A multi-physical field mechanism mining method and system based on optimal manifold embedding sub-domain

Abstract

A multi-physical field mechanism mining method and system based on optimal manifold embedding sub-domain, the method comprising: collecting multi-physical field time series data and standardizing; extracting dimensionless features based on dimension analysis theorem; constructing a physical tensor manifold, internalizing physical laws as inherent properties of manifold geometry; disassembling the manifold into quasi-conformal sub-domains and extracting topological features; performing constraint sign regression in each sub-domain and combining graph networks to complete cross-domain fusion, reconstructing the global coupled mechanism; and outputting an interpretable mechanism equation with a confidence interval through adaptive physical arbitration and uncertainty quantification. The system comprises six units: data acquisition, dimensionless extraction, manifold construction, conformal sub-domain, mechanism reconstruction, and physical arbitration output. The mechanism equation mined by the present application naturally satisfies the conservation law, has strict convergence guarantee and quantifiable confidence evaluation, while greatly reducing the computational complexity, and has physical authenticity, reliability and interpretability.

Description

Technical Field

[0001] This invention relates to artificial intelligence scientific computing, multiphysics coupling simulation, and intelligent analysis technology of equipment dynamics, and in particular to a method and system for mining multiphysics mechanisms based on optimal manifold embedded domain. Background Technology

[0002] Complex engineering equipment generally exhibits strong nonlinear coupling characteristics across multiple physical fields, including aerodynamics, hydrodynamics, structure, heat, and fluid dynamics. These systems are characterized by high dimensionality, hidden coupling mechanisms, and complex dynamic evolution. Accurately analyzing their inherent physical laws is a core prerequisite for equipment design optimization, fatigue assessment, early warning of extreme working conditions, and digital twin modeling.

[0003] Currently, the mainstream technical methods in the industry are divided into two main categories: numerical simulation and artificial intelligence mechanism mining. Both of these methods have significant technical shortcomings. The first category is high-fidelity numerical simulation methods, represented by simulation software such as OpenFAST and ANSYS. These methods rely on numerical methods such as finite element and finite volume to solve multi-field coupling equations, resulting in high simulation accuracy. However, single-condition simulations can take hours, incurring huge computational costs. This makes it impossible to meet the engineering requirements of batch wind field assessment, real-time digital twin response, and dynamic extrapolation throughout the entire life cycle. Real-time performance and large-scale application capabilities are severely limited.

[0004] The second category is AI for Science (scientific intelligence) intelligent mechanism mining methods, including traditional symbolic regression, SINDy algorithm, and Physical Information Neural Network (PINN). These are currently the mainstream technologies replacing traditional simulation, but they have four inherent fatal flaws: First, traditional symbolic regression and SINDy algorithm are prone to combinatorial explosion problems when facing high-dimensional coupled systems, are highly sensitive to monitoring noise and differential errors, and are extremely prone to overfitting and spurious mechanisms; Second, PINN-type methods rely on exogenous artificial penalty constraints to achieve physical regulation. The constraint weights are manually set, have poor adaptability, and the training process is prone to violating the laws of conservation of energy and momentum, resulting in serious "physical illusion" problems and low mechanism credibility; Third, existing AI models are all black-box fitting architectures, unable to establish an interpretable correlation between input features and physical mechanisms, and have poor transparency of high-dimensional coupled mechanisms, making it difficult to support engineering mechanism analysis; Fourth, traditional manifold dimensionality reduction and data fitting methods lack strict mathematical convergence boundaries, and the reconstruction error has no quantitative guarantee, which cannot meet the stringent requirements of reliability assessment for high-end equipment engineering.

[0005] In summary, existing technologies cannot simultaneously achieve real-time computation, physical authenticity, interpretability of mechanisms, controllable convergence, and engineering reliability. The industry urgently needs a fully automated physical mechanism mining technology solution that is supported by rigorous mathematical theory, has intrinsically embedded physical constraints, quantifiable error convergence, and is adaptable to high-dimensional multi-field coupled systems.

[0006] It should be noted that the information disclosed in the background section above is only for understanding the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] The main objective of this invention is to overcome the deficiencies in the aforementioned background technology and provide a method and system for mining multiphysics mechanisms based on optimal manifold embedded domains.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: A multiphysics mechanism mining method based on optimal manifold embedded domain includes the following steps: S1. Collect multi-physics time-series data of complex coupled equipment, and perform anomaly removal, statistical moment feature extraction and dimensionality reduction on the data to obtain standardized multi-physics data. S2. Construct a dimensional matrix of multiple physical quantities based on the dimensional analysis theorem, apply integer constraints to the dimensional matrix to solve the dimensionless feature set, and embed inherent physical constants of the engineering to constrain the algorithm search space to obtain dimensionless feature data under a unified reference coordinate. S3. Based on the dimensionless feature data, the equipment physical entity, coupling relationship and dynamic evolution behavior are mapped to a high-dimensional Riemannian manifold. The metric tensor, connection symbol and generalized dissipative force field of the manifold are solved endogenously by the system Lagrangian to construct the physical tensor manifold. S4. Decompose the physical tensor manifold into a finite number of quasi-conformal subdomains, adaptively determine the subdomain scheme with the optimization objective of minimizing the number of subdomains under a preset reconstruction accuracy, extract the topological features of each conformal subdomain, and establish the mapping relationship between the topological features and physical phenomena. S5. Constrained symbolic regression is performed in each conformal subdomain to mine local physical mechanisms. A graph network is constructed with conformal subdomains as nodes and the similarity of mechanisms between subdomains as edges. The cross-domain fusion of local mechanisms is completed through the graph network to reconstruct the global multi-physics coupling mechanism. S6. Construct an adaptive total loss function that includes data fitting loss and physical conservation loss, perform physical consistency verification and correction on the reconstructed global multiphysics coupling mechanism, quantify the uncertainty of mechanism prediction, and output an interpretable multiphysics coupling mechanism equation with confidence interval evaluation.

[0009] A multiphysics mechanism mining system based on optimal manifold embedded domain includes: The data acquisition and preprocessing unit is used to acquire multi-physics time-series data of complex coupled equipment, perform anomaly removal, statistical moment feature extraction and dimensionality reduction on the data, and output standardized multi-physics data. The dimensionless feature extraction unit, connected to the data acquisition and preprocessing unit, is used to construct a dimensional matrix of multiple physical quantities based on the dimensional analysis theorem, apply integer constraints to the dimensional matrix to solve for the dimensionless feature group, embed the inherent physical constant constraint algorithm search space, and output dimensionless feature data under a unified reference coordinate. The physical tensor manifold construction unit, connected to the dimensionless feature extraction unit, is used to construct a continuous and smooth physical tensor manifold based on the dimensionless feature data by endogenously solving the metric tensor, connection symbol, and generalized dissipative force field of the manifold through the system Lagrange. The conformal domain division and topology analysis unit is connected to the physical tensor manifold construction unit. It is used to decompose the physical tensor manifold into a finite number of quasi-conformal subdomains, adaptively determine the domain division scheme with the optimization objective of minimizing the number of domains under a preset reconstruction accuracy, and extract the topological features of each conformal subdomain. The global mechanism reconstruction unit connects the conformal subdomain and the topology analysis unit. It is used to perform constrained symbolic regression to mine local physical mechanisms in each conformal subdomain, and to construct a graph network with conformal subdomains as nodes and mechanism similarity between subdomains as edges. The graph network is used to complete the cross-domain fusion of local mechanisms and reconstruct the global multi-physics coupling mechanism. The physical arbitration and uncertainty output unit, connected to the global mechanism reconstruction unit, is used to construct an adaptive total loss function that includes data fitting loss and physical conservation loss to perform physical consistency verification and correction on the global multiphysics coupling mechanism, quantify the uncertainty of mechanism prediction, and output an interpretable multiphysics coupling mechanism equation with confidence interval evaluation.

