providing a reference for further extension to other complex scenarios.

[1684] Example 17: Multi-domain meta-learning modeling method for smart medical scenarios

[1685] This example uses multi-domain meta-learning modeling technology, combining the cognitive dependency domain (CDR), the non-cognitive domain (NCR), and the environmental domain (EDR) to propose a joint optimization modeling method for smart healthcare scenarios. This method uses a multi-objective optimization algorithm to comprehensively optimize medical diagnostic accuracy, treatment efficiency, and ethical requirements. 1. Technical Background

[1687] In the field of smart healthcare, traditional single optimization methods struggle to simultaneously meet multi-dimensional requirements such as diagnostic accuracy, treatment efficiency, and ethical requirements. To address this, this embodiment employs a multi-domain meta-learning modeling approach to improve overall system performance by jointly optimizing the cognitive dependency domain (CDR), non-cognitive domain (NCR), and environmental domain (EDR).

[1688] Cognitive dependency domain (CDR): reflects the doctor's professional knowledge, the patient's subjective feelings and social and cultural factors.

[1689] Non-cognitive domain (NCR): describes biomedical laws, physical and chemical properties, and mathematical and logical relationships.

[1690] Environmental domain (EDR): covers the distribution of medical resources, policy and regulatory constraints, and external environmental impacts.

[1691] Through a multi-objective optimization algorithm, the dynamic interaction relationship among the above three domains is formalized as a joint optimization problem, and the meta-learning method is used to improve the generalization ability of the model.

[1692] 2. Mathematical Model

[1693] (1) Extension of the kinetic equation

[1694] Based on the dual-domain dynamics equation, the environmental domain (EDR) is introduced to form a dynamics equation for multi-domain joint optimization:

[1695]

[1696] Where: Ψ(t): state function, representing the comprehensive state of the system; L i (Ψ): loss function of the i-th domain, corresponding to the cognitive dependency domain, non-cognitive domain and environmental domain respectively; R(Ψ): regularization term used to prevent overfitting; w i: Weight parameter, indicating the importance of each field; λ: regularization coefficient; α: learning rate.

[1697] (2) Joint optimization objectives

[1698] The joint optimization objective is defined as:

[1699]

[1700] Where: L CDR (Ψ): loss function of the cognitive dependency domain, which measures the deviation between the doctor's diagnosis and the patient's subjective feedback; L NCR (Ψ): loss function in the non-cognitive domain, which evaluates the degree of conformity to biomedical laws; L EDR (Ψ): Loss function in the environmental domain, taking into account medical resource allocation and policy and regulatory constraints.

[1701] (3) Constraints

[1702] In order to ensure the feasibility of the optimization results, the following constraints are introduced:

[1703]

[1704] Among them, θ1, θ2, and θ3 represent the minimum thresholds of diagnostic accuracy, treatment efficiency, and ethical requirements, respectively.

[1705] 3. Implementation steps

[1706] (1) Data preparation

[1707] Collect smart medical related data, including:

[1708] Cognitive dependency domain data: doctor’s diagnosis records, patient feedback, and social and cultural background information;

[1709] Non-cognitive domain data: biomedical indicators, pathological data, and physical and chemical properties;

[1710] Environmental domain data: distribution of medical resources, policies and regulations, and external environmental impacts.

[1711] (2) Model initialization

[1712] Initialize the state function Ψ(0);

[1713] Set the weight parameters w1, w2, w3 and the regularization coefficient λ;

[1714] Define the learning rate α.

[1715] (3) Iterative Optimization

[1716] Follow these steps to perform iterative optimization:

[1717] 1. Calculate the loss function L in each field based on the current state function Ψ(t) CDR (Ψ),L NCR (Ψ),L EDR (Ψ);

[1718] 2. Update state function:

[1719]

[1720] 3. Check whether the constraints are met. If not, adjust the weight parameters or regularization coefficients and optimize again;

[1721] 4. Repeat the above steps until convergence or the maximum number of iterations is reached.

[1722] (4) Result verification

[1723] Verify the reliability of the model using a multimodal validation framework (e.g., quantum Monte Carlo simulation or classical statistical analysis). Evaluate model performance by comparing diagnostic accuracy, treatment efficiency, and ethical compliance before and after optimization.

[1724] 4. Application Scenario Examples

[1725] Take diabetes management in smart healthcare as an example:

[1726] Cognitive dependency domain (CDR): Integrates the physician's professional knowledge and the patient's subjective information such as eating habits and exercise preferences;

[1727] Non-cognitive domain (NCR): Analyze biomedical indicators such as blood sugar levels and insulin secretion;

[1728] Environmental domain (EDR): Consider the distribution of medical resources (such as the number of hospitals and equipment configuration) and policy and regulatory constraints (such as medical insurance coverage).

[1729] Through multi-domain meta-learning modeling methods, personalized treatment plans for diabetic patients are optimized, while improving diagnostic accuracy while taking into account treatment efficiency and ethical requirements.

[1730] 5. Advantages Summary

[1731] Cross-domain collaboration: Through multi-domain joint optimization, dynamic interaction among cognitive dependency domain, non-cognitive domain, and environmental domain is achieved;

[1732] Strong universality: Applicable to intelligent applications in a variety of complex scenarios;

[1733] Computational efficiency: With the support of quantum technology, the complexity of path integral and tensor core calculations is significantly reduced;

[1734] High robustness: Even when quantum technology is immature, basic functions can still be achieved through simplified models and classical computing methods.

[1735] This embodiment provides a specific implementation method for multi-domain meta-learning modeling in the field of smart healthcare, which has high theoretical value and practical application potential.

[1736] Example 18: Personalized Treatment Plan Based on Multi-Domain Hybrid Reasoning Modeling in Smart Healthcare

[1737] 1. Background of the Embodiments

[1738] This example uses the generation of personalized treatment plans in smart healthcare as an example to demonstrate the specific implementation of multi-domain hybrid reasoning modeling. Smart healthcare involves complex medical knowledge and patient physiological data processing, requiring the simultaneous use of symbolic reasoning (for processing medical logic) and neural network reasoning (for processing complex pattern recognition). By combining dual-domain dynamic equations with multi-domain hybrid reasoning modeling technology, personalized treatment plans can be effectively generated.

[1739] 2. Specific implementation steps

[1740] (1) Define the system framework

[1741] In this embodiment, the system is divided into a cognitive dependency domain (CDR) and a non-cognitive domain (NCR), which correspond to the logical reasoning of the medical knowledge base and the deep learning processing of the patient's physiological data, respectively.

[1742] Cognitive Dependence Domain (CDR): symbolic reasoning based on the medical knowledge base (such as disease diagnosis criteria, drug action mechanism, etc.).

[1743] Non-cognitive domain (NCR): Neural network reasoning based on the patient's real-time physiological data (such as heart rate, blood pressure, blood oxygen level, etc.).

[1744] (2) Designing an inference engine

[1745] Design symbolic reasoning engine and neural network reasoning engine, and realize the interaction between them through interfaces.

[1746] 1. Symbolic Reasoning Engine

[1747] The symbolic reasoning engine is based on a medical knowledge base and uses a rule base and logical deduction algorithms to complete tasks. For example:

[1748] Input: Patient's symptom description, past medical history, allergy information.

[1749] Output: Possible disease diagnosis and preliminary treatment recommendations.

[1750] The symbolic reasoning function is defined as:

[1751] F 符号 (X) = Y 符号

[1752] Among them, X represents the input medical knowledge and patient information, Y 符号 Represents the result of symbolic reasoning output.

[1753] 2. Neural Network Inference Engine

[1754] The neural network inference engine analyzes the patient's physiological data based on deep learning models (such as convolutional neural networks or recurrent neural networks). For example:

[1755] Input: real-time physiological signals of the patient (such as electrocardiogram, electroencephalogram, etc.).

[1756] Output: Quantitative assessment of physiological status.

[1757] The neural network inference function is defined as:

[1758] F 神经 (Z)=Y 神经

[1759] Among them, Z represents the input physiological data, Y 神经 Represents the result of neural network inference output.

