Data model construction and simulation method for mathematical data operation processing

Abstract

The invention relates to a data model construction and simulation method for mathematical data operation processing. The method comprises the steps that self-supervised learning is conducted on multi-modal data of a physical system corresponding to a mathematical data operation processing scene, and a unified embedding space is constructed; based on the unified embedding space, constructing a quantum-neural differential equation hybrid model; based on a digital twin interface, synchronizing a physical system and a simulation environment according to the quantum-neural differential equation hybrid model to obtain a simulation result; and based on a simulation result, dynamically adjusting model parameters of the quantum-neural differential equation hybrid model through reinforcement learning to obtain a corrected quantum-neural differential equation hybrid model. According to the method, precise modeling and efficient simulation of the physical system in a complex mathematical data operation processing scene and dynamic optimization of model parameters are achieved, the simulation precision and adaptability to the physical system are effectively improved, and the problems of multi-modal data fusion processing, complex physical system dynamic evolution simulation and the like can be better solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of data processing, and particularly relates to a method for constructing and simulating a data model for mathematical data operation processing. Background Art

[0002] With the rapid increase in the demand for big data and complex system modeling, traditional mathematical modeling methods face significant challenges in dynamics, multi-source heterogeneous data processing, and real-time simulation. In the prior art, the construction of data models mostly relies on single mathematical equations or machine learning models, making it difficult to balance the interpretability of physical laws and the adaptability to high-dimensional data. For example, traditional parameter optimization algorithms have efficiency bottlenecks in global search and are sensitive to noise; in the data preprocessing stage, manual feature engineering is often used, and the ability to fuse and represent multi-modal data is insufficient, resulting in loss of model input information.

[0003] In recent years, the development of quantum computing and neural differential equations has provided new ideas for dynamic modeling, but the existing research has not effectively integrated their advantages: the quantum annealing algorithm is mostly used for independent optimization problems and is not combined with continuous system modeling; although neural differential equations can learn complex dynamics, they lack an efficient parameter optimization mechanism.

[0004] Therefore, there is an urgent need for an innovative method that integrates interdisciplinary technologies, supports multi-source data processing, and has both efficient optimization and real-time simulation to break through the accuracy and applicability bottlenecks of traditional modeling. Summary of the Invention

[0005] Based on this, it is necessary to provide a method for constructing and simulating a data model for mathematical data operation processing to address the above technical problems.

[0006] In a first aspect, the present application provides a method for constructing and simulating a data model for mathematical data operation processing, including:

[0007] Constructing a unified embedding space by performing self-supervised learning on multi-modal data of a physical system corresponding to a mathematical data operation processing scenario; wherein, the multi-modal data includes time-series data, spatial data, and unstructured data, and the unified embedding space is an embedding space that simultaneously represents multiple modal data, and in the same embedding space, data of different modalities have similar feature distributions;

[0008] Based on the unified embedding space, constructing a quantum-neural differential equation hybrid model; wherein, the quantum-neural differential equation hybrid model includes: a quantum optimization layer and a neural differential equation module; the neural differential equation module is used to learn the evolution law of the physical system through a neural network to generate a dynamic model of the system state of the physical system; the quantum optimization layer is used to globally optimize the model parameters of the dynamic model;

[0009] Based on the digital twin interface, synchronize the physical system and the simulation environment according to the quantum-neural differential equation hybrid model to obtain simulation results;

[0010] Based on the simulation results, dynamically adjust the model parameters of the quantum-neural differential equation hybrid model through reinforcement learning to obtain a modified quantum-neural differential equation hybrid model.

[0011] In a second aspect, the present application also provides a computer device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements a data model construction and simulation method for mathematical data operation processing as described in the first aspect.

[0012] In a third aspect, the present application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements a data model construction and simulation method for mathematical data operation processing as described in the first aspect.

[0013] The above-mentioned data model construction and simulation method for mathematical data operation processing constructs a unified embedding space through self-supervised learning to integrate multi-modal data, uses a quantum-neural differential equation hybrid model to learn the evolution law of the physical system and optimize the model parameters, then synchronizes the physical system and the simulation environment through the digital twin interface, and finally dynamically adjusts the model parameters based on reinforcement learning, so as to realize the accurate modeling, efficient simulation of the physical system in complex mathematical data operation processing scenarios, and the dynamic optimization of model parameters, effectively improving the simulation accuracy and adaptability of the physical system, and being able to better handle problems such as multi-modal data fusion processing and dynamic evolution simulation of complex physical systems, providing an innovative and efficient solution for data processing and system simulation in related fields. Description of the Drawings

[0014] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the following will briefly introduce the drawings required for use in the description of the embodiments or related technologies. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0015] Figure 1 It is a schematic flowchart of a data model construction and simulation method for mathematical data operation processing provided by the present invention;

[0016] Figure 2 It is a schematic flowchart of constructing a quantum-neural differential equation hybrid model in an optional embodiment of the present invention. Detailed Embodiments

[0017] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0018] refer to Figure 1 , which shows a flow chart of a data model construction and simulation method for mathematical data operation processing provided by the present application, the method comprising the following steps:

[0019] S1. Construct a unified embedding space by performing self-supervised learning on the multimodal data of the physical system corresponding to the mathematical data operation processing scenario; wherein the multimodal data includes time series data, spatial data and unstructured data, and the unified embedding space is an embedding space that simultaneously represents multiple modal data. In the same embedding space, data of different modalities have similar feature distributions.