[0010] The present invention has the following beneficial effects: This invention provides a multiphysics mechanism mining method and system based on Optimal Manifold Embedded Domain (OMED). It constructs a physical tensor manifold axiomatic system, internalizing the physical laws of high-dimensional systems into inherent properties of manifold geometry, completely abandoning the artificial exogenous penalty constraint mode and black-box data fitting architecture of the traditional PINN method. Relying on an innovative technical system comprised of conformal domain reconstruction, integer constraint dimensionless decomposition, manifold topology analysis, adaptive physical constraint arbitration, and uncertainty quantification, this invention fundamentally eliminates the problem of physical illusion. The mined mechanism equations naturally satisfy the laws of energy conservation and momentum conservation, exhibiting significantly higher physical reliability than existing AI mechanism mining methods.

[0011] Meanwhile, based on the power-law convergence error boundary established by OMED, ​​this invention provides a rigorous mathematical quantitative guarantee for the reconstruction error, overcoming the common industry shortcoming of traditional manifold dimensionality reduction and data fitting methods lacking convergence constraints, and meeting the stringent requirements of reliability assessment for high-end equipment engineering. In terms of computational efficiency, this invention significantly reduces the complexity of traditional high-dimensional algorithms through optimal conformal domain dimensionality reduction of high-dimensional manifolds and a divide-and-conquer parallel computing strategy, achieving an efficiency leap from traditional hour-level simulation to millisecond-level inference, and fully adapting to the timeliness requirements of real-time digital twin and batch evaluation scenarios.

[0012] Furthermore, this invention, through a one-to-one mapping between manifold topological features and physical phenomena, enables each set of mining equations to possess a clear physical interpretation, achieving visualized decoupling and transparent analysis of high-dimensional coupling mechanisms, overcoming the limitations of traditional AI models in terms of mechanistic explanation. Relying on physical prior constraints and topological feature extraction, this invention requires only a small amount of extreme operating condition data to complete high-precision modeling, accurately identifying system information boundaries, effectively suppressing data noise and overfitting problems, exhibiting excellent generalization ability, and adapting to complex marine extreme winds and waves, equipment extreme loads, and other special operating conditions.

[0013] Verified through an embodiment using a floating offshore wind turbine as a typical example, the multi-field coupling equations independently mined by this invention can accurately reproduce classical mechanics principles. The tower base bending moment prediction accuracy is high, nonlinear laws are accurately captured, and the overall inference speed is two orders of magnitude faster than traditional simulations. Furthermore, it avoids physical illusions and overfitting issues, demonstrating excellent convergence stability and engineering accuracy. This invention's technical solution relies on an integrated hardware and software architecture, which can be directly deployed on offshore wind farm monitoring terminals, industrial servers, and digital twin platforms. It can automatically complete multi-physics mechanism mining, dynamic response prediction, structural state assessment, and extreme condition early warning for complex equipment. It can be widely applied to numerical simulation, mechanism identification, state assessment, and real-time digital twin simulation scenarios for complex and strongly coupled equipment such as floating offshore wind turbines, aerospace power equipment, and new energy storage equipment. It possesses significant application value and industrialization prospects, demonstrating remarkable industrial practicality.

[0014] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the overall process of the multiphysics mechanism mining method based on optimal manifold embedding domain in this invention.

[0016] Figure 2 This is a technical roadmap diagram of the overall method of the present invention.

[0017] Figure 3 This is a schematic diagram of optimal conformal domain division and topological feature extraction of the PTM physical tensor manifold in this invention.

[0018] Figure 4 This is a block diagram of the overall architecture of the multiphysics mechanism mining system of the present invention. Detailed Implementation

[0019] The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary and not intended to limit the scope and application of the present invention.

[0020] This invention aims to overcome the technical shortcomings of existing numerical simulation methods, such as low efficiency, poor physical realism, weak interpretability, and lack of convergence guarantees. It proposes a multi-physics mechanism mining method and system based on optimal manifold embedded domain. By constructing a physical tensor manifold, the physical conservation laws are internalized into the inherent properties of the manifold geometry. Combined with conformal domain reduction, cross-domain fusion of graph networks, and adaptive physical arbitration, it achieves fully automatic mining of high-dimensional coupling mechanisms. It has strict power-law convergence error boundaries and quantifiable uncertainty assessment, eliminating physical illusions at the root. At the same time, it reduces the computational complexity from high-dimensional exponential (cubic complexity) to low-dimensional quadratic complexity, achieving a unity of mechanism credibility, engineering reliability, computational real-time performance, and interpretability.

[0021] See Figure 1 and Figure 2 This invention provides a multiphysics mechanism mining method based on Optimal Manifold Embedded Domain (OMED), comprising the following steps: Step S1: Collect multi-physics time-series data of complex coupled equipment, and perform anomaly removal, statistical moment feature extraction and dimensionality reduction on the data to obtain standardized multi-physics data.

[0022] In some embodiments, the data acquisition and preprocessing process in step S1 may specifically include: acquiring time-series physical data of the equipment under full operating conditions through a distributed sensor array or a high-precision numerical simulation platform deployed on complex coupled equipment, covering multi-dimensional variables such as aerodynamics, hydrodynamics, structure, and load; extracting the mean and standard deviation statistical moments of the data using a sliding window, and removing abnormal noise data by combining statistical criteria; completing the dimensionality reduction of high-dimensional data through matrix decomposition, retaining effective feature components with a cumulative variance ratio not lower than a preset threshold, and obtaining standardized multi-physics field data.

[0023] Step S2: Construct a dimensional matrix of multiple physical quantities based on the dimensional analysis theorem, apply integer constraints to the dimensional matrix to solve for the dimensionless feature set, and embed inherent physical constants of the engineering to constrain the algorithm search space to obtain dimensionless feature data under a unified reference coordinate.

[0024] In some embodiments, the solution process for the dimensionless feature set in step S2 includes: based on Buckingham's Pi dimensional analysis theorem, constructing a dimensional matrix according to the basic dimensions of each physical quantity in a multiphysics system, establishing a dimensional homogeneous constraint equation, solving the null space vector of the equation under integer weight constraints, and obtaining the dimensionless Pi feature set; for low- to medium-dimensional system conditions, using a lattice basis reduction algorithm to solve the integer constraint null space; for high-dimensional complex system conditions, using the alternating direction multiplier method to construct an optimization objective function with integer constraints for iterative solution; when the integer constraint null space has no strictly integer solution, at least one of the following engineering compensation strategies is used for processing: relaxing the integer constraints to half-integer or quarter-integer constraints, embedding inherent physical constants to expand the dimensional matrix, merging physical variables with consistent dimensions to reduce the solution dimension, and relaxing the error tolerance threshold of the dimensional homogeneous constraints; the inherent physical constants include half-integer constants and the constant of pi, and by fixing the constants in the dimensional matrix, the algorithm search space is constrained within a physically reasonable range.

[0025] Step S3: Based on the dimensionless feature data, the equipment physical entities, coupling relationships and dynamic evolution behavior are mapped to a high-dimensional Riemannian manifold. The metric tensor, connection symbol and generalized dissipative force field of the manifold are solved endogenously by the system Lagrangian to construct the physical tensor manifold (PTM).