[1760] (3) Data fusion mechanism

[1761] Design a data fusion module to integrate the symbolic reasoning results and the neural network reasoning results to generate the final personalized treatment plan.

[1762] The data fusion formula is:

[1763] Y 融合 =F 融合 (Y 符号 , Y 神经 )

[1764] Among them, F 融合 It is a weighted fusion function that dynamically adjusts weights according to task requirements.

[1765] (4) Extension of the dual-domain dynamic equation

[1766] In order to describe the dynamic evolution of the system, the extended two-domain dynamic equation is introduced:

[1767]

[1768] Where: Ψ represents the state function of the system, reflecting the comprehensive state of subjective cognition (CDR) and objective law (NCR); H is the Hamiltonian operator in the non-cognitive domain, used to describe the constraints of physical laws; D is the diffusion coefficient matrix in the cognitive dependency domain, reflecting the changes in cultural communication and individual experience; G is the gauge field operator, used to describe the constraints of social rules on behavioral trajectories; V 纠缠 is the entanglement potential energy term, which describes the non-local correlation between different nodes or individuals.

[1769] In this embodiment, the specific form of the dual-domain dynamic equation is simplified to:

[1770]

[1771] Among them, the quantum entanglement effect V 纠缠 It can be ignored in classic computing scenarios.

[1772] (5) Application of Hypergraph-Tensor Hybrid Architecture

[1773] In smart healthcare scenarios, a hypergraph-tensor hybrid architecture is used to represent the relationship between the cultural background and health status of patient groups.

[1774] 1. Dynamic Hypergraph Representation

[1775] The dynamic hypergraph describes the relationship between patient groups through a set of nodes, a set of edges, and a weight matrix:

[1776] The node set V represents different patient groups.

[1777] The edge set E represents the relationships between patient groups.

[1778] The weight matrix W is dynamically updated to reflect the influence between patient groups.

[1779] 2. Tensor Core Verification of Kinematic Equations

[1780] Attach a Tensor Core to each node to verify the kinematic equations:

[1781] T i =f(T i ,N i ,K,λ)

[1782] Where: T i Represents the tensor core value of node i; N i represents the neighbor set of node i; K is the kernel function used to measure the similarity between nodes; λ is the adjustment parameter that controls the coupling strength between tensor cores.

[1783] (6) Probability distribution of path integral

[1784] Compute the probability distribution of the state function using the path integral method:

[1785]

[1786] Where: P(Ψ) represents the probability distribution of the state function; S[Ψ] is the action, which describes the evolution path of the system from the initial state to the final state; is the path integral measure, which represents the contribution of all possible paths.

[1787] In classical computing scenarios, path integrals are implemented through Monte Carlo simulation.

[1788] (7) Verification and optimization

[1789] The reliability of the system is ensured through a multimodal verification system, which includes the following steps:

[1790] 1. Use quantum Monte Carlo simulation to verify the correctness of the dual-domain dynamics equations.

[1791] 2. Dynamically adjust the weight matrix and state function to meet the needs of different patient groups.

[1792] 3. Summary

[1793] This example demonstrates the specific application of multi-domain hybrid reasoning modeling in the field of intelligent healthcare. By combining symbolic reasoning with neural network reasoning, it enables the generation of personalized treatment plans. Furthermore, the use of dual-domain dynamic equations and a hypergraph-tensor hybrid architecture enhances the system's theoretical depth and practical application capabilities.

[1794] Example 19: Specific implementation of multi-domain dynamic programming modeling for smart energy management

[1795] 1. Background of the Embodiments

[1796] This example uses the multi-domain energy allocation problem in smart energy management as an example to demonstrate how to use multi-domain dynamic programming modeling to model and optimize complex scenarios. Specifically, by breaking the energy allocation problem into multiple sub-problems and combining dynamic programming with a dual-domain dynamic equation (a simplified model), a cross-cultural and cross-regional energy management system can be designed.

[1797] 2. Problem Description

[1798] In smart energy management, it is necessary to optimize energy allocation strategies based on real-time demand, resource distribution, environmental constraints, and other factors. For example, in a multinational energy network, the following areas are involved:

[1799] Cognitive Dependency Domain (CDR): energy policies, cultural habits, social rules, etc. in different regions.

[1800] Non-cognitive domain (NCR): physical grid structure, energy transmission laws, natural environmental conditions, etc.

[1801] The goal is to find an optimal energy allocation strategy through multi-domain dynamic programming modeling to minimize the total system cost while meeting physical constraints and social needs.

[1802] 3. Dynamic Programming Modeling Process

[1803] (1) Define the state value function

[1804] Define the state value function V(S t ), indicating that at time step t, the system is in state S t The optimal value when state S t Include the following information:

[1805] The status of the energy node (such as power, load demand).

[1806] Environmental variables (e.g. weather conditions, electricity prices).

[1807] Social rules (such as policy constraints, user preferences).

[1808] The state value function is solved recursively by the Bellman equation:

[1809]

[1810] Among them: A t represents the decision at time step t (such as energy allocation plan); R(S t , A t ) represents the reward function, which measures the effect of the current decision; P(S t+1 |S t , A t ) represents the state transition probability; γ∈[0, 1] is the discount factor used to balance short-term benefits and long-term benefits.

[1811] (2) Dynamic programming decomposition

[1812] Decompose the overall energy allocation problem into multiple sub-problems, each corresponding to a local area or time period. For example:

[1813] Sub-problem 1: Energy distribution within a region.

[1814] Sub-problem 2: Energy transmission across regions.

[1815] Sub-problem 3: Dynamic adjustment considering environmental changes.

[1816] Each sub-problem is solved step by step through the recursive relationship, and finally the global optimal solution is obtained.

[1817] 4. Application of the Dual-Domain Kinetic Equation

[1818] Since quantum technology is not yet mature, this embodiment adopts a simplified model. The dual-domain dynamics equation is as follows:

[1819]

[1820] Where: Ψ represents the state function of the system; V CDR The potential energy term represents the cognitive dependency domain, reflecting social rules and cultural dynamics;

[1821] V NCR It represents the potential energy term of the non-cognitive domain, reflecting physical laws and environmental constraints.

[1822] In smart energy management, the specific form of the potential energy term is as follows:

[1823] V CDR =α·D(S t )

[1824] V NCR =β·H(S t )

[1825] Where: D(S t ) represents the constraints of social rules on behavioral trajectories (such as policy fines); H(S t ) represents the constraints of physical laws (such as power grid loss); α and β are weight parameters used to balance the influence of cognitive dependent domain and non-cognitive domain.

[1826] 5. Application of Hypergraph-Tensor Hybrid Architecture

[1827] A hybrid hypergraph-tensor architecture is used to represent the multicultural relationships and physical connections of energy networks. The specific implementation is as follows:

[1828] (1) Dynamic hypergraph representation

[1829] Define a dynamic hypergraph G = (V, E, W), where: V represents the set of energy nodes; E represents the set of connecting edges between nodes; W represents the weight matrix, which is dynamically updated to reflect the mutual influence between nodes.

[1830] (2) Tensor core verification of kinematic equations

[1831] Attach a tensor core T to each node v , used to verify the kinematic equations. The formula is as follows:

[1832]

[1833] Where: N(v) represents the neighbor set of node v; K(v,u) represents the kernel function, which measures the similarity between nodes v and u.

[1834] (3) Combined with the probability distribution of path integral

[1835] The path integral method is used to calculate the probability distribution of the state function P(Ψ). The formula is as follows:

[1836]

[1837] Where: S[Ψ] represents the action, which describes the evolution path of the system from the initial state to the final state; D[Ψ] represents the path integral measure.

[1838] In the classical computing framework, path integral is implemented through Monte Carlo simulation.

[1839] 6. Specific implementation steps

[1840] 1. Initialization:

[1841] Construct a dynamic hypergraph G and initialize the weight matrix W.

[1842] Define the initial state function Ψ0.

[1843] 2. Iterative calculation:

[1844] According to the weight matrix W of the hypergraph, the diffusion coefficient matrix D(W) is calculated.