[0020] Specifically, "the physical system corresponding to the mathematical data operation and processing scenario" can be understood as: in a specific mathematical data operation and processing scenario, the system composed of the physical entities in the real world involved and the physical laws they follow. For example, in the mathematical data operation and processing scenario of the power system, the corresponding physical system is the power network composed of physical equipment such as generators, transmission lines, transformers, and user electrical appliances, as well as the physical laws of electromagnetism, mechanics, etc. followed by these devices; in the mathematical data operation and processing scenario of the motion control of the robot arm, the corresponding physical system is the robot arm itself, including its various joints, connecting rods and other components, as well as the physical laws such as Newton's laws of motion followed by these components.

[0021] In mathematical data processing scenarios, physical systems often generate multiple types of data, including time series data (such as a sequence of sensor measurements that changes over time), spatial data (such as location information data in a geographic information system), and unstructured data (such as text descriptions, images, etc.). These multimodal data contain rich information, but their formats and feature representations are different. Through self-supervised learning, it is possible to mine the internal structure and associations of these data without explicit external annotations, and construct a unified embedding space so that data of different modalities can be presented in the space with similar feature distributions, which is convenient for subsequent comprehensive analysis and processing.

[0022] The implementation process of this step can be as follows: First, collect multimodal data of the physical system corresponding to the mathematical data operation and processing scenario. For time series data, preprocessing can be performed, such as time alignment, noise removal, etc.; for spatial data, coordinate transformation, spatial interpolation, etc. can be carried out; for unstructured data, specific feature extraction methods can be adopted, such as word embedding of text, convolutional neural network feature extraction of images, etc. Then, using self-supervised learning algorithms, let the model learn the consistency and correlation between different modal data by itself, so as to construct a unified embedding space. Among them, in this unified embedding space, if data points of different modalities represent similar meanings or states in the physical system, their distances will be relatively close, and the feature distributions show similarity.

[0023] S2. Based on the unified embedding space, construct a quantum-neural differential equation hybrid model; among them, the quantum-neural differential equation hybrid model includes: a quantum optimization layer and a neural differential equation module; the neural differential equation module is used to learn the evolution law of the physical system through a neural network and generate a dynamic model of the system state of the physical system; the quantum optimization layer is used to globally optimize the model parameters of the dynamic model.

[0024] Specifically, the quantum-neural differential equation hybrid model is an innovative model architecture that combines the advantages of quantum computing and the powerful modeling ability of neural differential equations. Among them, the neural differential equation module is mainly composed of a neural network, which can learn the evolution law of the physical system and generate a dynamic model of the system state of the physical system by modeling the change of the system state over time. For example, when describing the motion of a mechanical system, the neural differential equation can learn the dynamic change relationship of state variables such as its acceleration, velocity, and displacement over time. The quantum optimization layer, on the other hand, uses the characteristics of quantum computing, such as quantum superposition and quantum entanglement, to globally optimize the model parameters of the dynamic model. It can quickly search for a better parameter combination in the complex parameter space and has higher efficiency and better global search ability compared with traditional optimization methods, thus improving the performance and accuracy of the entire model.

[0025] When constructing this hybrid model, first, the structure of the neural differential equation can be designed according to the characteristics of the physical system, and parameters such as the number of layers, the number of nodes, and the activation function of the neural network can be determined. Then, build the quantum optimization layer and select a suitable quantum algorithm, such as quantum genetic algorithm, quantum particle swarm algorithm, etc., to optimize the model parameters. During the training process, input the actual data of the physical system into the model. The neural differential equation module continuously learns and adjusts its own parameters to fit the dynamic behavior of the system, while the quantum optimization layer globally optimizes the parameters of the entire model according to the set optimization objective function (such as minimizing the prediction error, etc.), so that the model can more accurately describe the state evolution of the physical system.

[0026] S3. Based on the digital twin interface, synchronize the physical system and the simulation environment according to the quantum-neural differential equation hybrid model to obtain the simulation results.

[0027] Specifically, the digital twin interface acts as a bridge between the physical system and the simulation environment in this step. It can obtain the actual operation data of the physical system in real time and transmit it to the simulation environment. At the same time, it can also transfer the feedback information in the simulation environment back to the physical system.

[0028] The specific process of this step can be to first input the real-time data of the physical system into the quantum-neural differential equation hybrid model through the digital twin interface. Based on these data and the physical system evolution laws learned by itself, the model performs simulation calculations to obtain the corresponding simulation results. The simulation results not only include the current state prediction of the system but also can cover information such as the state change trend in a future period of time.

[0029] Among them, to ensure the synchronization of the physical system and the simulation environment, it is necessary to design the digital twin interface efficiently and stably to ensure the real-time and accuracy of data transmission. During the simulation process, appropriate simulation step sizes and precisions should be set according to the specific characteristics of the physical system, so that the simulation results can truly reflect the operation of the physical system. At the same time, the simulation results can be visually displayed to facilitate users to intuitively understand the state and change trend of the physical system, providing a basis for subsequent decision-making and optimization.