[0026] In some embodiments, the construction process of the physical tensor manifold in step S3 includes: using the dimensionless eigenvectors output in step S2 as the coordinate input of the manifold, defining and solving the symmetric positive definite metric tensor of the manifold based on the second-order partial derivative of the system dynamics Lagrangian (the difference between the system's kinetic and potential energy) with respect to the generalized velocity, wherein the metric tensor determines the local curvature and spatial scale of the manifold; solving the Levi-Civita connection symbol based on the inverse matrix of the metric tensor and the first-order partial derivative of the metric tensor with respect to the generalized coordinates, wherein the connection symbol is used to realize the parallel translation of the tensor on the manifold and the calculation of geodesics; and using the degree The inverse matrix of the metric tensor acts on the generalized nonconservative dissipative forces of the multiphysics system to obtain the generalized dissipative force field on the tangent bundle of the manifold. The generalized nonconservative dissipative forces include fluid viscous drag and structural damping forces. The initial topology of the manifold is constructed using a diffusion mapping algorithm. The dimensionless eigenvectors are subjected to temporal filtering and numerical differentiation to solve for the generalized velocity term. The global metric tensor is solved point by point and regularization is applied to ensure the positive definiteness of the matrix. Global smooth interpolation of discrete connection symbols is completed based on radial basis functions. The global embedding of the dissipative force vector field is completed by combining the measured dissipative power of the system, resulting in a continuous and smooth physical tensor manifold.

[0027] In some embodiments, after the physical tensor manifold is constructed, a manifold dynamic evolution characterization step is further included: the dynamic evolution behavior of the system under the combined action of conservative and non-conservative forces is characterized by a forced geodesic equation, wherein the conservative forces are anchored to the metric tensor of the manifold and the geometric properties of the manifold represented by the connection symbol, and the non-conservative dissipative forces are characterized by the generalized dissipative force field, and the system evolution trajectory is obtained by solving the forced geodesic equation; the effectiveness of the constructed manifold is verified by a manifold accuracy verification step, wherein the verification step includes: comparing the actual evolution trajectory of the system with the evolution trajectory obtained by solving the forced geodesic equation to ensure that the relative deviation of the trajectory fitting meets the preset threshold requirement.

[0028] Step S4: Decompose the physical tensor manifold into a finite number of quasi-conformal subdomains, adaptively determine the subdomain scheme with the optimization objective of minimizing the number of subdomains under a preset reconstruction accuracy, extract the topological features of each conformal subdomain, and establish the mapping relationship between the topological features and physical phenomena.

[0029] Its processing procedure is as follows Figure 3 As shown: After optimal conformal partitioning, a high-dimensional PTM manifold (large surface) is divided into several two-dimensional conformal subdomains (multiple small surfaces). Each subdomain and its discrete point cloud are further constructed into a simple complex. Then, persistent barcodes are generated through persistent homology analysis to extract the topological features of each subdomain, thereby achieving a unified description of the global topological information and local geometric features of the manifold.

[0030] In some embodiments, the decomposition process of the quasi-conformal subdomain in step S4 includes: using quasi-conformal submanifold embedding to reduce the dimensionality of the high-dimensional manifold to a two-dimensional subdomain; controlling local geometric distortion during the dimensionality reduction process so that the deviation between the high-dimensional manifold metric tensor and the low-dimensional subdomain Euclidean metric at each point is constrained to a second-order infinitesimal, wherein the point-by-point deviation is jointly determined by the point-by-point conformal scaling factor and the single-domain scale; calculating the global convexity radius and Lipschitz smoothness constant of the physical tensor manifold as domain initialization parameters, and initializing the domain scale and initial number of domains in combination with the preset reconstruction accuracy requirements; uniformly sampling topological base points on the surface of the high-dimensional manifold, performing eigenvalue decomposition on the metric tensor of each base point, selecting the principal curvature direction as the orthogonal basis, and so on. Quasi-conservative subdomains are generated through manifold exponential mapping. The number of subdomains is adjusted iteratively using a bisection method. After each iteration, the global reconstruction error is calculated and compared with a preset accuracy until the reconstruction error meets the preset accuracy requirement. The reconstruction error has a power-law convergence boundary, which is jointly defined by geometric constants, the number of subdomains, the original manifold dimension, the submanifold dimension, the system Lipschitz constant, and the global smoothness coefficient of the manifold. The overlap between adjacent subdomains is controlled to maintain a predetermined degree, and the continuous smoothness at the boundary of adjacent subdomains is guaranteed based on the partition unit function. The boundary of each subdomain is defined by the manifold geodesic surface. For engineering multiphysics systems below a predetermined dimension, the number of subdomains is directly determined by the ratio of the original manifold dimension to the target submanifold dimension.

[0031] In some embodiments, the extraction of topological features in step S4 and the mining of local physical mechanisms in step S5 include: extracting topological features of each quasi-conservational domain using persistent homology analysis, setting a noise filtering threshold to remove false topological features caused by data noise, retaining topological features including vibration periodic features, structural steady-state features, and coupling periodic features, and establishing a one-to-one mapping relationship between the topological features and the physical response of the equipment; mining local physical mechanisms in each quasi-conservational domain using a constrained genetic symbolic regression algorithm, using a composite fitness function as the optimization objective to guide the symbolic regression process, the composite fitness function being a weighted sum of the mean square error term of data fitting and the equation complexity penalty term, used to achieve a balance between fitting accuracy and equation simplicity, and suppress overfitting; the constrained genetic symbolic regression algorithm using a dimensionless feature set as the variable space, and using physically reliable basic operations and elementary functions to form an operator set, and evolutionarily screening local mechanism equations within the search space constrained by the inherent physical constants of the engineering.

[0032] Step S5: Perform constrained symbolic regression to mine local physical mechanisms in each conformal subdomain, construct a graph network with conformal subdomains as nodes and mechanism similarity between subdomains as edges, and complete cross-domain fusion of local mechanisms through the graph network to reconstruct the global multi-physics coupling mechanism.

[0033] In some embodiments, the cross-domain fusion of local mechanisms via graph networks in step S5 includes: using each conformal subdomain as a node of the graph network, calculating the similarity of mechanism associations between subdomains as the weight of the connecting edges between nodes, and establishing undirected connecting edges when the similarity between two subdomains reaches a preset threshold, thereby constructing a domain-specific association graph; the initial features of each node are the encoded feature vectors of the local mechanism equations of the corresponding subdomains; a two-layer graph convolutional network is used for cross-domain feature interaction, and each layer of the graph convolutional network performs neighborhood aggregation and nonlinear transformation on the node features of the previous layer based on a normalized adjacency matrix with added self-loops, wherein the normalized adjacency matrix is ​​calculated from the adjacency matrix of the domain-specific association graph and its corresponding degree matrix; after feature interaction is completed by the graph convolutional network, the local mechanisms of each subdomain are fused by attention weighting to obtain a globally unified cross-domain coupling mechanism equation, wherein the attention weights reflect the degree of contribution of each subdomain to the global mechanism, and the local mechanisms of each subdomain are projected onto the global manifold space through the manifold smooth partitioning unit function and the orthogonal projection operator from the global manifold to the subdomain and then participate in the fusion.

[0034] Step S6: Construct an adaptive total loss function that includes data fitting loss and physical conservation loss, perform physical consistency verification and correction on the global multiphysics coupling mechanism reconstructed in Step S5, quantify the uncertainty of mechanism prediction, and output an interpretable multiphysics coupling mechanism equation with confidence interval evaluation.

[0035] In some embodiments, the physical consistency verification and correction in step S6 includes: constructing a total loss function containing a data fitting loss term and a physical conservation loss term, wherein the physical conservation loss term is obtained by applying energy conservation residual constraints and momentum conservation residual constraints to the global multiphysics coupling mechanism equation, and the data fitting loss term measures the fitting deviation of the mechanism equation to standardized multiphysics data; the weight between the data fitting loss term and the physical conservation loss term in the total loss function is an adaptive dynamic weight, which is dynamically updated according to the ratio of the data fitting loss to the physical conservation loss in the current iteration step to achieve an adaptive balance between fitting accuracy and physical reality; with the goal of minimizing the total loss function, the undetermined parameters in the global multiphysics coupling mechanism equation are iteratively corrected through backpropagation until the physical conservation residual meets the preset threshold requirement, thereby outputting a mechanism equation that conforms to the physical conservation law.