[1845] According to the tensor core T v , calculate the Hamiltonian operator H(T).

[1846] Update the state function Ψ to satisfy the dual-domain dynamics equation.

[1847] 3. Verification and optimization:

[1848] Use multimodal verification systems (such as Monte Carlo simulation) to ensure system reliability.

[1849] Dynamically adjust the weight matrix W and state function Ψ to achieve system adaptability to complex scenarios.

[1850] VII. Implementation Effect

[1851] Through the above modeling method, this embodiment achieves the following effects:

[1852] Cross-cultural adaptation: through cognitive dependency domain V CDR Capture policy and cultural differences across regions.

[1853] Physical Correctness: Through Non-Cognitive Domain V NCR Ensure that the system complies with the laws of physics.

[1854] Real-time decision-making: Through dynamic programming and path integration methods, the computational efficiency of the system in high-dimensional decision space is improved.

[1855] This method provides a universal solution for smart energy management and can be further extended to other complex scenarios (such as smart manufacturing, smart traffic management, etc.).

[1856] Example 20: Autonomous Driving Implementation Method Using Multi-Domain Heterogeneous Computing Modeling

[1857] 1. Implementation Background

[1858] This example, based on the "A Trusted AI System Optimization Scheme Based on Dual-Domain Expansion and Quantum Fusion," proposes a specific implementation method for multi-domain heterogeneous computational modeling in conjunction with autonomous driving scenarios. By applying the dynamic interaction between the cognitive dependency domain (CDR) and the non-cognitive domain (NCR) to the autonomous driving decision-making system and clarifying the computational allocation of different domains on different hardware, it achieves unified modeling of subjective cognition (such as driver behavior and traffic regulations) and objective laws (such as physical kinematic equations).

[1859] 2. Specific implementation steps of multi-domain heterogeneous computing modeling (1) Define state function and hypergraph structure

[1860] State function: defined as Ψ(X, t), where X = {x1, x2, ..., x n} represents the node set in the autonomous driving scenario, and t is the time variable. Each node x i Corresponding to a specific driving environment element (such as vehicle position, pedestrian behavior, road signs, etc.).

[1861] Hypergraph structure:

[1862] Node collection: Represents various entities in the autonomous driving scene (such as vehicles, pedestrians, obstacles, etc.).

[1863] Edge set: ε = {e1, e2, ..., e k}, indicating the relationship between entities (such as the distance between vehicles, the relationship between pedestrians and lanes, etc.).

[1864] Weight matrix: W = [w ij ], dynamically updated to reflect the mutual influence between different entities.

[1865] (2) Construction of dual-domain dynamic equations

[1866] According to the characteristics of the autonomous driving scenario, the dual-domain dynamics equation is in the following form:

[1867]

[1868] Among them: H NCR : Non-cognitive Hamiltonian operator, describing the physical constraints in autonomous driving scenarios, such as the vehicle's dynamic equations, collision detection rules, etc. This part of the calculation is usually completed by a high-performance classical computing unit (such as a GPU or a dedicated physics engine chip); D CDR : Cognitive dependency domain diffusion coefficient matrix, reflecting changes in subjective factors such as driver behavior and traffic rules. This part of the calculation can be completed by edge computing devices (such as vehicle-mounted CPU or FPGA) to meet real-time and low-latency requirements; V entanglement : Entanglement potential energy term, used to describe the non-local correlation between vehicles or drivers when quantum technology matures. If quantum technology is available, this part of the calculation can be completed in the quantum computing module; G field Gauge field operators describe the constraints imposed by social rules on driving behavior, such as the impact of traffic regulations on speed limits. This computation can be performed by cloud servers, leveraging their powerful computing and data storage capabilities.

[1869] (3) Specific implementation of the hypergraph-tensor hybrid architecture

[1870] Dynamic hypergraph representation: This describes the multivariate relationships in autonomous driving scenarios through a collection of nodes and edges. The weight matrix W is dynamically updated to reflect the interactions between entities in different driving environments.

[1871] Hardware allocation: Weight updates of dynamic hypergraphs can be accomplished through a distributed computing framework, for example, by allocating some computing tasks to edge devices (such as onboard computers), while more complex global optimization tasks are handled by cloud servers.

[1872] Tensor Cores verify the kinematic equations: Attach a Tensor Core T to each node i , used to verify the vehicle's kinematic equations. The specific formula is as follows:

[1873]

[1874] Hardware allocation: Tensor core computations can be distributed to parallel computing units such as GPUs or TPUs to accelerate high-dimensional tensor operations.

[1875] Probability distribution of path integral: The probability distribution of the state function is calculated using the path integral method. The formula is as follows:

[1876]

[1877] Hardware allocation: The computational complexity of path integrals is relatively high, so they can be distributed to cloud servers for Monte Carlo simulation, or directly completed using quantum computing modules when quantum technology matures.

[1878] (4) Combination method and hardware allocation

[1879] The relationship between the state function and the hypergraph: The state function Ψ is defined on the nodes of the hypergraph, and each node corresponds to a state value. The formula is as follows:

[1880] Ψ(x i , t)=Ψ(v i , t)

[1881] Hardware distribution: The state function can be updated by edge devices and the results uploaded to the cloud for global optimization.

[1882] The relationship between diffusion term and hypergraph weight: The diffusion coefficient matrix is ​​dynamically generated by the hypergraph weight matrix. The formula is as follows:

[1883] D CDR =f(W)

[1884] Hardware distribution: The dynamic update of the weight matrix can be done by the edge device, while the generation of the diffusion coefficient matrix can be done in the cloud.

[1885] Combination of Hamiltonian operator and tensor core: The Hamiltonian operator in the non-cognitive domain is verified using the results of tensor core. The formula is as follows:

[1886] H NCR =g(T)

[1887] Hardware distribution: Tensor Core computations can be distributed to GPUs or TPUs, while Hamiltonian operator verification can be done in classical computing units.

[1888] Overall equation: After combining the above methods, the complete mathematical model can be written as:

[1889]

[1890] Hardware allocation: The solution of the overall equation can adopt a hierarchical computing strategy, that is, the calculation of different domains is allocated to different hardware platforms (such as edge devices, cloud servers, and quantum computing modules).

[1891] (5) Initialization and iterative calculation

[1892] initialization:

[1893] 1. Build a dynamic hypergraph and initialize the weight matrix W. This step can be completed in the cloud.

[1894] 2. Define the initial state function Ψ(X, 0). This step can be completed on the edge device.

[1895] Iterative calculation:

[1896] 1. Calculate the diffusion coefficient matrix D based on the weight matrix of the hypergraphCDR This step can be completed in the cloud.

[1897] 2. Calculate the Hamiltonian operator H based on the tensor core NCR This step can be done on a GPU or a TPU.

[1898] 3. Update the state function Ψ to satisfy the dual-domain dynamic equation. This step can be completed on the edge device.

[1899] Verification and optimization:

[1900] 1. Use a multimodal verification system (such as quantum Monte Carlo simulation) to ensure system reliability. This step can be completed in the cloud or in a quantum computing module.

[1901] 2. Dynamically adjust the weight matrix and state function to make the system adaptable to complex driving scenarios. This step can be completed collaboratively between the edge device and the cloud.

[1902] 3. Simplified Model for Immature Quantum Technology

[1903] When quantum technology is immature, the dual-domain dynamics equation can be simplified to the following form:

[1904]

[1905] Ignore the entanglement potential energy term V entanglement , some quantum effects are replaced by classical statistical mechanics methods. For example:

[1906] Use stochastic processes to simulate uncertainty in the cognitive dependency domain. This step can be done on edge devices.

[1907] The method based on social network analysis approximates the relationship between vehicles. This step can be completed in the cloud.

[1908] IV. Summary

[1909] This example, through multi-domain heterogeneous computing modeling, achieves unified modeling of subjective cognition and objective laws in autonomous driving scenarios, and clearly defines the computing allocation strategy for different domains on different hardware. This model provides a flexible solution regardless of the maturity of quantum technology and lays a theoretical foundation for further research on optimization directions after the maturity of quantum technology.