[0030] S4. Based on the simulation results, dynamically adjust the model parameters of the quantum-neural differential equation hybrid model through reinforcement learning to obtain the modified quantum-neural differential equation hybrid model.

[0031] Specifically, reinforcement learning is a machine learning method. Through the interaction between the agent and the environment, it learns the optimal behavior strategy according to the reward signal feedback from the environment. In this step, the quantum-neural differential equation hybrid model is regarded as the agent, and the gap between the model performance reflected by the simulation results and the actual expected target is used as the basis for the reward signal. The goal is to enable the model to automatically learn how to dynamically adjust its own model parameters through the reinforcement learning algorithm to continuously improve the accuracy and reliability of the simulation results, so that the model can better adapt to the actual operation and possible changes of the physical system.

[0032] During the reinforcement learning process, the model performs simulations based on the current parameter settings. After obtaining the simulation results, it calculates the reward value by comparing with the state of the actual physical system or the expected goal. Then, according to the reinforcement learning algorithm (such as Q-learning, Deep Deterministic Policy Gradient algorithm, etc.), the model updates its own parameters in the hope of obtaining a higher reward in the next simulation. This process is continuously iterated, and the model parameters are gradually optimized and corrected. Eventually, a modified quantum-neural differential equation hybrid model that can more accurately model and simulate the physical system is obtained, thereby improving the effectiveness and practicality of the data model construction and simulation method for the entire mathematical data operation and processing.

[0033] The above-mentioned data model construction and simulation method for mathematical data operation and processing constructs a unified embedding space through self-supervised learning to integrate multi-modal data, uses a quantum-neural differential equation hybrid model to learn the evolution law of the physical system and optimize the model parameters, then synchronizes the physical system and the simulation environment through a digital twin interface, and finally dynamically adjusts the model parameters based on reinforcement learning, so as to achieve accurate modeling, efficient simulation of the physical system in complex mathematical data operation and processing scenarios, and dynamic optimization of the model parameters, effectively improving the simulation accuracy and adaptability of the physical system, and being able to better handle problems such as multi-modal data fusion processing and dynamic evolution simulation of complex physical systems, providing an innovative and efficient solution for data processing and system simulation in related fields.

[0034] Reference Figure 2 , in an optional embodiment, based on the unified embedding space, a quantum-neural differential equation hybrid model is constructed, including the following steps:

[0035] S21. Extract features from the data in the unified embedding space to obtain data features; among them, the data features include temporal features, spatial features, and unstructured features.

[0036] Specifically, in the unified embedding space, the data can include three modalities: temporal, spatial, and unstructured. The feature extraction methods for each modality are different. Temporal feature extraction focuses on the laws of data changes over time, such as trends, periodicity, temporal correlations, etc. Technologies such as sliding windows and wavelet transforms can be used to capture time dynamic information. Spatial feature extraction methods focus on the spatial distribution and positional relationships of geographical spatial location data, etc. For example, technologies such as spatial filtering and spatial autocorrelation analysis are used to obtain spatial patterns and features. Unstructured feature extraction targets unstructured data such as text and images, and methods such as text embedding and convolutional neural networks are used to extract meaningful features from complex unstructured information, such as the key semantics of text and the key visual information of images.

[0037] The implementation process of this step can be as follows: First, preprocess the time series data, including time series cleaning, filling in missing values, aligning data, etc. Then use time series feature extraction algorithms, such as extracting the mean, variance, slope of the time series, and the high-frequency and low-frequency components after wavelet decomposition. For spatial data, perform spatial transformation, such as the projection transformation of geographical coordinates, and then apply spatial analysis methods, such as calculating the spatial adjacency matrix and using geographic information system tools to extract land use patterns. For unstructured data, for text data, use methods such as word segmentation, removing stop words, and using word vector models to extract text features; for image data, use convolutional neural networks for feature extraction to learn the spatial hierarchical features of the image. Finally, integrate the various extracted features to form a multi-modal fusion data feature set for subsequent model construction.

[0038] S22. Set the initial parameters of the quantum optimization layer according to the data features; among them, the initial parameters include the number of qubits and quantum gates.

[0039] Specifically, the setting of the initial parameters of the quantum optimization layer includes the number of qubits and quantum gates. Qubits are the basic information units of quantum computing, and their number can affect the expressive power of the model. Generally speaking, the higher the complexity of the physical system, the stronger the expressive power required by the model, and the more qubits may be needed. However, it is necessary to balance the computing resources, as too many qubits will lead to too high a computing cost. Quantum gates are tools for operating qubits, and their number and type determine the structure and information processing ability of the model. The initial number of quantum gates can be determined according to the expected function of the model and the experience of quantum algorithms for similar complex problems.

[0040] The process of setting the parameters can be as follows: Suppose the constructed model needs to process a physical system with 10 state variables. It is initially estimated that 20 qubits are needed to fully represent the state space of the system. Then, according to the experience of quantum circuit design, considering that single-qubit gates and two-qubit gates need to be operated on these qubits, and referring to the setting of the number of quantum gates in similar-scale problems, the number of quantum gates is set to about 50. However, these initial parameters are only the starting point and can be dynamically adjusted according to the actual situation in subsequent training optimization to achieve a better balance between model performance and efficiency.