[0036] In some embodiments, the uncertainty quantification in step S6 includes: based on a Bayesian variational inference framework, performing posterior distribution inference on the model parameters in the constructed global multiphysics coupling mechanism equation, and using a Gaussian likelihood function to characterize the reconstruction error distribution between the predicted values ​​and actual observations of the mechanism equation; based on Bayes' theorem, combining the prior distribution of the model parameters with the Gaussian likelihood function, and approximating the posterior distribution of the model parameters through variational inference; based on the posterior distribution of the model parameters, calculating the variance of the mechanism prediction result using an uncertainty propagation formula, which is calculated based on the gradient of the mechanism prediction result with respect to each model parameter and the posterior variance of the parameters; the variance of the mechanism prediction result simultaneously quantifies the sources of random uncertainty in the data and the sources of cognitive uncertainty in the manifold domain; based on the variance of the mechanism prediction result, calculating the confidence interval of the mechanism prediction result as the uncertainty evaluation index of the final output mechanism equation.

[0037] See Figure 4 This invention also provides a multiphysics mechanism mining system based on optimal manifold embedding domain, used to implement the mechanism mining method described in the above-mentioned method embodiments. Specifically, the system includes a data acquisition and preprocessing unit, a dimensionless feature extraction unit, a physical tensor manifold construction unit, a conformal domain division and topology analysis unit, a global mechanism reconstruction unit, and a physical arbitration and uncertainty output unit.

[0038] The data acquisition and preprocessing unit is used to acquire multi-physics time-series data of complex coupled equipment, perform anomaly removal, statistical moment feature extraction and dimensionality reduction on the data, and output standardized multi-physics data.

[0039] The dimensionless feature extraction unit is connected to the data acquisition and preprocessing unit. It is used to construct a dimensional matrix of multiple physical quantities based on the dimensional analysis theorem, apply integer constraints to the dimensional matrix to solve for the dimensionless feature group, embed the inherent physical constant constraint algorithm search space, and output dimensionless feature data under a unified reference coordinate.

[0040] The physical tensor manifold construction unit, connected to the dimensionless feature extraction unit, is used to construct a continuous and smooth physical tensor manifold based on the dimensionless feature data by endogenously solving the metric tensor, connection symbol, and generalized dissipative force field of the manifold using the system Lagrange.

[0041] The conformal domain division and topology analysis unit is connected to the physical tensor manifold construction unit. It is used to decompose the physical tensor manifold into a finite number of quasi-conformal subdomains, adaptively determine the domain division scheme with the optimization objective of minimizing the number of domains under a preset reconstruction accuracy, and extract the topological features of each conformal subdomain.

[0042] The global mechanism reconstruction unit connects the conformal subdomain and the topology analysis unit. It is used to perform constrained symbolic regression to mine local physical mechanisms in each conformal subdomain, and to construct a graph network with conformal subdomains as nodes and mechanism similarity between subdomains as edges. The graph network is used to complete the cross-domain fusion of local mechanisms and reconstruct the global multi-physics coupling mechanism.

[0043] The physical arbitration and uncertainty output unit is connected to the global mechanism reconstruction unit. It is used to construct an adaptive total loss function that includes data fitting loss and physical conservation loss to perform physical consistency verification and correction on the global multi-physics coupling mechanism, quantify the uncertainty of mechanism prediction, and output an interpretable multi-physics coupling mechanism equation with confidence interval evaluation.

[0044] Optionally, the above-mentioned units can be implemented using software modules configured on industrial servers, or using hardware such as application-specific integrated circuits (ASICs) or field-programmable gate arrays (FPGAs). Data transmission between units is completed through data buses or network interfaces.

[0045] The method and system of this invention internalize physical conservation laws into geometrically inherent properties by constructing a physical tensor manifold, replacing traditional artificial penalty constraints, eliminating physical illusions at the source, and ensuring that the mechanistic equations naturally satisfy the conservation of energy and momentum. Based on the optimal manifold embedding domain theory, a strict power-law convergence error boundary is established to provide quantitative assurance for reconstruction accuracy, overcoming the shortcomings of traditional methods that lack convergence constraints. At the same time, a high-dimensional manifold conformal domain reduction strategy is adopted to reduce the algorithm complexity from high-dimensional exponential to low-dimensional quadratic, achieving a leap in simulation efficiency from hours to milliseconds. Furthermore, relying on the one-to-one mapping between manifold topological features and physical phenomena, each set of mining equations is given a clear physical interpretation, breaking through the black box limitation. Accurate modeling can be achieved with only a small amount of extreme working condition data, and it has both strong generalization ability and engineering reliability.

[0046] The following further describes specific embodiments of the present invention, algorithm examples, and experimental verification.

[0047] A multiphysics mechanism mining method and system based on Optimal Manifold Embedded Domain (OMED) is proposed. This method abandons the artificial exogenous constraints and black-box data fitting mode. Based on the OMED theory, it constructs a physical tensor manifold (PTM) axiomatic system. Relying on a complete set of technologies such as conformal domain reconstruction, integer constraint dimensionless decomposition, manifold topology analysis, adaptive physical constraint arbitration, and uncertainty quantification, the physical laws of high-dimensional systems are internalized into the inherent properties of manifold geometry, realizing fully automatic, interpretable, convergent, and physically reliable mining of multiphysics coupling mechanisms.

[0048] Multiphysics Mechanism Mining Method Based on Optimal Manifold Embedding Domain The method of the present invention includes the following steps: Step S1, Multiphysics Data Acquisition and Standardization Preprocessing: Collect time-series physical data of the equipment under full operating conditions through a distributed sensor array or high-precision numerical simulation platform deployed on complex coupled equipment, covering multi-dimensional variables such as aerodynamics, hydrodynamics, structure, and load; use a 10-minute sliding window to extract the data mean and standard deviation statistical moments, combine with the 3σ criterion to remove abnormal noise data, complete the dimensionality reduction of high-dimensional data through SVD singular value decomposition, and retain effective feature components with a cumulative variance of not less than 95% to obtain standardized multiphysics data.

[0049] Step S2, Integer Constraint Tensor Dimensionless Feature Extraction (ICTD): Based on Buckingham's Pi dimensional analysis theorem, a multi-physical quantity dimensional matrix is ​​constructed, and dimensional homogeneous constraint equations are established. The null space of the dimensional matrix is ​​solved through integer weight constraints to obtain a physically reliable set of dimensionless Pi features, eliminating the heterogeneous differences in the dimensions of multiple physical quantities and providing a unified reference coordinate for manifold construction; the core constraint formula is as follows:

[0050] In the formula, It is a multi-dimensional matrix of physical quantities. Given an integer constraint weight vector, the resulting null space vector is the dimensionless Pi feature set.

[0051] Simultaneously, embedding inherent physical constants of the engineering process completes hard constraints on the search space:

[0052] By fixing classical physical constants, the algorithm's search space is constrained within a physically reasonable range, thus avoiding non-physical solutions and invalid fittings from the source.

[0053] The solution employs a two-layer integer solution algorithm: for low- to medium-dimensional conditions, the LLL lattice basis reduction algorithm is used to quickly find the shortest integer solution through matrix decomposition, lattice basis compression, and normalization; for high-dimensional complex conditions, the ADMM alternating direction multiplier method is used to construct an optimization objective function with integer constraints.

[0054] To address situations in engineering scenarios where strictly integer solutions may not be available, an engineering compensation strategy is configured: integer constraints are relaxed to half-integer or quarter-integer constraints to accommodate the dimensional representation of nonlinear physical quantities; dimensional matrices are expanded by supplementing with inherent physical constants such as gravitational acceleration and pi; physical variables with consistent dimensions are merged to reduce the dimensionality of the matrix solution; and the constraint threshold is relaxed to... It meets the actual usage requirements of the project.