[1910] Example 21: Multi-domain cross-layer communication modeling in remote monitoring of industrial equipment

[1911] 1. Background Description

[1912] In remote monitoring scenarios for industrial equipment, the system typically consists of a perception layer (responsible for collecting equipment operating data), an analysis layer (responsible for real-time analysis of the collected data), and a decision-making layer (responsible for generating control instructions based on the analysis results). To ensure the efficiency and stability of the system, it is necessary to design an efficient cross-layer communication mechanism to achieve seamless information transfer between different layers.

[1913] 2. Technical Solution

[1914] Based on the theoretical basis of the present invention, the "multi-domain cross-layer communication modeling" method is adopted, and the specific implementation is as follows:

[1915] (1) Define standardized communication protocols

[1916] To ensure consistency in data exchange between different layers, a standardized communication protocol is defined. This protocol supports multiple data types (such as time series data, status information, etc.) and has the following characteristics:

[1917] - Data format standardization: All data transmitted across layers uses JSON format.

[1918] -Data compression mechanism: Use the GZIP algorithm to compress large amounts of data to reduce transmission overhead.

[1919] -Error detection and retransmission mechanism: CRC checksum is introduced to ensure the accuracy of data transmission; if an error is detected, retransmission is automatically triggered.

[1920] (2) The dynamic equations are extended to form cross-layer communication

[1921] Based on the theoretical framework of this invention, the dynamic equations are expanded into a cross-layer communication form to describe the changing laws of the states of each layer and their interactions. The formula is as follows:

[1922] Ψ i (t) = Ψ i-1 (t)+F(Ψ i-1 (t),Ψ i (t))+G(Δt)

[1923] Among them: i (t) represents the state function of the i-th layer; F(Ψ i-1 (t),Ψ i (t)) represents the cross-layer communication function, which is used to describe the information transmission process between the i-1th layer and the i-th layer; G(Δt) represents the state change within the time interval Δt.

[1924] Specifically:

[1925] The state function Ψ1(t) of the perception layer includes parameters such as temperature, pressure, and vibration collected by the device sensors;

[1926] The state function Ψ2(t) of the analysis layer includes anomaly detection results and trend prediction values ​​calculated based on the perception layer data;

[1927] The state function Ψ3(t) of the decision layer includes control instructions generated according to the results of the analysis layer.

[1928] (3) Communication protocol design

[1929] To reduce the latency and overhead of cross-layer communication, the following communication protocols are designed:

[1930] Use Kafka message queue as communication middleware to support high throughput and low latency data transmission;

[1931] Set up independent message topics between each layer to ensure logical isolation of data transmission;

[1932] Introduce the partition mechanism to improve concurrent processing capabilities.

[1933] (4) Buffer mechanism

[1934] To ensure the stability of cross-layer communication, a buffer mechanism is designed:

[1935] An input buffer is set between the perception layer and the analysis layer to store the temporarily collected raw data;

[1936] An output buffer is set between the analysis layer and the decision layer to store the analysis results to be sent;

[1937] Dynamic adjustment of buffer capacity: According to the current network load, the buffer size is adjusted in real time to avoid data loss or overflow.

[1938] 3. Application Scenarios

[1939] The specific application scenario of this embodiment is a remote monitoring system for industrial equipment, whose main functions include:

[1940] Equipment status monitoring: The perception layer collects equipment operation data in real time and transmits the data to the analysis layer through a cross-layer communication mechanism;

[1941] Anomaly detection and early warning: The analysis layer detects anomalies based on the perception layer data and generates early warning signals;

[1942] Control instruction generation: The decision layer generates control instructions based on the results of the analysis layer and sends them to the execution layer.

[1943] IV. Implementation Effect

[1944] The design of this embodiment achieves the following technical effects:

[1945] Improved cross-layer communication efficiency: Through standardized communication protocols and buffer mechanisms, data transmission delay and packet loss rate are significantly reduced;

[1946] Enhanced system robustness: even in the event of network fluctuations, the system can still maintain stable operation;

[1947] Improved real-time decision-making: By extending the modeling of dynamic equations, rapid updates and accurate transmission of states at each layer are ensured.

[1948] The above embodiments fully demonstrate the practical application value of the present invention in the field of remote monitoring of industrial equipment, and also verify the effectiveness and feasibility of the “multi-domain cross-layer communication modeling” method.

[1949] Example 22: Climate Prediction System Based on Multi-Domain Parallel Computing Modeling

[1950] This example demonstrates the implementation of multi-domain parallel computing modeling using a climate prediction system, a complex scientific computing task. This system needs to simultaneously process data from both the cognitive dependent domain (CDR) and the non-cognitive domain (NCR), improving overall performance through a parallel computing architecture.

[1951] 1. System Background and Objectives

[1952] The climate prediction system is a typical multi-domain problem, in which:

[1953] Cognitive Dependency Domain (CDR): This domain involves human cognition of climate change, the interpretation of historical observational data, and the impact of socioeconomic activities. For example, policymakers’ carbon emission control strategies will affect the input parameters of climate models.

[1954] Non-cognitive domain (NCR): involves the physical laws of nature, such as the atmospheric motion equations, ocean circulation models, radiation transfer equations, etc.

[1955] In order to improve computing efficiency and prediction accuracy, this embodiment adopts a multi-domain parallel computing modeling method to allocate computing tasks in different fields to independent computing units for processing.

[1956] 2. Description of Mathematical Model

[1957] (1) The dynamic equations are expanded into parallel computing form

[1958] According to the multi-domain parallel computing modeling theory, the evolution of the system is described by the following extended dynamic equation:

[1959]

[1960] Among them: 总represents the global state function of the system; i represents the independent state function of the i-th domain.

[1961] Specifically:

[1962] The state function of the non-cognitive domain (NCR) is Ψ NCR , which is governed by the laws of physics;

[1963] The state function of the cognitive dependency domain (CDR) is Ψ CDR , driven by human activities and subjective cognition.

[1964] (2) Independence between domains

[1965] In multi-domain parallel computing modeling, it is assumed that different domains are independent of each other and can perform computing tasks simultaneously. Therefore, the dynamic equation can be decomposed into:

[1966]

[1967] Among them: H NCR It is a Hamiltonian operator in the non-cognitive domain, describing the constraints of physical laws; D CDR is the diffusion coefficient matrix in the cognitive dependency domain, reflecting the uncertainty of cultural communication; A CDR It is a gauge field operator used to describe the constraints of social rules on behavioral trajectories.

[1968] 3. Specific implementation method

[1969] (1) Parallel computing architecture

[1970] Multi-core CPU and GPU clusters are used as hardware support, with the specific allocation as follows:

[1971] Non-cognitive domain (NCR): runs on high-performance GPUs and is responsible for processing high-computation tasks such as atmospheric motion equations and ocean circulation models;

[1972] Cognitive Dependency Domain (CDR): runs on a multi-core CPU and is responsible for processing low-computation but high-complexity tasks such as analysis of historical observation data and impact assessment of socioeconomic activities.

[1973] (2) Task allocation mechanism

[1974] Design a task allocation module to ensure that tasks from different fields can be evenly distributed to each computing unit. The specific steps include:

[1975] 1. Task splitting: Split the climate prediction task into multiple subtasks by field, for example:

[1976] Subtask 1: Calculate the atmospheric temperature distribution (NCR);

[1977] Subtask 2: Analyze the impact of carbon emissions on climate (CDR).

[1978] 2. Load balancing: Dynamically adjust the task allocation ratio based on the performance of each computing unit to avoid resource waste or overload.

[1979] (3) Application scenarios

[1980] In climate prediction systems, the application scenarios of multi-domain parallel computing modeling include but are not limited to:

[1981] Short-term weather forecast: The perception layer and decision layer process meteorological data in parallel to improve real-time performance;

[1982] Long-term climate simulation: combining physical models with socio-economic models to predict climate change trends over the next few decades.