[0041] S23. Define the neural network and the differential equation, and obtain the neural differential equation of the neural differential equation module according to the neural network structure and the differential equation.

[0042] Specifically, the neural network architecture in this step can be a multi-layer perceptron, a recurrent neural network, etc. Taking the multi-layer perceptron as an example, it consists of an input layer, a hidden layer, and an output layer. The input layer receives feature data, the hidden layer performs feature transformation through a non-linear activation function, and the output layer converts the processing result into a result in the form of a differential equation. The differential equation is established based on physical laws, system dynamics knowledge, etc., and describes the evolution law of the physical system state. For example, in a mechanical system, a differential equation related to displacement, velocity, and acceleration may be established according to Newton's laws of motion.

[0043] The process of obtaining the neural differential equation can be: embedding the neural network into the parameters or function expressions of the differential equation, so that part or all of the differential equation is learned and approximated by the neural network. For example, consider a simple ordinary differential equation If the form of the f function is uncertain, the neural network can be used to replace f, and the neural differential equation is where θ is the neural network parameter. Through the learning ability of the neural network, the unknown differential equation form that conforms to physical laws can be automatically mined from the data and used to describe the dynamic behavior of the physical system.

[0044] S24. Embed the quantum optimization layer into the neural differential equation module, and use the quantum optimization layer to optimize the parameters of the neural differential equation in the neural differential equation module to obtain a fusion model.

[0045] Specifically, embedding the quantum optimization layer into the neural differential equation module mainly optimizes the parameters of the neural differential equation module through quantum optimization algorithms. Quantum optimization algorithms such as quantum genetic algorithms and quantum particle swarm optimization algorithms can globally optimize the weights, biases of the neural network, and unknown parameters in the differential equation. The quantum optimization layer will participate in the parameter initialization, update, and adjustment processes, and use the characteristics of quantum bit state superposition and quantum entanglement to quickly search for better solutions in the parameter space.

[0046] The parameter optimization process can be: First, initialize the quantum bits and quantum gate parameters of the quantum optimization layer. Then, connect the quantum optimization layer with the neural differential equation module, take the neural differential equation module as the object to be optimized, and set the optimization objective function (such as minimizing the prediction error, etc.). In each optimization iteration, the quantum optimization layer calculates the value of the objective function according to the current model parameters, and then adjusts the parameters through quantum operations (such as quantum gate operations) to evolve in a better direction. This process is similar to the traditional genetic algorithm, but based on the principles of quantum mechanics, it has stronger global exploration ability and can effectively avoid the local optimum problem that traditional optimization algorithms may fall into.

[0047] S25. Use the training data to train the fusion model to obtain a quantum-neural differential equation hybrid model.

[0048] Specifically, the training data needs to cover different states and operating scenarios of the physical system, including normal and abnormal states. The amount of data should be large enough so that the model can learn the comprehensive evolution law. At the same time, the data needs to be labeled as a guide for training.

[0049] The model training process can be as follows: Load the training data into the fusion model and input the feature data in the unified embedding space. The model calculates and outputs the simulation results, compares them with the actual data, and calculates the loss function (such as mean square error, mean absolute error). The optimizer adjusts the model parameters to reduce the loss. Iterate repeatedly until the loss converges or reaches a predetermined condition. During the training process, techniques such as regularization and data augmentation can be introduced to reduce overfitting and improve the generalization ability of the model. Adopt staged training, transfer learning, etc. to improve the training efficiency and effect. For example, in the initial stage of training, the parameters may be adjusted quickly to significantly reduce the error, and then finely adjusted in the later stage to improve the accuracy.

[0050] In an alternative embodiment, the expression of the neural differential equation is:

[0051]

[0052] where f θ is a neural network, h(t) is the system state variable of the physical system, x(t) is the data feature, and t represents time.

[0053] Specifically, the neural network in this neural differential equation is used to learn and approximate the complex nonlinear relationship of the physical system. The structure of the neural network can be designed according to the characteristics of the physical system. For example, for a system with temporal characteristics, a recurrent neural network (RNN) or its variants, such as long short-term memory network (LSTM), gated recurrent unit (GRU), etc. can be used. These networks can effectively process sequence data and capture the dependencies over time. For a system with more prominent spatial features, a convolutional neural network (CNN) may be a better choice, which can extract the spatial hierarchical features of the data. The input of the neural network includes information such as the state variable of the physical system, data feature, and time. Through the activation functions and weight parameters of multiple layers of neurons, it outputs the prediction or description of the system state change.

[0054] The system state variable is a key variable that describes the current state of the physical system and is also one of the core parts of the neural differential equation. The selection of these variables depends on the specific physical system. For example, in a mechanical system, it may include position, velocity, acceleration, etc.; in an electrical circuit system, it may include voltage, current, etc. The system state variables usually change over time, and the goal of the neural differential equation is to accurately describe the evolution law of these variables over time through the learning ability of the neural network.