[0055] Step S3: Construct the Physical Tensor Manifold (PTM): Based on the three core axioms of OMED theory, all physical entities, coupling relationships, and dynamic evolution behaviors of the equipment are uniformly mapped to a compact, smooth, high-dimensional Riemannian manifold, establishing a one-to-one correspondence between the system's physical behavior and the manifold's geometric properties; the three axioms are as follows: Entity axiom: Each physical entity in the equipment corresponds one-to-one with a compact submanifold of the PTM manifold, and the geometric properties of the submanifold are uniquely determined by the physical parameters of the entity, ensuring that the physical quantities are bounded and reasonable. Coupling axiom: The multiphysics coupling between entities corresponds to a smooth tensor mapping between submanifolds, which strictly follows the laws of conservation of momentum and energy; Evolutionary axiom: The dynamic evolution of the system corresponds to the forced geodesic motion of the manifold. Conservative forces anchor the manifold metric and curvature, while non-conservative dissipative forces are characterized as tangent bundle vector fields.

[0056] The dynamic evolution of the system is accurately characterized using the forced geodesic equation:

[0057] In the formula, The Christofel connection symbol represents the local curvature properties of the manifold. It is the generalized dissipative force vector of the system, representing the energy dissipation effects of wind waves, damping, etc.

[0058] This invention relies on the system dynamics Lagrangian to intrinsically solve for all geometric parameters of the Riemannian manifold, eliminating the need for manually setting additional parameters. The core calculation formula is as follows: (1) The manifold metric tensor determines the manifold curvature and spatial scale:

[0059] in, L = T - V For the system's Lagrange quantity, T As the system's kinetic energy, V This represents the system's potential energy. It is a symmetric positive definite second-order metric tensor.

[0060] (2) Levi-Civita non-bending communication symbol, realizing parallel manifold movement:

[0061] in, To measure the inverse matrix of a tensor, satisfy the orthogonality constraint. , Let Kronecker function be used.

[0062] (3) Generalized dissipative force field of manifold tangent bundle:

[0063] in, It is a generalized nonconservative dissipative force for multiphysics systems, including components such as fluid viscous drag and structural damping force.

[0064] The dimensionless feature vector output from the agent's data preprocessing stage As the manifold coordinate input, Savitzky-Golay filtering combined with central difference is used to solve the temporal characteristic velocity term to suppress noise interference from the measured data; the global metric tensor is solved point-by-point to add a small regularization term. To ensure the matrix is ​​positive definite; to perform discrete connection numerical global interpolation based on radial basis functions to guarantee the overall smoothness of the manifold; to complete the global embedding of the dissipation force vector field by combining the measured dissipation power of the system; and to complete the manifold accuracy verification through forced geodesic equations to ensure that the relative deviation of the trajectory fitting is lower than [a certain value]. The underlying supporting algorithm uses diffusion mapping to complete the initial topology construction of the manifold, and iteratively corrects the manifold metric using the OMED geodesic optimization algorithm, adapting to unlabeled multiphysics field measured data scenarios.

[0065] Step S4, Optimal Conformal Subdomains and Topological Feature Extraction: Based on the OMED finite coverage theorem, global reconstruction theorem, and power convergence theorem, the high-dimensional PTM manifold is decomposed into a finite number of two-dimensional optimal conformal subdomains, achieving dimensionality reduction and decoupling of the high-dimensional complex system; the number of subdomains satisfies the finite coverage constraint, and the reconstruction error has a strict power convergence boundary.

[0066] In the formula, are geometric constants. To preserve the number of corner subfields, The original manifold dimension, For the dimension of the submanifold, Let Lipschitz be the system constant. is the global smoothness coefficient of the manifold.

[0067] This invention employs quasi-containment manifold embedding to ensure that there is no significant distortion in the local geometry after dimensionality reduction of the high-dimensional manifold. The constraint formula is as follows:

[0068] In the formula, This is a point-by-point conformal scaling factor. For low-dimensional subfield Euclidean metric, It is a single-domain scale, and the global geometric error is controlled to be a second-order infinitesimal.

[0069] The model is constrained to minimize the number of domains while maintaining a fixed reconstruction accuracy.

[0070] The adaptive conformal subdomain algorithm steps are as follows: Calculate the intrinsic parameters of the PTM manifold, including the global convexity radius and the Lipschitz smoothness constant; initialize the subdomain scale and the initial number of subdomains based on the preset reconstruction accuracy; uniformly sample topological base points on the high-dimensional manifold surface and perform eigenvalue decomposition on the metric tensor of each base point; select the principal curvature direction as the orthogonal basis and generate independent conformal subdomains through manifold exponential mapping; iteratively adjust the number of subdomains using the bisection method until the global reconstruction error meets the preset accuracy requirements; control the overlap of adjacent subdomains to 15% to ensure the continuous smoothness of the partition unit function.

[0071] The boundaries of each subdomain are manifold geodesic surfaces. For engineering multiphysics systems of 12 dimensions and below, the number of domains can be quickly determined directly using the following formula: .

[0072] The persistent homology analysis method is used to extract the topological features of each conformal subdomain, and a noise filtering threshold is set to remove false topological features, thus establishing an accurate mapping relationship between manifold topological features and physical phenomena.

[0073] Step S5, Local Mechanism Mining and Global Cross-Domain Coupling Reconstruction: Within each conformal subdomain, constrained genetic symbolic regression is performed using the MSE-MDL composite fitness function to simultaneously mine local physical mechanisms in each region, balancing fitting accuracy and equation simplicity while suppressing overfitting. The composite fitness function is as follows:

[0074] In the formula, The mean square error of the data fit. This is a penalty term for the minimum description length complexity of the equation. For a fixed penalty coefficient, For real physical quantities, To predict physical quantities for the model.

[0075] The similarity of mechanistic associations in different conformal subdomains is calculated, and a graph convolutional network (GCN) is used to fuse local mechanisms and reconstruct the global multiphysics coupling mechanism. The formula for calculating subdomain similarity is as follows:

[0076] In the formula, For the subdomain topological feature set, For PTM manifold geometric distance, This is the scaling factor.

[0077] Constructing a domain-specific association graph: Each conformal domain corresponds to an independent graph node. When the similarity between two domains is greater than or equal to 0.3, an undirected connection edge is established. The local mechanism equations of each subdomain are uniformly encoded as 128-dimensional topological feature vectors as node features.

[0078] A two-layer graph convolutional network is used to complete cross-domain feature interaction. The single-layer feature update formula is:

[0079] in, To add a self-loop adjacency matrix, For the graph degree matrix, For trainable weights of the network, This is the ReLU activation function.

[0080] The global coupling mechanism equation is obtained by attention-weighted fusion of local mechanisms in each subdomain:

[0081] in, For cross-domain attention weights, For smooth partitioning units of the manifold, It is the global manifold to subdomain orthogonal projection operator.

[0082] This allows for the reconstruction of the global multiphysics coupling mechanism.

[0083] Step S6, Physical Consistency Arbitration and Uncertainty Quantification Verification: Construct an adaptive total loss function that fuses data fitting loss and physical conservation loss to achieve a dynamic balance between fitting accuracy and physical reality. The mechanism equation is corrected through energy and momentum conservation residual constraints to eliminate physical illusions. The total loss function and adaptive weight formulas are as follows:

[0084]

[0085] In the formula, For data fitting loss, For physical conservation residual loss, For adaptive dynamic weights, As the initial weights, It is a minimal smoothing coefficient.

[0086] This module implements uncertainty quantification propagation based on Bayesian variational inference, and its mathematical framework is as follows: The Bayesian posterior inference formula is:

[0087] in, For the set of parameters of the mechanism model,D For the observation dataset, p (Θ) is the prior distribution. p ( D |Θ) is the likelihood function. p ( D () represents the marginal likelihood.