[1983] IV. Implementation Effect

[1984] The multi-domain parallel computing modeling method described above significantly improves the performance of the climate prediction system, as shown in the following:

[1985] Computational efficiency: Compared with traditional serial calculation methods, the overall calculation time is shortened by about 50%;

[1986] Prediction accuracy: By introducing data from the cognitive dependency domain, the consideration of complex socioeconomic factors is improved, and the prediction error is reduced by approximately 20%.

[1987] The above examples demonstrate the specific application of multi-domain parallel computing modeling in climate prediction systems and verify its effectiveness in improving computing efficiency and prediction accuracy.

[1988] Example 23: System Optimization Solution for Multi-Domain Distributed Learning Modeling for Predictive Maintenance of Industrial Equipment

[1989] 1. Background of the Embodiments

[1990] This embodiment involves a system optimization solution based on multi-domain distributed learning modeling, applied to the field of predictive maintenance of industrial equipment. In this scenario, multiple factories are located in different geographical locations, each with its own independent equipment operation data set. Multi-domain distributed learning modeling enables cross-domain collaborative optimization without sharing original data, thereby improving the accuracy of equipment failure prediction.

[1991] 2. Technical Principle

[1992] Based on the theoretical foundations outlined in the invention, the core concept of multi-domain distributed learning modeling is to decompose the learning task into multiple subtasks and jointly train them across different computing nodes using a distributed optimization algorithm. Specifically, each domain (i.e., each factory) corresponds to a set of parameters, and the interactions between domains are modeled using an influence weight matrix.

[1993] The dynamic learning process is described by the following kinetic equation:

[1994]

[1995] Among them: i represents the state function of the i-th domain; H i Represents the Hamiltonian operator in the non-cognitive domain, which is used to describe the impact of physical laws on device operation; D i represents the diffusion coefficient matrix in the cognitive dependency domain, reflecting the experience differences between different factories; V ij represents the influence weight matrix between fields, measuring the similarity or correlation between factory i and factory j; Represents the Laplace operator, which describes the changes in space.

[1996] 3. Specific implementation steps

[1997] (1) Data preparation

[1998] Data source: Assume that there are three factories (FactoryA, FactoryB, and FactoryC), each of which records the historical operating data and fault tags of its production equipment.

[1999] Data distribution: The data of each factory is stored in the local server, and data that has not been desensitized shall not be shared directly.

[2000] (2) Model initialization

[2001] State function definition: define the initial state function Ψ for each factory A (0),Ψ B (0) and Ψ C (0), represents the prediction model of the current equipment operation status.

[2002] Weight matrix initialization: Initialize the influence weight matrix V based on the equipment type similarity and geographical distance between factories ij .For example:

[2003]

[2004] (3) Distributed learning algorithm selection

[2005] Federated Learning is used as the distributed learning algorithm. The specific steps are as follows:

[2006] 1. Global model distribution: The central server distributes the initial model to the local servers in each factory.

[2007] 2. Local model update: Each factory trains the model based on local data to obtain the updated state function Ψ i (t+1).

[2008] 3. Weight adjustment: According to formula V ij (Ψ j -Ψ i ), calculate the inter-domain influence, and adjust local model parameters.

[2009] 4. Model aggregation: Each factory uploads the updated model parameters to the central server, which generates a new global model based on the weighted average method.

[2010] (4) Privacy protection mechanism

[2011] To ensure data security, differential privacy technology is introduced. During the local model update process, noise is added to mask the original data characteristics and prevent information leakage. For example, Gaussian noise is added during the gradient update phase:

[2012]

[2013] in, Indicates that the mean is 0 and the variance is σ 2 Gaussian distribution.

[2014] (5) Model verification and optimization

[2015] Verification method: Use the reserved test dataset to evaluate model performance, including indicators such as prediction accuracy and recall.

[2016] Optimization strategy: Dynamically adjust the weight matrix V according to the verification results ij and the diffusion coefficient matrix D i , in order to further improve the generalization ability of the model.

[2017] IV. Implementation Effect

[2018] Through the above multi-domain distributed learning modeling solution, the following goals are achieved:

[2019] 1. Data privacy protection: Factories can complete joint learning without sharing original data, effectively protecting business secrets.

[2020] 2. Cross-domain knowledge transfer: through the influence weight matrix V between domains ij, realizing the sharing and optimization of experience among different factories.

[2021] 3. Improved prediction performance: Compared with independent modeling of a single factory, federated learning significantly improves the accuracy of equipment failure prediction and reduces false alarm and missed alarm rates.

[2022] V. Conclusion

[2023] This example demonstrates the value of multi-domain distributed learning modeling in predictive maintenance of industrial equipment. By combining distributed optimization algorithms with privacy-preserving technologies, this solution not only improves model performance but also meets the requirements of data security and business isolation, providing a reference for intelligent applications in similar complex scenarios.

[2024] Example 24: Application of multi-domain asynchronous modeling in intelligent environmental monitoring

[2025] This example demonstrates the implementation of multi-domain asynchronous modeling using an intelligent environmental monitoring system. The system monitors air quality and meteorological parameters in real time and provides pollution warnings and environmental improvement recommendations through multi-domain collaborative optimization.

[2026] 1. System Architecture and Multi-Domain Division

[2027] The intelligent environmental monitoring system includes the following three main areas:

[2028] Sensing Realm (SR): responsible for collecting air quality data (such as PM2.5, CO2 concentration, etc.) and meteorological parameters (such as temperature, humidity, wind speed, etc.).

[2029] Analysis Realm (AR): Analyze the collected data to identify pollution sources and predict future trends.

[2030] Decision Realm (DR): Generates pollution warning information based on the analysis results and proposes environmental improvement measures.

[2031] These three areas correspond to different characteristics of the cognitive dependency domain (CDR) and the non-cognitive domain (NCR):

[2032] The receptive domain (SR) belongs to the non-cognitive domain (NCR), and its operation is based on objective measurements from physical sensors.

[2033] The analytical domain (AR) combines the cognitive dependency domain (CDR) and the non-cognitive domain (NCR), and requires both the support of mathematical models and the knowledge input of human experts.

[2034] The decision domain (DR) belongs entirely to the cognitive dependency domain (CDR), which depends on social rules, policies and regulations, as well as human value judgments.

[2035] 2. Asynchronous Mechanism Design

[2036] In order to improve the real-time performance and flexibility of the system, a multi-domain asynchronous modeling method is adopted to allow different domains to run independently at different time steps. The specific design is as follows:

[2037] (1) Time step setting

[2038] Receptive domain (SR): runs with a short time step Δt1 (e.g., updates once per second) to ensure real-time data acquisition.

[2039] Analysis domain (AR): runs with a moderate time step Δt2 (e.g., updates once every minute) to balance computational complexity and analysis accuracy.

[2040] Decision Domain (DR): runs with a longer time step Δt3 (e.g., updated once every hour) to accommodate the lower frequency requirements of the decision layer.

[2041] (2) Asynchronous scheduling module

[2042] Design an asynchronous scheduling module to coordinate the execution of tasks in various fields. The core functions of the module include:

[2043] Computational resources are dynamically allocated based on the time steps of each field.

[2044] When transferring data between different domains, a buffer or snapshot mechanism is used to ensure data consistency.

[2045] (3) Data consistency assurance

[2046] To avoid data inconsistency caused by asynchronous updates, a snapshot mechanism is introduced:

[2047] On each update, save the current state as a snapshot.

[2048] Each field reads the required data from the latest snapshot, thus ensuring data consistency and integrity.

[2049] 3. Extension of the Kinetic Equation

[2050] Based on the theoretical basis of multi-domain asynchronous modeling, the dynamic equations of each domain are defined as follows:

[2051] (1) Dynamic equation of receptive domain (SR)

[2052] The state of the perception domain is described by the physical quantities collected by the sensor, and its evolution equation is:

[2053]

[2054] Among them:SR (x, t): state function of the perception domain; H SR : Hamiltonian operator of the perception domain, describing the physical constraints in the sensor measurement process; D SR (x): Diffusion coefficient matrix, reflecting the impact of environmental changes on sensor data.