[0055] Data features are extracted from a unified embedding space, including temporal features, spatial features, and unstructured features, etc. These features provide richer information for the neural network, helping the neural network better understand the operating state and laws of the physical system. For example, temporal features can help the neural network capture the changing trend of the system state over time, spatial features can help the neural network understand the distribution and interaction of the system in space, and unstructured features can provide some additional context information, such as text descriptions, images, etc., further enhancing the neural network's ability to model the physical system.

[0056] Time is an important dimension in neural differential equations, which represents the process of the change of the physical system state. In neural differential equations, time is used as one of the inputs of the neural network, and the rate of change of the system state over time is directly reflected in the form of differential equations. By modeling time, neural differential equations can describe the state of the physical system at different time points and the dynamic change relationship between states, so as to achieve accurate prediction and simulation of the evolution process of the physical system.

[0057] In an optional embodiment, a quantum optimization layer is used to optimize the parameters of the neural differential equation, including the following steps:

[0058] S241. The quantum optimization layer obtains the initial value of the global optimal solution of the parameters of the neural differential equation through the quantum annealing algorithm.

[0059] Specifically, the quantum annealing algorithm is a global optimization algorithm based on the principles of quantum mechanics. This algorithm uses the quantum state superposition and quantum tunneling effect of qubits to perform a global search in the parameter space. During the search process, the quantum annealing algorithm can jump out of the local optimal solution with a certain probability, so it is more likely to find the global optimal solution. Specifically, the quantum annealing algorithm initializes the superposition state of qubits, and then gradually reduces the temperature of the system (i.e., the intensity of quantum fluctuations), so that the qubits gradually evolve from the superposition state to the ground state, and finally obtains the global optimal solution of the system.

[0060] In the optimization of the neural differential equation parameters, the parameters of the neural differential equation are regarded as the optimization variables in the quantum annealing algorithm. First, the superposition state of qubits is initialized, corresponding to the initial guess value of the parameters. Then, through the quantum annealing process, the qubits perform a global search in the parameter space to find the parameter combination that minimizes the prediction error of the neural differential equation. During this process, the quantum tunneling effect enables the algorithm to cross the energy barrier in the parameter space and avoid falling into the local optimal solution. Finally, the quantum annealing algorithm obtains the initial value of the global optimal solution of the neural differential equation parameters, providing a better starting point for subsequent parameter updates.

[0061] S242. According to the initial value of the global optimal solution, the adjoint sensitivity method is used to perform gradient backpropagation and parameter update on the neural differential equation.

[0062] Specifically, the adjoint sensitivity method is an efficient method for calculating gradients, especially suitable for neural differential equations with a large number of parameters and complex structures. This method transforms the calculation of the gradient of the prediction error of the neural differential equation with respect to the parameters into the solution of the adjoint variables by introducing adjoint variables. Specifically, the adjoint sensitivity method first solves the forward propagation of the neural differential equation to obtain the solution of the system state variables; then, according to the prediction error, it solves the adjoint equation to obtain the solution of the adjoint variables; finally, it uses the adjoint variables and the results of the forward propagation to calculate the gradient of the parameters.

[0063] After obtaining the initial value of the global optimal solution of the neural differential equation parameters, the adjoint sensitivity method is used for gradient backpropagation and parameter update. First, the initial value of the global optimal solution is used as the initial value of the parameters, and the forward propagation of the neural differential equation is performed to obtain the predicted values of the system state variables. Then, according to the error between the predicted values and the actual data, the adjoint equation is solved to obtain the solution of the adjoint variables. Next, the gradient of the parameters is calculated using the adjoint variables and the results of the forward propagation. Finally, according to the gradient information, optimization algorithms (such as gradient descent method, Adam algorithm, etc.) are used to update the parameters. In this way, combining the initial value of the global optimal solution obtained by the quantum annealing algorithm and the efficient gradient calculation of the adjoint sensitivity method can quickly optimize the parameters of the neural differential equation and improve the accuracy and convergence speed of the model.

[0064] In an alternative embodiment, the target Hamiltonian of the quantum annealing algorithm is:

[0065]

[0066] where is the spin operator of the i-th qubit, and J ij is the coupling strength between the i-th qubit and the j-th qubit, and h i is the local magnetic field strength of the i-th qubit.

[0067] Specifically, in the quantum annealing algorithm, the spin operator of the qubit represents the state of the qubit. The spin operator can take different values, usually represented by |↑〉 and |↓〉 for the two possible states of the qubit. The role of the spin operator in the Hamiltonian is to describe the contribution of the spin state of the qubit to the energy of the system. For example, in a simple qubit system, the values of the spin operator may correspond to different energy levels, thus affecting the overall energy state of the system.

[0068] The coupling strength describes the interaction between different qubits. During quantum annealing, the coupling strength determines how qubits influence and co-evolve with each other. The coupling strength can be positive or negative. A positive coupling strength indicates that qubits tend to take the same state, while a negative coupling strength indicates that qubits tend to take opposite states. For example, in a system with a positive coupling strength, if a qubit is in the |↑〉 state, then the qubit it is coupled to is also more likely to be in the |↑〉 state, thus reducing the energy of the system.