[0088] The reconstruction error is represented by the Gaussian likelihood function:

[0089] In the formula, These are the model's predicted values. These are measured values. This represents the variance of the data noise.

[0090] The formula for global uncertainty propagation is:

[0091] in, For the first k The variances of the parameters are obtained through the posterior covariance matrix inferred by Bayesian inference.

[0092] The 95% confidence interval for the mechanism prediction results is:

[0093] This module synchronizes the random uncertainty of data with the cognitive uncertainty of manifold domains, eliminating the need for large-scale Monte Carlo sampling, resulting in lower computational overhead and making it suitable for real-time industrial mechanism mining scenarios.

[0094] As shown above, by quantifying data noise and manifold projection error through the Uncertainty Manifold Propagation (UMP) module, the 95% confidence interval of the mechanism model is output, the validity of the mechanism is determined, and finally an interpretable, convergent, and physically reliable global multiphysics coupling mechanism equation is output.

[0095] Multiphysics Mechanism Mining System Based on Optimal Manifold Embedding Domain This system is used to implement the above-mentioned mechanism mining method, and includes a hardware acquisition unit and a software algorithm unit connected in sequence, specifically comprising: 1. Data Acquisition and Preprocessing Unit: Equipped with a distributed sensor array, data acquisition terminal and industrial server, it is used to collect multi-physics time-series data of complex equipment and complete anomaly removal, sliding window statistics, SVD dimensionality reduction and data standardization processing. 2. ICTD Dimensionless Feature Extraction Unit: Connects to the data acquisition and preprocessing unit, used to construct the dimensional matrix, solve the integer-constrained dimensionless Pi feature group, and complete the unified adaptation of multi-dimensional data and physical search space constraints; 3. PTM Manifold Construction Unit: Connects to the ICTD dimensionless feature extraction unit, and constructs a high-dimensional compact and smooth physical tensor manifold that fits the physical characteristics of the equipment based on the three axioms of OMED and the forced geodesic equation. 4. Conformal Partitioning and Topology Analysis Unit: Connecting the PTM manifold building unit, the optimal conformal partitioning of the high-dimensional manifold is completed based on the OMED convergence theorem. Effective topological features are extracted through persistent homology analysis to filter out noise interference. 5. Global Mechanism Reconstruction Unit: Connects conformal domain division and topology analysis unit, mines local mechanisms through constrained symbolic regression, and completes global cross-domain coupling mechanism fusion and reconstruction by combining subdomain similarity and graph convolutional network; 6. Physical Arbitration and Uncertainty Output Unit: Connects to the global mechanism reconstruction unit, completes physical consistency verification through an adaptive weight loss function, quantifies mechanism prediction uncertainty, and selects and outputs the optimal physical mechanism model.

[0096] Experimental Example This example uses the NREL 5MW OC4-DeepCwind floating offshore wind turbine as a typical application object. It adopts the OpenFAST simulation dataset of the 50-year full life cycle of this model, with a sampling frequency of 1Hz and a wind field that meets the IEC 61400-1 IB level deep-sea working condition standard to fully implement and verify the technical solution of this invention.

[0097] Implement data preparation The original dataset contains 184 wind turbine aerodynamic, hydrodynamic, structural, and mooring monitoring variables. Redundant variables were removed through correlation analysis, and 12 core coupled variables were selected and retained. The training and test sets were randomly divided into 8:2 stratified groups. The mean and standard deviation of the data were calculated using a 10-minute sliding window. Outliers were removed using the 3σ criterion. SVD dimensionality reduction was used to retain more than 95% of the effective variance components, and the data standardization preprocessing was completed.

[0098] Dimensionless Feature Extraction and Search Space Constraints Based on Buckingham's Pi theorem, a multi-physical dimension matrix is ​​constructed, and the integer-constrained null space vector is solved to obtain the dimensionless Pi characteristic set suitable for the wind-wave-structure coupling system of a floating wind turbine; fixed engineering inherent physical constants are then obtained. , This constrains the search space of the algorithm and avoids fitting solutions that have no physical meaning.

[0099] PTM manifold construction and dynamic evolution characterization The five physical entities of the floating wind turbine—rotor, tower, floating body, air domain, and sea area—are mapped as independent compact submanifolds to construct a global PTM high-dimensional Riemannian manifold. The dynamic evolution behavior of the wind turbine structure under wind and wave loads is characterized by the forced geodesic equation, anchoring the manifold geometric properties of the system's conservative forces and dissipative forces, and ensuring that the system evolution conforms to the laws of physical conservation throughout the entire process.

[0100] Optimal conformal domain division and topological feature extraction Based on the OMED finite cover theorem, a nearly 100-dimensional high-dimensional PTM manifold is decomposed into several two-dimensional optimal conformal subdomains, and the precision of the subdomains is set. It meets industrial-grade accuracy requirements; it uses persistent coherence analysis to extract topological features such as vibration period, structural steady state, and wind-wave coupling period, sets thresholds to filter out noise and false features, and establishes the correspondence between topological features and wind turbine physical response.

[0101] Local mechanism mining and global coupling reconstruction Constrained genetic symbol regression was carried out in each conformal subdomain, with a population size of 500, an evolutionary generation of 100, a crossover probability of 0.7, and a mutation probability of 0.1. Simple and high-precision local mechanism equations were selected by optimizing the MSE-MDL composite function. The mechanism similarity of each subdomain was calculated, and the wind-wave-structure local mechanism fusion was completed through a 2-layer GCN network to reconstruct the global multiphysics coupling equation set.

[0102] Physical arbitration and result output An adaptive weighted total loss function is enabled, and the mechanism equation is corrected by energy conservation residual constraints, with the energy residual threshold set to 0.02. The uncertainty of prediction is quantified by the UMP module, and a 95% confidence interval is output. The optimal mechanism model is selected by Pareto multi-objective criteria and physical authenticity discrimination rules.

[0103] Effect verification Eight sets of multi-field coupling equations for floating wind turbines, fully consistent with physical properties, were independently obtained, including four sets of aerodynamic coupling equations and four sets of structural coupling equations; these equations can accurately reproduce the principles of classical cantilever beam mechanics and provide a test set for predicting the bending moment of the tower base. It is highly consistent with classical theory; it accurately captures the nonlinear law of wind turbine thrust and the cross-domain modulation relationship of wind and waves, and the quantification results of variable contribution are completely consistent with engineering reality; the overall inference speed is two orders of magnitude faster than traditional OpenFAST simulation, with no physical illusions or overfitting, and excellent convergence stability and engineering accuracy.

[0104] Compared with the prior art, the present invention has the following outstanding technical advantages and beneficial effects: 1. Eliminating physical illusions at the source, with extremely high physical realism. This invention abandons the traditional PINN artificial exogenous penalty constraint mode, and embeds the physical laws of energy and momentum conservation through the endogenous geometric topological constraints of PTM manifold. All the extracted mechanism equations naturally satisfy the physical conservation laws, with no energy violations and no spurious coupling. The aerodynamic and structural field reconstruction errors are only 1.0% and 1.2%, respectively, and the physical credibility is far higher than that of existing AI algorithms.

[0105] 2. It possesses strict mathematical convergence guarantees and high engineering reliability. Based on the innovative OMED optimal manifold embedding domain division concept, this invention establishes a quantifiable power-law convergence error boundary, solving the industry shortcomings of traditional manifold dimensionality reduction and data fitting methods that lack error constraints, and fully meeting the reliability assessment requirements of marine engineering and high-end equipment.

[0106] 3. Solve the problem of high-dimensional explosion, significantly improving computational efficiency. By using conformal partitioning of high-dimensional manifolds for dimensionality reduction and divide-and-conquer parallel computation, the complexity of traditional high-dimensional algorithms is reduced from... Down to This enables a leap from traditional hour-level simulation to millisecond-level inference, meeting the timeliness requirements of real-time digital twin and batch wind field assessment scenarios.