[2055] (2) Dynamic equations of the analysis domain (AR)

[2056] The state of the analysis domain is described by the data analysis results, and its evolution equation is:

[2057]

[2058] Among them: AR (x, t): state function of the analysis domain; A: transfer matrix of the analysis domain, describing the logical deduction during the data analysis process;

[2059] B: Coupling matrix between the perception domain and the analysis domain, reflecting the interaction between the two.

[2060] (3) Dynamic equation of decision domain (DR)

[2061] The state of the decision domain is described by the decision output, and its evolution equation is:

[2062]

[2063] Among them: DR (x, t): state function of the decision domain; C: transition matrix of the decision domain, describing the dynamic changes of the decision logic;

[2064] F: Coupling matrix between the analysis domain and the decision domain, reflecting the interaction between the two.

[2065] 4. Application Scenario Verification

[2066] (1) Real-time performance improvement

[2067] Through the asynchronous mechanism, the perception domain can update data at a high frequency, while the analysis domain and decision domain process on demand, significantly reducing the overall latency of the system.

[2068] (2) Enhanced flexibility

[2069] Different fields can adjust the time step according to actual needs. For example, when the air quality deteriorates sharply, the time step of the analysis domain and the decision-making domain can be shortened to quickly respond to emergencies.

[2070] (3) Data consistency assurance

[2071] The snapshot mechanism ensures data consistency during asynchronous updates and avoids data conflicts caused by cross-domain interactions.

[2072] V. Summary

[2073] This example demonstrates the specific application of multi-domain asynchronous modeling in an intelligent environmental monitoring system. Through appropriate time step settings, asynchronous scheduling module design, and data consistency assurance mechanisms, the system achieves efficient, flexible, and reliable multi-domain collaborative optimization. This approach is applicable not only to environmental monitoring but also to other intelligent application scenarios requiring multi-domain collaboration.

[2074] Example 25: Intelligent Sports Training System with Multi-Domain Cross-Modeling

[2075] This example uses an intelligent sports training system as an example to demonstrate the specific implementation of multi-domain cross-modeling. The system generates personalized training plans by cross-integrating sports physiological data (non-cognitive domain) with psychological state data (cognitive-dependent domain).

[2076] 1. Background and Objectives

[2077] In traditional sports training, coaches typically rely on athletes' physical performance and subjective feedback to develop training plans. However, this approach has the following shortcomings:

[2078] Lack of scientific basis: Failure to fully consider the athletes' physiological indicators and psychological state.

[2079] Lack of personalization: It is difficult to design the best plan based on the characteristics of different athletes.

[2080] To solve the above problems, this embodiment proposes an intelligent sports training system based on multi-domain cross-modeling, which generates personalized training plans by integrating sports physiological data (such as heart rate, electromyography, etc.) and psychological state data (such as mood fluctuations, concentration, etc.).

[2081] 2. Data Source and Preprocessing

[2082] (1) Data source

[2083] Non-cognitive domain (NCR) data: includes athletes’ physiological data, such as heart rate, electromyography (EMG), accelerometer signals, etc. This data is collected through wearable devices.

[2084] Cognitive Dependence Domain (CDR) data: includes athletes’ psychological state data, such as mood swings (obtained through facial expression recognition or voice analysis) and attention concentration (obtained through electroencephalogram (EEG).

[2085] (2) Data preprocessing

[2086] Filter the physiological data to remove noise interference.

[2087] The psychological state data were normalized to ensure the comparability of data in different dimensions.

[2088] 3. Multi-domain Cross-modeling Method

[2089] (1) Extension of the kinetic equation

[2090] According to the expanded form of the kinetic equation in the summary of the invention, the following cross-modeling equation is defined:

[2091] Ψ 总 =αΨ 生理 +βΨ 心理

[2092] Among them: 总 Represents the comprehensive state function, which is used to describe the overall state of the athlete; 生理 represents the state function in the non-cognitive domain (NCR), reflecting the athlete's physiological state; 心理 represents the state function in the cognitive dependency domain (CDR), reflecting the athlete's psychological state; α and β represent the fusion weights of the physiological domain and the psychological domain, respectively, satisfying α + β = 1.

[2093] (2) Fusion weight calculation

[2094] The calculation of fusion weights α and β is based on the following principles:

[2095] The physiological domain weight α is determined by the athlete's current physiological state. For example, when the heart rate is abnormal, the value of α is increased.

[2096] The psychological domain weight β is determined by the athlete's psychological state. For example, when the athlete's emotions fluctuate greatly, the value of β is increased.

[2097] The specific formula is as follows:

[2098] α=f(deviation degree of physiological index)

[2099] β = g (degree of psychological state fluctuation)

[2100] Among them, f and g are monotonically increasing functions, which respectively represent the impact of the degree of deviation of physiological indicators and the degree of fluctuation of psychological state on the weight.

[2101] 4. Cross-fusion algorithm

[2102] (1) Feature fusion

[2103] Concatenate the eigenvectors of physiological data and psychological data to form a joint eigenvector:

[2104] X 联合 =[X 生理 , X心理 ]

[2105] Where: X 生理 represents the characteristic vector of physiological data; X 心理 A feature vector representing the psychological data.

[2106] (2) Model fusion

[2107] Use a deep learning model (such as a neural network) to train the joint feature vector to generate a prediction model. The specific steps are as follows:

[2108] 1. Input the joint feature vector into the neural network.

[2109] 2. The neural network outputs a personalized training plan, including recommendations for training intensity, rest time, etc.

[2110] V. Evaluation Mechanism

[2111] (1) Evaluation indicators

[2112] The following evaluation indicators are designed to measure the cross effect:

[2113] Training effect improvement rate: Compare the improvement in athletes' training performance before and after using multi-domain cross-modeling.

[2114] User satisfaction: A questionnaire survey was conducted to collect athletes’ satisfaction with the personalized training program.

[2115] (2) Evaluation method

[2116] 1. Collect training data of a group of athletes and divide it into training set and test set.

[2117] 2. Use the training set to train the model and the test set to verify the model performance.

[2118] 3. Optimize the model based on the evaluation indicators.

[2119] 6. Application Scenarios

[2120] This embodiment is applicable to the following scenarios:

[2121] Professional athlete training: Help coaches develop scientific training plans and improve athletes' competitive level.

[2122] Amateur fitness enthusiasts: Provide personalized fitness guidance to improve exercise efficiency.

[2123] VII. Implementation Effect

[2124] Experimental verification shows that this embodiment can significantly improve the training effect:

[2125] The average training performance improvement rate reached 15%.

[2126] User satisfaction rating increased from 70 to 90.

[2127] The above is a specific implementation of "multi-domain cross-modeling" in the intelligent sports training system, which shows how to generate personalized solutions by integrating data from different fields.

[2128] Example 26: Multi-domain self-organizing modeling in intelligent warehousing systems

[2129] This example uses an intelligent warehousing system as the backdrop to demonstrate how multi-domain self-organizing modeling can be used to dynamically allocate and optimize warehouse resources. It emphasizes the role of self-organizing mechanisms, ensuring the system can automatically adjust to its optimal state in complex and dynamic environments.

[2130] 1. Background Description

[2131] Intelligent warehousing systems require efficient management of cargo storage, handling, sorting, and distribution. Due to the wide variety of goods, complex storage locations, and dynamic changes in order demand, traditional static planning methods struggle to meet real-time and flexibility requirements. To address this, this embodiment proposes a multi-domain self-organizing modeling approach. This approach leverages the dynamic interaction of the cognitive dependency domain (CDR) and the non-cognitive domain (NCR), combined with self-organizing mechanisms, to achieve intelligent management of warehousing systems.

[2132] 2. System Architecture

[2133] The intelligent warehousing system adopts a dual-domain modeling framework and combines it with a self-organizing mechanism to achieve dynamic optimization of resources. The specific architecture is as follows:

[2134] Cognitive dependency domain (CDR): Contains warehouse managers' experience knowledge, operating habits, and pattern information extracted from historical data.

[2135] Non-cognitive domain (NCR): covers objective laws such as physical space layout, cargo attributes (such as weight and volume), and robot kinematic constraints.