[0069] The local magnetic field strength acts on a single qubit and affects the probability distribution of its spin state. The local magnetic field strength can be regarded as an external control parameter used to adjust the state preference of the qubit. For example, a positive local magnetic field strength increases the probability that the qubit is in the |↑〉 state, while a negative local magnetic field strength increases the probability that the qubit is in the |↓〉 state. By adjusting the local magnetic field strength, the qubits can be guided to evolve towards the desired state during quantum annealing.

[0070] The target Hamiltonian is the core of the quantum annealing algorithm, which defines the energy landscape of the quantum system. During quantum annealing, the system spontaneously evolves towards the state with the lowest energy, i.e., the ground state of the target Hamiltonian. By designing the target Hamiltonian, the problem of optimizing the parameters of the neural differential equation can be transformed into the problem of finding the ground state of the target Hamiltonian. Specifically, the ground state of the target Hamiltonian corresponds to the global optimal solution of the parameters of the neural differential equation, and the task of the quantum annealing algorithm is to find this ground state through the evolution of quantum states.

[0071] In an alternative embodiment, the gradient calculation formula of the adjoint sensitivity method is:

[0072]

[0073] where \(t_0\) is the initial time of the differential equation; \(t_1\) is the termination time of the differential equation; \(a(t)\) is the adjoint state vector, and \(a(t)\) represents the sensitivity of the loss function used for optimizing the neural differential equation to the system state variable \(h(t)\).

[0074] Specifically, the initial time and the termination time define the solution interval of the neural differential equation. The initial time usually corresponds to the starting state of the physical system, while the termination time corresponds to the final state that is desired to be predicted or optimized. When calculating the gradient, it is necessary to solve the neural differential equation and the adjoint equation over the entire time interval to obtain the complete information of the system state variable and the adjoint state vector.

[0075] The adjoint state vector is a core concept in the adjoint sensitivity method, which represents the sensitivity of the loss function to the system state variables. Specifically, the adjoint state vector describes the rate of change of the loss function with respect to the system state variables, that is, how the loss function will change when the system state variables undergo a small change. By solving the adjoint equation, the solution of the adjoint state vector can be obtained, and then the gradient of the parameters can be calculated.

[0076] The system state variables are the solutions of the neural differential equations, which describe the states of the physical system at different time points. In gradient calculation, the system state variables are combined with the adjoint state vector to calculate the gradient of the loss function with respect to the parameters. The solution of the system state variables usually requires numerical methods, such as the Euler method, the Runge-Kutta method, etc., to solve the neural differential equations.

[0077] The calculation process of the formula: First, given the initial conditions and parameters, the neural differential equation is solved forward to obtain the solution of the system state variables within the time interval. Then, according to the definition of the loss function, the gradient of the loss function with respect to the system state variables, that is, the adjoint state vector, is calculated. Next, using the adjoint state vector and the system state variables, the gradient of the loss function with respect to the parameters of the neural differential equation is calculated through the gradient calculation formula. This gradient information will be used to guide the update and optimization of the parameters.

[0078] In an alternative embodiment, a unified embedding space is constructed by performing self-supervised learning on the multi-modal data of the physical system corresponding to the mathematical data operation processing scenario, including the following steps:

[0079] S11. Clean the multi-modal data to obtain the cleaned data; wherein, the cleaning process includes removing outliers using the quantile method.

[0080] Specifically, before constructing the unified embedding space, the purpose of cleaning the multi-modal data of the physical system corresponding to the mathematical data operation processing scenario is to remove noise, outliers, and irrelevant information in the data, improve the quality and reliability of the data, so as to make the subsequent process of constructing the unified embedding space more accurate and effective. Specifically, the removal of outliers can avoid model deviation and increased prediction errors caused by extreme values, and ensure that the multi-modal data can truly reflect the operating state and characteristics of the physical system.

[0081] The quantile method is a statistical-based outlier detection method. It determines the distribution range of data by calculating the quantiles of the data (such as quartiles), and identifies outliers that exceed the normal range according to the set rules. For example, generally, the lower quartile (Q1) minus 1.5 times the interquartile range (IQR = Q3 - Q1) can be used as the lower limit, and the upper quartile (Q3) plus 1.5 times the interquartile range as the upper limit. Any data point that is below the lower limit or above the upper limit is determined to be an outlier. In multimodal data, the quantile method can be applied to each modality of data separately to remove outliers. For time series data, the quartiles of the entire time series can be calculated and outliers removed; for spatial data, the quantile method can be applied to the data at each spatial location; for unstructured data, it may be necessary to first convert it into structured data (such as through feature extraction) and then apply the quantile method.

[0082] S12. Use a conditional generative adversarial network to fill in the missing data in the cleaned data and generate synthetic data that is consistent with the original distribution of the cleaned data.

[0083] Specifically, the generative adversarial network (GAN) is a deep learning model composed of two parts: a generator and a discriminator. The goal of the generator is to generate samples that can pass for real, while the goal of the discriminator is to distinguish between the generated samples and real samples. Through the mutual confrontation and optimization of the generator and the discriminator, the generator can learn the distribution of real data and generate high-quality synthetic data.