[0107] 4. Excellent interpretability of mechanisms, breaking through the limitations of black boxes. By mapping manifold topological features to physical phenomena one-to-one, high-dimensional coupling mechanisms are visualized and analyzed. Each set of mining equations has a clear physical interpretation, solving the pain point of traditional AI models being unable to explain mechanisms.

[0108] 5. Strong generalization ability, adaptable to extreme and complex working conditions. Relying on physical prior constraints and topological feature extraction, high-precision modeling can be completed with only 10% of extreme working condition data. It can accurately identify system information boundaries, effectively suppress data noise and overfitting problems, and is suitable for special working conditions such as complex ocean extreme wind and waves and equipment extreme loads.

[0109] This invention, based on an integrated hardware and software architecture, can be directly deployed on offshore wind farm monitoring terminals, industrial servers, and digital twin platforms. It can automatically perform multi-physics mechanism mining, dynamic response prediction, structural state assessment, and extreme condition early warning for complex equipment. Compared to traditional technologies, this invention balances ultra-high computational efficiency, rigorous physical realism, strong interpretability, and engineering reliability. It can be widely applied in offshore wind power, aerospace, new energy equipment, high-end manufacturing, and other fields, possessing significant application value and promising prospects for industrialization, demonstrating remarkable industrial practicality.

[0110] This invention also provides a storage medium for storing a computer program, which, when executed, performs at least the methods described above.

[0111] This invention also provides a control device, including a processor and a storage medium for storing a computer program; wherein the processor executes the computer program by performing at least the method described above.

[0112] This invention also provides a processor that executes a computer program, at least performing the methods described above.

[0113] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), magnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disc or CD-ROM; magnetic surface memory can be disk storage or magnetic tape storage. The storage media described in the embodiments of this invention are intended to include, but are not limited to, these and any other suitable types of memory.

[0114] In the several embodiments provided by this invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0115] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0116] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0117] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0118] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0119] The methods disclosed in the several method embodiments provided by this invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0120] The features disclosed in the several product embodiments provided by this invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0121] The features disclosed in the several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method or device embodiments.

[0122] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or application, should be considered within the scope of protection of the present invention.

Claims

1. A method for mining multiphysics mechanisms based on optimal manifold embedded domains, characterized in that, Includes the following steps: S1. Collect multi-physics time-series data of complex coupled equipment, and perform anomaly removal, statistical moment feature extraction and dimensionality reduction on the data to obtain standardized multi-physics data. S2. Construct a dimensional matrix of multiple physical quantities based on the dimensional analysis theorem, apply integer constraints to the dimensional matrix to solve the dimensionless feature set, and embed inherent physical constants of the engineering to constrain the algorithm search space to obtain dimensionless feature data under a unified reference coordinate. S3. Based on the dimensionless feature data, the equipment physical entity, coupling relationship and dynamic evolution behavior are mapped to a high-dimensional Riemannian manifold. The metric tensor, connection symbol and generalized dissipative force field of the manifold are solved endogenously by the system Lagrangian to construct the physical tensor manifold. The construction process of the physical tensor manifold in step S3 includes: Using the dimensionless eigenvectors output in step S2 as the coordinate input of the manifold, the symmetric positive definite metric tensor of the manifold is defined and solved based on the second-order partial derivative of the system dynamics Lagrangian with respect to the generalized velocity. The metric tensor determines the local curvature and spatial scale of the manifold. Based on the inverse matrix of the metric tensor and the first-order partial derivative of the metric tensor with respect to generalized coordinates, the Levi-Civita connection symbol is solved. The connection symbol is used to realize the parallel translation of tensors on the manifold and the calculation of geodesics. By applying the inverse matrix of the metric tensor to the generalized nonconservative dissipative force of the multiphysics system, a generalized dissipative force field on the tangent bundle of the manifold is obtained. The generalized nonconservative dissipative force includes fluid viscous drag and structural damping force. The initial topology of the manifold is constructed using the diffusion mapping algorithm. The dimensionless eigenvectors are subjected to temporal filtering and numerical differentiation to solve the generalized velocity term. The global metric tensor is solved point by point and regularization is applied to ensure the positive definiteness of the matrix. The global smooth interpolation of the discrete connection symbols is completed based on the radial basis function. The global embedding of the dissipation force vector field is completed by combining the measured dissipation power of the system, resulting in a continuous and smooth physical tensor manifold. S4. The physical tensor manifold is decomposed into a finite number of quasi-conformal subdomains. A domain division scheme is adaptively determined with the optimization objective of minimizing the number of subdomains under a preset reconstruction accuracy. The topological features of each conformal subdomain are extracted, and a mapping relationship between the topological features and physical phenomena is established. The decomposition process of the quasi-conformal subdomains in step S4 includes: Quasi-conformal submanifold embedding is used to reduce the dimension of a high-dimensional manifold to a two-dimensional subdomain. During the dimension reduction process, local geometric distortion is controlled so that the deviation between the high-dimensional manifold metric tensor and the low-dimensional subdomain Euclidean metric at each point is constrained to a second-order infinitesimal. The point-by-point deviation is determined by the point-by-point conformal scaling factor and the single-domain scale. The global convexity radius and Lipschitz smoothness constant of the physical tensor manifold are calculated as domain initialization parameters, and the domain scale and initial number of domains are initialized in combination with the preset reconstruction accuracy requirements. Uniformly sample topological base points on the surface of a high-dimensional manifold, perform eigenvalue decomposition on the metric tensor of each base point, select the principal curvature direction as the orthogonal basis, and generate each quasi-conservative subdomain through manifold exponential mapping; The number of domains is adjusted iteratively using a bisection method. After each iteration, the global reconstruction error is calculated and compared with a preset accuracy until the reconstruction error meets the preset accuracy requirement. The reconstruction error has a power-law convergence boundary, which is jointly defined by geometric constants, the number of domains, the original manifold dimension, the submanifold dimension, the system Lipschitz constant, and the global smoothness coefficient of the manifold. Maintain a predetermined overlap between adjacent subdomains, and ensure continuous smoothness at the boundaries of adjacent subdomains based on the partitioning unit function; The boundaries of each subdomain are defined by the manifold geodesic surface. For engineering multiphysics systems below a predetermined dimension, the number of subdomains is directly determined by the ratio of the original manifold dimension to the target submanifold dimension. S5. Constrained symbolic regression is performed in each conformal subdomain to mine local physical mechanisms. A graph network is constructed with conformal subdomains as nodes and the similarity of mechanisms between subdomains as edges. The cross-domain fusion of local mechanisms is completed through the graph network to reconstruct the global multi-physics coupling mechanism. S6. Construct an adaptive total loss function that includes data fitting loss and physical conservation loss, perform physical consistency verification and correction on the reconstructed global multiphysics coupling mechanism, quantify the uncertainty of mechanism prediction, and output an interpretable multiphysics coupling mechanism equation with confidence interval evaluation.

2. The multiphysics mechanism mining method based on optimal manifold embedding domain as described in claim 1, characterized in that, The process of solving the dimensionless characteristic set in step S2 includes: Based on Buckingham’s Pi dimensional analysis theorem, a dimensional matrix is ​​constructed according to the basic dimensions of each physical quantity in a multiphysics system. A dimensional homogeneous constraint equation is established, and the null space vector of the equation under integer weight constraints is solved to obtain the dimensionless Pi characteristic set. For low- to medium-dimensional system conditions, the lattice basis reduction algorithm is used to solve the integer-constrained null space; for high-dimensional complex system conditions, the alternating direction multiplier method is used to construct an optimization objective function with integer constraints and solve iteratively. When the integer constraint null space has no strictly integer solution, at least one of the following engineering compensation strategies is adopted for processing: relaxing the integer constraint into a half-integer or quarter-integer constraint, embedding inherent physical constants to expand the dimensional matrix, merging physical variables with consistent dimensions to reduce the solution dimension, and relaxing the error tolerance threshold of the homogeneous dimensional constraint. The inherent physical constants of the project include half-integer constants and the constant of pi. By fixing these constants in the dimensional matrix, the search space of the algorithm is constrained within a physically reasonable range.