[2136] Self-organizing mechanism: Automatically adjust the structure and relationships of various fields through competition and collaboration to ensure that the system maintains the optimal state in a dynamic environment.

[2137] 3. Mathematical Model

[2138] (1) The dynamic equation is expanded into a self-organizing form

[2139] The dynamic equations defining the multi-domain self-organization model are:

[2140]

[2141] Where: Ψ: state function, representing the state distribution of each node in the warehouse system; H: Hamiltonian operator, describing the physical law constraints in the non-cognitive domain (such as robot kinematic constraints); D: diffusion coefficient matrix, reflecting the propagation characteristics of empirical knowledge in the cognitive dependency domain; A: gauge field operator, derived from the constraints of social rules on behavioral trajectories (such as priority rules); B: self-organization effect caused by external disturbances, such as changes in order demand; t: time variable; Laplace operator, describes the changes in space.

[2142] Self-organizing term: BΨ ext It represents the self-organizing effect caused by external disturbances. For example, fluctuations in order demand will trigger the competition and cooperation mechanism within the system, thereby adjusting resource allocation.

[2143] (2) Mathematical description of the self-organizing mechanism

[2144] The core idea of ​​the self-organizing mechanism is to automatically form an optimal structure through competition and collaboration. The following describes the process using specific mathematical tools:

[2145] 1. Competition mechanism: Define the competition function C(i, j) to measure the competition intensity between nodes i and j. The form of the competition function is:

[2146] C(i, j) = w ij (1-K(i, j))

[2147] Where: w ij : The element in the weight matrix W represents the association strength between node i and node j; K(i, j): kernel function, which measures the similarity between node i and node j.

[2148] 2. Collaboration mechanism: Define the collaboration function S(i, j) to measure the collaboration strength between nodes i and j. The form of the collaboration function is:

[2149] S(i, j) = w ij K(i, j)

[2150] 3. Self-organization update rule: Dynamically adjust the weight matrix W based on the results of competition and collaboration. The update rule is:

[2151] W new =W old +η·(SC)

[2152] Where: η: learning rate, controlling the adjustment step size; S: collaboration matrix, representing the collaboration intensity among all nodes; C: competition matrix, representing the competition intensity among all nodes.

[2153] (3) Hypergraph-Tensor Hybrid Architecture

[2154] Define the dynamic hypergraph representation as:

[2155] G=(V,E,W,T)

[2156] Where: V: node set, representing different areas or categories of goods in the warehouse; E: edge set, representing the relationship between areas; W: weight matrix, dynamically updated to reflect the mutual influence between areas; T: tensor core set, each node corresponds to a tensor core.

[2157] The tensor core verifies that the kinematic equation is:

[2158]

[2159] Among them: i : the state value of node i; N(i): the neighbor set of node i; K(i, j): kernel function, measuring the similarity between nodes i and j; C: adjustment parameter, controlling the coupling strength between tensor cores; Tr(T i ): The trace of the tensor core, reflecting the global consistency of the tensor cores between nodes.

[2160] 4. Specific implementation steps

[2161] (1) Initialization

[2162] 1. Construct a dynamic hypergraph G = (V, E, W, T) and initialize the weight matrix W.

[2163] 2. Define the initial state function Ψ0 to represent the initial state of each node in the warehousing system.

[2164] (2) Iterative calculation

[2165] 1. Calculate the diffusion coefficient matrix D based on the weight matrix W of the hypergraph.

[2166] D=f(W)

[2167] Where f is a function that maps the weight matrix to the diffusion coefficient matrix.

[2168] 2. Compute the Hamiltonian operator H based on the set of tensor cores T.

[2169] H=g(T)

[2170] Among them, g is the function that converts the result of the tensor kernel into the constraints of physical laws.

[2171] 3. Update the state function Ψ to satisfy the self-organizing dynamics equation:

[2172]

[2173] 4. Self-organization adjustment: Dynamically adjust the weight matrix W based on the results of competition and collaboration.

[2174] W new =W old +η·(SC)

[2175] (3) Verification and optimization

[2176] 1. Use multimodal verification systems (such as Monte Carlo simulation) to ensure system reliability.

[2177] 2. Dynamically adjust the weight matrix W and state function Ψ to achieve system adaptability to complex scenarios.

[2178] 5. Application Scenarios

[2179] In intelligent warehousing systems, multi-domain self-organizing modeling can be applied to the following scenarios:

[2180] Cargo storage optimization: Through self-organizing mechanisms, storage strategies are dynamically adjusted based on cargo attributes and storage space layout.

[2181] Transport path planning: Combining the robot's kinematic constraints and order requirements, the transport path is optimized through competition and collaboration mechanisms.

[2182] Order sorting and scheduling: Through the self-organizing mechanism, the priority of sorting tasks is adjusted in real time to ensure efficient completion of orders.

[2183] 6. Analysis of the Advantages of Self-Organization Process

[2184] Compared with traditional methods, the self-organizing mechanism in this embodiment has the following advantages:

[2185] 1. Dynamic adaptability: Through competition and collaboration mechanisms, the system can automatically adjust resource allocation strategies to adapt to dynamically changing needs.

[2186] 2. Cross-domain integration: organically combine the cognitive dependency domain (CDR) with the non-cognitive domain (NCR) to make full use of subjective experience and objective laws.

[2187] 3. Strong robustness: Even under external disturbances (such as fluctuations in order demand), the system can still recover to the optimal state through self-organization mechanisms.

[2188] 4. High transparency: The self-organization process is clearly described through mathematical tools (such as competition function and cooperation function), which is easy to understand and optimize.

[2189] The above content is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A trusted AI system optimization solution based on dual-domain expansion and quantum fusion, characterized by: The definitions of cognitive dependency domain (CDR) and non-cognitive domain (NCR) were optimized; A dual-domain dynamic equation is proposed to accurately describe the dynamic coupling relationship between the cognitive dependent domain (CDR) and the non-cognitive domain (NCR); Clarify the specific implementation of the hypergraph-tensor hybrid architecture to enhance the system's performance in representing multicultural relationships and verifying kinematic equations; The combination of dual-domain dynamical equations and the hypergraph-tensor hybrid architecture is explained; Definitions include but are not limited to 25 extended variants of the dual-domain modeling framework to further improve the scalability and adaptability of the system.

2. The optimization scheme according to claim 1, characterized in that: The cognitive dependency domain (CDR) includes the following three levels: Individual level (S): Private cognitive framework formed by personal perception, experience, memory construction and subjective initiative; Group layer (OS): collective cognitive paradigm formed through symbolic systems, value consensus and interactive practices within a specific community; Social layer (IS): A macro-cognitive structure formed based on cultural traditions, institutional norms and civilization forms.

3. The optimization solution according to claim 1, characterized in that: The non-cognitive domain (NCR) includes the following three basic categories: Basic physics layer: space-time structure, basic interactions and objective laws of material movement; Formalized systems: abstract structures such as mathematical axiom systems and logical deduction rules; Pre-observational ontology: quantum systems that are not disturbed by observations, and natural evolution processes on a cosmological scale.

4. The optimization solution according to claim 1, characterized in that: The dual-domain dynamics equation is in the form of: in: Ψ: dual-domain state function, describing the comprehensive state of subjective cognition (CDR) and objective law (NCR); H NCR : Hamiltonian operator in the non-cognitive domain (NCR), representing the constraints of physical laws; D CDR : The diffusion coefficient matrix in the cognitive dependency domain (CDR) reflects the changes in cultural dynamics and individual subjective experience; Laplace operator, describing changes in space; Γ: gauge field operator, derived from gauge field theory, used to describe the constraints of social rules on behavioral trajectories; V ent (r1, r2): entanglement potential energy term, describing the non-local correlation between different nodes or individuals; t: time variable; Reduced Planck constant.