[0084] The conditional generative adversarial network (cGAN) is an extended model that introduces conditional information based on the traditional GAN. When filling in the missing data of multimodal data, the existing cleaned data can be used as conditional information and input into the cGAN. The generator generates synthetic data that is consistent with the real data distribution based on the conditional information to fill in the missing values. Specifically, the generator will generate synthetic data corresponding to the missing part according to the input conditional data, so that the entire data is consistent with the cleaned data in terms of structure and distribution. For example, in time series data, the generator can generate the missing data points in the middle according to the data points before and after in the time series; in spatial data, it can generate the data at the missing location according to the data at the surrounding spatial locations; in unstructured data, it can generate the missing unstructured features according to the context information. The synthetic data generated in this way not only fills in the missing data but also maintains the distribution characteristics of the original data, providing a more complete and reliable data basis for subsequent construction of a unified embedding space.

[0085] S13. Jointly represent the synthetic data through a contrastive learning model to construct a unified embedding space.

[0086] Specifically, contrastive learning is a self-supervised learning method that maps data into a unified feature space by learning the similarities and differences between data. The contrastive learning model defines a loss function that encourages data belonging to the same category or having similar semantics to be close to each other in the embedding space, while data from different categories or with large semantic differences are far from each other. Through contrastive learning, multi-modal data can have a similar feature distribution in the unified embedding space, thus achieving the fusion and joint representation of multi-modal data.

[0087] The process of constructing the unified embedding space can be as follows: First, the synthetic data after cleaning and filling is input into the contrastive learning model. The model will automatically learn the correlation and internal connection between multi-modal data and extract representative features. For example, in time-series data, the model can learn the time-dynamic features of the data; in spatial data, it can learn the spatial distribution features of the data; in unstructured data, it can learn the context semantic features of the data. Then, through the training of the contrastive learning model, the model parameters are adjusted to make the representations of different modal data in the embedding space closer and more consistent. Finally, the obtained unified embedding space can convert multi-modal data into a unified feature representation form, providing basic support for the construction and simulation of the subsequent quantum-neural differential equation hybrid model.

[0088] In an optional embodiment, the loss function used by the contrastive learning model during training is:

[0089]

[0090] where q and k + are positive sample pairs formed by different augmented views of the same data entity in the training data of the contrastive learning model, k l represents the l-th negative sample in the training data of the contrastive learning model that does not belong to the same data entity as q, N represents the number of negative samples, sim(·) represents the cosine similarity function, and τ represents the temperature parameter used to adjust the smoothness of the similarity distribution, τ > 0.

[0091] Specifically, in contrastive learning, positive sample pairs are formed by different augmented views of the same data entity. By performing different data augmentation operations (such as rotation, flipping, cropping, etc.) on the same data entity, multiple different views can be generated. Although these views are different in terms of presentation form, they essentially represent the same data entity. The purpose of constructing positive sample pairs is to let the model learn the similarity of the same data entity under different views, so as to map these views to nearby positions in the embedding space.

[0092] A negative sample refers to a sample that does not belong to the same data entity as the samples in a positive sample pair. During the training process, the role of negative samples is to provide a feature distribution different from that of positive sample pairs, helping the model learn the differences between different data entities. By comparing negative samples with positive sample pairs, the model can better adjust the structure of the embedding space, enabling the feature representations of different data entities to be separated from each other in the embedding space.

[0093] The cosine similarity function is used to measure the similarity between two vectors, and its value ranges from -1 to 1. In a contrastive learning model, the cosine similarity function is used to calculate the similarity between positive sample pairs and negative samples. Through the cosine similarity function, the similarity value of positive sample pairs can be raised, and the similarity value of negative samples can be lowered, thereby achieving the training and optimization of the model.

[0094] The temperature parameter is used to adjust the smoothness of the similarity distribution. The larger the temperature parameter, the smoother the similarity distribution; the smaller the temperature parameter, the sharper the similarity distribution. By adjusting the temperature parameter, the model's ability to distinguish between positive sample pairs and negative samples can be controlled, thereby affecting the training effect and performance of the model.

[0095] The loss function of the contrastive learning model guides the model's training process by comprehensively considering the similarities of positive sample pairs and negative samples, as well as the influence of the temperature parameter. Specifically, the loss function encourages the model to increase the similarity value of positive sample pairs and decrease the similarity value of negative samples, so that different augmented views of the same data entity are closer in the embedding space, and the feature representations of different data entities are more separated. By minimizing the loss function, the model can learn more effective feature representations, providing a better basis for the subsequent construction of a unified embedding space and the construction of a quantum-neural differential equation hybrid model.

[0096] The above-mentioned method for constructing and simulating a data model for mathematical data operation processing integrates multi-modal data features by constructing a unified embedding space, fills in missing data using a conditional generative adversarial network, and uses a contrastive learning model for joint representation to construct a more accurate feature space. Then, a quantum-neural differential equation hybrid model is built, and the quantum annealing algorithm is used to obtain the initial value of the globally optimal solution of the parameters. The adjoint sensitivity method is used for gradient backpropagation and parameter update to optimize the model. At the same time, the contrastive learning model with a specific loss function is used to improve the training effect, thereby achieving accurate modeling, efficient simulation, and dynamic optimization of model parameters for physical systems in complex mathematical data operation processing scenarios, effectively improving the simulation accuracy of physical systems, enhancing the generalization ability and adaptability of the model, and being able to better handle problems such as multi-modal data fusion processing and dynamic evolution simulation of complex physical systems, providing an innovative and efficient solution for data processing and system simulation in related fields.