3. The multiphysics mechanism mining method based on optimal manifold embedding domain as described in claim 1, characterized in that, After the physical tensor manifold is constructed, the following step is also included: manifold dynamic evolution characterization step: The forced geodesic equation characterizes the dynamic evolution behavior of the system under the combined action of conservative and non-conservative forces. In the forced geodesic equation, the conservative forces are anchored to the metric tensor of the manifold and the geometric properties of the manifold represented by the connection symbol, while the non-conservative dissipative forces are characterized by the generalized dissipative force field. The system evolution trajectory is obtained by solving the forced geodesic equation. The effectiveness of the constructed manifold is verified through a manifold accuracy verification step, which includes comparing the actual evolution trajectory of the system with the evolution trajectory obtained by solving the forced geodesic equation to ensure that the relative deviation of the trajectory fitting meets the preset threshold requirement.

4. The multiphysics mechanism mining method based on optimal manifold embedding domain as described in claim 1, characterized in that, The extraction of topological features in step S4 and the mining of local physical mechanisms in step S5 include: The topological features of each quasi-conservation subdomain are extracted using the persistent cohomology analysis method. A noise filtering threshold is set to remove false topological features caused by data noise. The retained topological features include vibration period features, structural steady-state features, and coupling period features. A one-to-one mapping relationship between the topological features and the physical response of the equipment is established. Within each quasi-conservation subdomain, a constrained genetic symbolic regression algorithm is used to mine local physical mechanisms. A composite fitness function is used as the optimization objective to guide the symbolic regression process. The composite fitness function is composed of a weighted sum of the mean square error term of the data fitting and the equation complexity penalty term, which is used to achieve a balance between fitting accuracy and equation simplicity and suppress overfitting. The constrained genetic symbolic regression algorithm uses a dimensionless feature set as the variable space and a set of operators composed of physically reliable basic operations and elementary functions to evolve and screen local mechanism equations within the search space constrained by the inherent physical constants of the engineering.

5. The multiphysics mechanism mining method based on optimal manifold embedding domain as described in claim 1, characterized in that, Step S5, which describes cross-domain fusion of local mechanisms via graph networks, includes: Using each conformal subdomain as a node in the graph network, the similarity of the mechanism association between each subdomain is calculated as the weight of the connection edge between nodes. When the similarity between two subdomains reaches a preset threshold, an undirected connection edge is established, thereby constructing a domain-specific association graph. The initial features of each node are the encoded feature vectors of the local mechanism equations of the corresponding subdomain; A two-layer graph convolutional network is used for cross-domain feature interaction. Each layer of the graph convolutional network performs neighborhood aggregation and nonlinear transformation on the node features of the previous layer based on a normalized adjacency matrix with added self-loops. The normalized adjacency matrix is ​​calculated from the adjacency matrix of the domain association graph and its corresponding degree matrix. After feature interaction is completed by graph convolutional network, the local mechanisms of each subdomain are fused by attention weighting to obtain a globally unified cross-domain coupling mechanism equation. The attention weight reflects the degree of contribution of each subdomain to the global mechanism. The local mechanisms of each subdomain are projected to the global manifold space by the smooth partitioning unit function of the manifold and the orthogonal projection operator from the global manifold to the subdomain and then participate in the fusion.

6. The multiphysics mechanism mining method based on optimal manifold embedding domain as described in claim 1, characterized in that, The physical consistency verification and correction in step S6 includes: A total loss function is constructed that includes a data fitting loss term and a physical conservation loss term. The physical conservation loss term is obtained by applying energy conservation residual constraints and momentum conservation residual constraints to the global multiphysics coupling mechanism equation. The data fitting loss term measures the fitting deviation of the mechanism equation to the standardized multiphysics data. The weight between the data fitting loss term and the physical conservation loss term in the total loss function is an adaptive dynamic weight. The adaptive dynamic weight is dynamically updated according to the ratio of the data fitting loss to the physical conservation loss in the current iteration step, so as to achieve an adaptive balance between fitting accuracy and physical reality. With the goal of minimizing the total loss function, the undetermined parameters in the global multiphysics coupling mechanism equation are iteratively corrected through backpropagation until the physical conservation residual meets the preset threshold requirement, thereby outputting the mechanism equation.

7. The multiphysics mechanism mining method based on optimal manifold embedding domain as described in claim 1, characterized in that, The uncertainty quantification mentioned in step S6 includes: Based on the Bayesian variational inference framework, the posterior distribution of the model parameters in the constructed global multiphysics coupling mechanism equation is inferred, and the Gaussian likelihood function is used to characterize the reconstruction error distribution between the predicted values ​​of the mechanism equation and the actual observed values. Based on Bayes' theorem, the prior distribution of the model parameters is combined with the Gaussian likelihood function, and the posterior distribution of the model parameters is approximately solved by variational inference. Based on the posterior distribution of the model parameters, the variance of the mechanism prediction results is calculated using the uncertainty propagation formula, which is obtained by calculating the gradient of each model parameter and the posterior variance of the parameter based on the mechanism prediction results. The variance of the predicted results from the mechanism simultaneously quantifies the sources of random uncertainty in the data and the sources of cognitive uncertainty in the manifold domain; Based on the variance of the predicted mechanism, the confidence interval of the predicted mechanism is used as the uncertainty assessment index for the final output mechanism equation.

8. A multiphysics mechanism mining system based on optimal manifold embedded domain, used to implement the multiphysics mechanism mining method based on optimal manifold embedded domain as described in any one of claims 1 to 7, characterized in that, include: The data acquisition and preprocessing unit is used to acquire multi-physics time-series data of complex coupled equipment, perform anomaly removal, statistical moment feature extraction and dimensionality reduction on the data, and output standardized multi-physics data. The dimensionless feature extraction unit, connected to the data acquisition and preprocessing unit, is used to construct a dimensional matrix of multiple physical quantities based on the dimensional analysis theorem, apply integer constraints to the dimensional matrix to solve for the dimensionless feature group, embed the inherent physical constant constraint algorithm search space, and output dimensionless feature data under a unified reference coordinate. The physical tensor manifold construction unit, connected to the dimensionless feature extraction unit, is used to construct a continuous and smooth physical tensor manifold based on the dimensionless feature data by endogenously solving the metric tensor, connection symbol, and generalized dissipative force field of the manifold through the system Lagrange. The conformal domain division and topology analysis unit is connected to the physical tensor manifold construction unit. It is used to decompose the physical tensor manifold into a finite number of quasi-conformal subdomains, adaptively determine the domain division scheme with the optimization objective of minimizing the number of domains under a preset reconstruction accuracy, and extract the topological features of each conformal subdomain. The global mechanism reconstruction unit connects the conformal subdomain and the topology analysis unit. It is used to perform constrained symbolic regression to mine local physical mechanisms in each conformal subdomain, and to construct a graph network with conformal subdomains as nodes and mechanism similarity between subdomains as edges. The graph network is used to complete the cross-domain fusion of local mechanisms and reconstruct the global multi-physics coupling mechanism. The physical arbitration and uncertainty output unit, connected to the global mechanism reconstruction unit, is used to construct an adaptive total loss function that includes data fitting loss and physical conservation loss to perform physical consistency verification and correction on the global multiphysics coupling mechanism, quantify the uncertainty of mechanism prediction, and output an interpretable multiphysics coupling mechanism equation with confidence interval evaluation.

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