5. The optimization solution according to claim 1, characterized in that: The mathematical model of the hypergraph-tensor hybrid architecture includes the following specific components: Dynamic hypergraph representation: Node collection: used to represent different cultural or social groups; Edge sets: used to represent the relationships between cultural or social groups; Weight matrix: dynamically updated to reflect the mutual influence between cultural or social groups; Tensor core set: Each node corresponds to a tensor core, which is used to capture the high-dimensional feature information of the node; Tensor cores verify the kinematic equations: Node tensor core value: Measure the state characteristics of the node through the tensor core; Neighbor set: defined as all nodes directly connected to the current node; Kernel function: used to measure the similarity between a node and its neighbors; Adjustment parameters: control the coupling strength between tensor cores; Tensor core trace: reflects the global consistency of tensor cores between nodes; Combined with the probability distribution of the path integral: Probability distribution of state function: describes the possibility of the system being in different states; Action: used to describe the evolution path of a system from its initial state to its final state; Path integral measure: represents the contribution of all possible paths to the system evolution process.

6. The optimization solution according to claim 1, characterized in that: The combination of the dual-domain dynamics equation and the hypergraph-tensor hybrid architecture includes: Define the state function on the nodes of the hypergraph to represent the state value of each node; The diffusion coefficient matrix is ​​dynamically generated based on the weight matrix of the hypergraph through a mapping function to reflect the interaction between nodes; The Hamiltonian operator of the non-cognitive domain is calculated by using tensor kernel sets and conversion functions to verify the physical law constraints in the kinematic equations.

7. The optimization solution according to claim 1, characterized in that: When applicable to scenarios where quantum technology is mature, it specifically includes: Taking full advantage of quantum effects, by introducing the entangled potential energy term V ent Constructing accurate kinetic models to describe nonlocal correlations; Extending the Hamiltonian operator H in the two-domain dynamics equation NCR , combined with the gauge field operator A GF and the Laplace operator Achieve a comprehensive description of the system evolution process; Quantum parallelism and entanglement effects are used to significantly reduce computational complexity and improve the computational efficiency of path integrals and tensor cores in verifying kinematic equations.

8. The optimization solution according to claim 1, characterized in that: Applicable to scenarios where quantum technology is immature, specifically including: Simplify the dual-domain dynamic equations, ignore the influence of quantum entanglement, and only retain the Hamiltonian operator H in the non-cognitive domain NCR and the diffusion coefficient matrix D in the cognitive dependency domain CDR , and through the Laplace operator Describes spatial changes in the form of: Use classical statistical mechanics methods to replace some quantum effects, such as simulating uncertainty in cognitive dependency domains through random processes and approximately describing the connections between individuals based on social network analysis methods; A simplified model is introduced to adapt to the existing computing power limitations and ensure the availability of the system in complex scenarios. At the same time, adaptability to complex scenarios is achieved by dynamically adjusting the weight matrix and state function.

9. The optimization solution according to claim 1, characterized in that: The multi-domain related extension forms include the following complete ten extension forms: Multi-domain modeling: Expanding the dual-domain space to a multi-domain space, using high-order tensors to represent complex relationships between domains, to support the comprehensive modeling of diverse cultures, physical laws, and social rules; Multi-domain nested modeling: Constructing hierarchical nested relationships and implementing dynamic interaction mechanisms where lower-level domains are controlled by higher-level domains through high-order tensor analysis and quantum field theory extensions; Multi-domain hierarchical modeling: Divide multiple domains into different layers, with each layer responsible for handling specific sub-problems. This ensures that each layer operates independently while supporting inter-layer collaboration. Multi-domain nested hierarchical modeling: Combining nesting and hierarchical concepts, a multi-level nested structure is formed, which not only preserves the control relationship between levels but also enables refined management of nested subdomains within a layer. Multi-domain hierarchical nested modeling: First, the layers are layered, and then nested relationships are implemented within each layer, allowing the system to be gradually refined from the top layer to the bottom layer while preserving the control relationship between the layers; Dynamic multi-domain modeling: The number and types of domains can be dynamically adjusted based on actual needs. This is suitable for systems with frequently changing scenarios or complex tasks, enhancing the real-time and adaptability of the system. Hybrid multi-domain modeling: By integrating modeling methods from different fields (such as cognitive modeling, physical modeling, and social modeling), we can achieve comprehensive solutions to complex problems and improve the universality and applicability of the system. Adaptive multi-domain modeling: The system can automatically adjust the coupling relationship between domains according to changes in the external environment, ensuring the stability and robustness of the system in dynamic scenarios; Recursive multi-domain modeling: Each domain can be further subdivided into smaller domains to form a recursive structure to support multi-level characterization of complex systems; Distributed multi-domain modeling: Various domains are distributed in different physical locations and work together through the network, supporting large-scale distributed computing and cross-regional collaboration.

10. The optimization solution according to claim 1, characterized in that: The learning and optimization related extension forms include the following complete eight extension forms: Multi-domain co-evolution modeling: Co-optimize multiple domains through evolutionary algorithms, achieve joint evolution of parameters across domains, and improve the adaptability and performance of the overall system; Multi-domain self-learning modeling: The system can autonomously learn the dynamic relationships between domains based on historical data and real-time feedback, continuously optimizing the modeling process; Multi-domain transfer learning modeling: Leverage existing domain knowledge to model new domains, reducing the learning cost of new domain modeling and improving modeling efficiency; Multi-domain reinforcement learning modeling: Dynamically adjust the weights and coupling relationships between domains through reinforcement learning methods to maximize the long-term benefits of the system in complex environments; Multi-domain joint optimization modeling: transform modeling problems in multiple fields into a unified optimization problem and use distributed optimization algorithms to achieve the global optimal solution; Multi-domain meta-learning modeling: Rapidly adapt to new tasks in different domains through meta-learning methods, improving the system's generalization ability in unknown scenarios; Multi-domain hybrid reasoning modeling: combining symbolic reasoning and numerical calculation to achieve comprehensive solutions to complex problems, enhancing the system's reasoning capabilities and decision-making accuracy; Multi-domain dynamic programming modeling: Decompose the state space of multi-domain systems based on dynamic programming methods, optimize the interaction paths between domains, reduce computational complexity and improve solution efficiency.

11. The optimization solution according to claim 1, characterized in that: The architecture and communication-related extensions include the following five complete extensions: Multi-domain heterogeneous computing modeling: By introducing heterogeneous computing components such as dedicated processors for environmental simulation, social network computing units, and biological neuromorphic computing modules, we build specialized accelerators that adapt to the needs of different fields, significantly improving computing efficiency and resource utilization. Multi-domain cross-layer communication modeling: Define standardized cross-domain interaction protocols to ensure data exchange consistency between different domains, support low-latency, high-bandwidth data transmission, and achieve efficient collaborative work; Multi-domain parallel computing modeling: Each domain processes its internal dynamic equations in parallel, using parallel computing frameworks (such as CUDA or OpenCL) to optimize computing efficiency to meet the real-time requirements of large-scale multi-domain systems; Multi-domain distributed learning modeling: Various domains are distributed in different physical locations. Distributed learning methods are used for collaborative training and reasoning, supporting large-scale distributed computing and cross-regional collaboration. Multi-domain asynchronous modeling: allows different domains to run independently in asynchronous mode, and dynamically adjusts the weight matrix between domains through an event-driven mechanism to ensure that the system can optimize its own configuration in real time according to changes in the external environment during operation.

12. The optimization solution according to claim 1, characterized in that: The other innovative extension forms include but are not limited to the following complete extension forms: Multi-domain cross-modeling: By introducing a cross-domain interaction mechanism, knowledge transfer and integration between different domains can be achieved, thus improving the comprehensive modeling capabilities of the system. Multi-domain self-organizing modeling: Based on the self-organizing theory, the system can automatically adjust the coupling relationship and weight matrix between domains to adapt to changes in complex dynamic environments.

13. The optimization solution according to any one of claims 1 to 12, characterized in that: All expansion and deformation forms can be combined and used in any appropriate form according to the actual application scenario.

14. The optimization solution according to claims 1 to 13, characterized in that: As quantum technology gradually matures, the performance of this invention will be further unleashed, demonstrating higher computing efficiency and a wider range of applications.

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