[0097] It should be understood that although the steps in the flowcharts involved in the above-described embodiments are sequentially shown according to the indication of the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless there is a clear description in this article, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above-described embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be executed alternately or in turn with at least a part of the steps or stages in other steps or other steps.

[0098] An embodiment of the present application further provides a computer device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the steps in the foregoing method embodiments are implemented.

[0099] An embodiment of the present application further provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the steps in the foregoing method embodiments are implemented.

[0100] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to the partial descriptions of the method embodiments. The device embodiments described above are only illustrative. The components described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the present disclosure solution. Those of ordinary skill in the art can understand and implement it without creative efforts.

[0101] The above-described embodiments only represent several implementation manners of the embodiments of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the patent scope of the application embodiments. It should be noted that for those of ordinary skill in the art, without departing from the concept of the embodiments of the present application, several deformations and improvements can still be made, and these all belong to the protection scope of the embodiments of the present application.

Claims

1. A data model construction and simulation method for mathematical data operation processing, characterized in that: The method comprises: A unified embedding space is constructed by performing self-supervised learning on multimodal data of a physical system corresponding to a mathematical data operation processing scenario; wherein the multimodal data includes time series data, spatial data, and unstructured data, and the unified embedding space is an embedding space that simultaneously represents multiple modal data, and in the same embedding space, data of different modalities have similar feature distributions; Based on the unified embedding space, a quantum-neural differential equation hybrid model is constructed; wherein the quantum-neural differential equation hybrid model includes: a quantum optimization layer and a neural differential equation module; the neural differential equation module is used to learn the evolution law of the physical system through a neural network and generate a dynamic model of the system state of the physical system; the quantum optimization layer is used to globally tune the model parameters of the dynamic model; Based on the digital twin interface, the physical system and the simulation environment are synchronized according to the quantum-neural differential equation hybrid model to obtain simulation results; Based on the simulation results, the model parameters of the quantum-neural differential equation hybrid model are dynamically adjusted through reinforcement learning to obtain a revised quantum-neural differential equation hybrid model.

2. The method according to claim 1, characterized in that The step of constructing a quantum-neural differential equation hybrid model based on the unified embedding space includes: Extracting features from the data in the unified embedding space to obtain data features; wherein the data features include time series features, spatial features, and unstructured features; According to the data characteristics, setting the initial parameters of the quantum optimization layer; wherein the initial parameters include the number of quantum bits and quantum gates; Define a neural network and a differential equation, and obtain a neural differential equation of the neural differential equation module according to the neural network structure and the differential equation; Embedding the quantum optimization layer into the neural differential equation module, and optimizing the parameters of the neural differential equation in the neural differential equation module using the quantum optimization layer to obtain a fusion model; The fusion model is trained using training data to obtain the quantum-neural differential equation hybrid model.

3. The method according to claim 2, characterized in that The neural differential equation is: Among them, f θ is the neural network, h(t) is the system state variable of the physical system, x(t) is the data feature, and t represents time.

4. The method according to claim 2, characterized in that: The step of optimizing the parameters of the neural differential equation by using the quantum optimization layer includes: The quantum optimization layer obtains the global optimal solution initial value of the parameters of the neural differential equation through a quantum annealing algorithm; According to the initial value of the global optimal solution, the adjoint sensitivity method is used to perform gradient backpropagation and parameter update on the neural differential equation.

5. The method according to claim 4, characterized in that The target Hamiltonian of the quantum annealing algorithm is: in, is the spin operator of the ith quantum bit, J ij is the coupling strength between the ith qubit and the jth qubit, h i is the local magnetic field strength of the ith quantum bit.

6. The method according to claim 4, characterized in that The gradient calculation formula of the adjoint sensitivity method is: Among them, t0 is the initial time of the differential equation; t1 is the termination time of the differential equation; a(t) is the accompanying state vector, and a(t) represents the sensitivity of the loss function used when optimizing the neural differential equation to the system state variable h(t).

7. The method according to claim 1, characterized in that The method constructs a unified embedding space by performing self-supervised learning on multimodal data of a physical system corresponding to a mathematical data operation processing scenario, including: Performing cleaning processing on the multimodal data to obtain cleaned data; wherein the cleaning processing includes removing outliers using a quantile method; Filling missing data of the cleaned data using a conditional generative adversarial network to generate synthetic data consistent with the original distribution of the cleaned data; The synthetic data is jointly represented by a contrastive learning model to construct the unified embedding space.

8. The method according to claim 7, characterized in that The loss function used in the training of the contrastive learning model is: Among them, q and k + k is a positive sample pair formed by different enhanced views of the same data entity in the training data of the contrastive learning model, l represents the lth negative sample that does not belong to the same data entity as q in the training data of the contrastive learning model, N represents the number of negative samples, sim(·) represents the cosine similarity function, τ represents the temperature parameter for adjusting the smoothness of the similarity distribution, τ>0.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 8 is implemented.

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