Physical field domain modeling method and device, electronic equipment and storage medium

Abstract

The invention provides a physical field domain modeling method and device, electronic equipment and a storage medium. The physical field domain modeling method and device can automatically analyze user requirements, obtain a to-be-modeled field domain type and modeling parameters, determine a corresponding partial differential equation, generate a modeling parameter code block, a loss function code block and a training algorithm code block, and construct a neural network model. And generating an initial hyper-parameter group based on a preset optimization target and the historical hyper-parameter group, training the model and dynamically adjusting the model until the optimization target is met, calculating an equation solution and constructing a field domain model. The method realizes efficient and automatic solution of the partial differential equation, improves the modeling precision and efficiency, and is suitable for engineering scenes such as complex electromagnetic fields, flow fields, thermal fields and the like.

Description

Technical Field

[0001] The present disclosure relates to the technical field of physical information modeling, and in particular to a physical field modeling method, device, electronic device, and storage medium. Background Art

[0002] Partial differential equations are widely present in engineering modeling problems such as heat conduction, structural mechanics, fluid dynamics, and electromagnetic analysis. Although traditional solution methods such as the finite element method (FEM) and the finite difference method (FDM) have highly mature theoretical and tool support, they face the following key bottlenecks: manual construction of discrete grids and boundary conditions is required, resulting in a long modeling cycle; the solution efficiency for complex geometry and nonlinear boundary problems is low; and it is difficult to adapt to the needs of fast iteration and online computing in data-driven scenarios.

[0003] In recent years, physics-informed neural networks (PINNs) have become an important alternative to traditional numerical methods due to their ability to directly embed partial differential constraints into neural network training. Their advantages include modeling physical constraints through automatic differentiation, supporting meshless solutions and data fusion, and have demonstrated their potential in various research fields. However, the application threshold of PINNs remains high. Key reasons include: the neural network structure and loss function design require manual coding, relying heavily on expert experience; poor adaptability to diverse equations, boundary conditions, and sampling regions; high parameter tuning costs, and a lack of intelligent collaborative tuning mechanisms during the training process. Summary of the Invention

[0004] The embodiments of the present disclosure provide at least one physical field modeling method, device, electronic device, and storage medium, which can automatically analyze user needs, generate model configurations, schedule computing resources, and complete high-precision modeling and prediction, thereby achieving efficient and automated solution of corresponding partial differential equations. This significantly improves the automation level and solution efficiency of physical information neural networks in solving partial differential equations, and provides efficient and reliable technical support for engineering applications in complex electromagnetic fields, flow fields, thermal fields, and other environments.

[0005] The present disclosure provides a physical field modeling method, including: Acquire the type of the field to be modeled and modeling parameters, determine the modeling partial differential equation corresponding to the type of the field to be modeled, and generate a modeling parameter code block corresponding to the modeling parameters; Generate a loss function code block embedded in the modeling partial differential equation and a training algorithm code block corresponding to the training algorithm selected by the user, and build a neural network model based on the modeling parameter code block, the loss function code block and the training algorithm code block; Generate an initial hyperparameter group according to a preset optimization target and a historical hyperparameter group corresponding to the type of field to be modeled, train the neural network model using the initial hyperparameter group and record the corresponding loss function value; The initial hyperparameter group is dynamically adjusted according to the change of the loss function value until the neural network model meets the optimization goal, the solution of the modeling partial differential equation is calculated through the trained neural network model, and the field model corresponding to the field type to be modeled is constructed according to the solution of the equation.

[0006] In an optional implementation, obtaining the type of field to be modeled and modeling parameters, determining the modeling partial differential equation corresponding to the field type to be modeled, and generating a modeling parameter code block corresponding to the modeling parameters specifically includes: Obtaining a field modeling requirement input by a user, parsing the field modeling requirement, and determining the field type to be modeled, domain information, initial value condition information, and boundary condition information included therein; Retrieving the modeling partial differential equation that matches the type of the field to be modeled from a preset partial differential equation library, and adjusting equation parameters of the modeling partial differential equation accordingly in response to a parameter adjustment operation by a user; Generate a corresponding domain code block according to the domain information, generate a corresponding initial value condition code block according to the initial value condition information, and generate a corresponding boundary condition code block according to the boundary condition information; The definition domain code block, the initial value condition code block and the boundary condition code block are determined as the modeling parameter code block.

[0007] In an optional embodiment, an initial hyperparameter group is generated according to a preset optimization target and a historical hyperparameter group corresponding to the type of field to be modeled, and the neural network model is trained using the initial hyperparameter group and the corresponding loss function value is recorded, specifically including: Inputting the preset optimization target and the modeling partial differential equation into a preset large language model, analyzing parameter features corresponding to the modeling partial differential equation through the large language model, and generating the initial hyperparameter group in combination with the historical hyperparameter group; The large language model is pre-trained using hyperparameters and corresponding meanings described in natural language as prior knowledge, wherein the hyperparameters include at least the number of initial boundary values, the number of configuration points, the number of network layers, the number of neurons, the number of optimization steps, and the learning rate; The neural network model is trained according to the initial hyperparameter group, and the loss function value corresponding to the initial hyperparameter group is monitored and recorded in real time.

[0008] In an optional implementation, dynamically adjusting the initial hyperparameter set according to changes in the loss function value until the neural network model meets the optimization objective specifically includes: Mark the initial hyperparameter group and the corresponding loss function value as a first real-time feedback array; Analyzing, by the large language model, the change in the loss function value and the prior knowledge, updating the initial hyperparameter group to a first updated hyperparameter group, training the neural network model with the first updated hyperparameter group, and recording the corresponding loss function value; Marking the first updated hyperparameter group and the corresponding loss function value as a second real-time feedback array, using the first real-time feedback array as a historical feedback array, and updating the first updated hyperparameter group to a second updated hyperparameter group based on a change trend between the historical feedback array and the loss function value corresponding to the second real-time feedback array; Training the neural network model with the second updated hyperparameter set, recording the corresponding loss function value, and marking the second updated hyperparameter set and the corresponding loss function value as a third real-time feedback array; The second real-time feedback array is added to the historical feedback array, and the steps of updating the hyperparameter group according to the change trend between the corresponding loss function values in the historical feedback array and the real-time feedback array are repeated, and the neural network model is trained with the updated hyperparameter group until the neural network model meets the optimization objective.

[0009] In an optional embodiment, when the neural network model is completed, the method further includes: Obtain and store model weight checkpoints corresponding to the neural network model, each of the model weight checkpoints including at least model weight information, training progress information, and timestamp information; The model weight checkpoint is stored in a preset model library for the user to call when selecting the training algorithm, wherein the model library pre-stores a variety of neural network algorithms.

[0010] In an optional implementation, when the neural network model needs to be optimized, the method further includes: Filter the optimal model weight checkpoint based on historical training records and current task requirements; Determine the training progress information corresponding to the model weight checkpoint, and use the current number of training steps, the loss function value, and the hyperparameter group indicated by the training progress information as the starting point of a new round of training.

[0011] The present disclosure also provides a physical field modeling device, including: A partial differential equation determination module is used to obtain the type of field to be modeled and modeling parameters, determine the modeling partial differential equation corresponding to the type of field to be modeled, and generate a modeling parameter code block corresponding to the modeling parameters; A neural network model construction module is used to generate a loss function code block embedded in the modeling partial differential equation and a training algorithm code block corresponding to the training algorithm selected by the user, and to construct a neural network model based on the modeling parameter code block, the loss function code block, and the training algorithm code block; An initial training module is used to generate an initial hyperparameter group according to a preset optimization target and a historical hyperparameter group corresponding to the type of field to be modeled, train the neural network model using the initial hyperparameter group, and record the corresponding loss function value; A hyperparameter update module is used to dynamically adjust the initial hyperparameter group according to the change of the loss function value until the neural network model meets the optimization goal, calculate the solution of the modeling partial differential equation through the trained neural network model, and construct the field model corresponding to the field type to be modeled according to the solution of the equation.

[0012] In an optional implementation, the hyperparameter updating module is specifically configured to: Mark the initial hyperparameter group and the corresponding loss function value as a first real-time feedback array; Analyzing, by the large language model, the change in the loss function value and the prior knowledge, updating the initial hyperparameter group to a first updated hyperparameter group, training the neural network model with the first updated hyperparameter group, and recording the corresponding loss function value; Marking the first updated hyperparameter group and the corresponding loss function value as a second real-time feedback array, using the first real-time feedback array as a historical feedback array, and updating the first updated hyperparameter group to a second updated hyperparameter group based on a change trend between the historical feedback array and the loss function value corresponding to the second real-time feedback array; Training the neural network model with the second updated hyperparameter set, recording the corresponding loss function value, and marking the second updated hyperparameter set and the corresponding loss function value as a third real-time feedback array; The second real-time feedback array is added to the historical feedback array, and the steps of updating the hyperparameter group according to the change trend between the corresponding loss function values in the historical feedback array and the real-time feedback array are repeated, and the neural network model is trained with the updated hyperparameter group until the neural network model meets the optimization objective.

[0013] An embodiment of the present disclosure also provides an electronic device, including: a processor, a memory and a bus, wherein the memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor and the memory communicate through the bus, and when the machine-readable instructions are executed by the processor, the above-mentioned physical field modeling method or the steps in any possible implementation of the above-mentioned physical field modeling method are performed.

[0014] An embodiment of the present disclosure also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the computer program executes the above-mentioned physical field modeling method, or the steps of any possible implementation of the above-mentioned physical field modeling method.

[0015] The embodiments of the present disclosure also provide a computer program product, including a computer program / instruction, which, when executed by a processor, implements the above-mentioned physical field modeling method, or the steps in any possible implementation of the above-mentioned physical field modeling method.

[0016] The embodiments of the present disclosure provide a physical field modeling method, device, electronic device and storage medium, which obtain the field type and modeling parameters to be modeled, determine the modeling partial differential equation corresponding to the field type to be modeled, and generate a modeling parameter code block corresponding to the modeling parameters; generate a loss function code block embedded in the modeling partial differential equation and a training algorithm code block corresponding to the training algorithm selected by the user, and construct a neural network model based on the modeling parameter code block, the loss function code block and the training algorithm code block; generate an initial hyperparameter group based on a preset optimization target and a historical hyperparameter group corresponding to the field type to be modeled, use the initial hyperparameter group to train the neural network model and record the corresponding loss function value; dynamically adjust the initial hyperparameter group based on changes in the loss function value until the neural network model meets the optimization target, calculate the equation solution corresponding to the modeling partial differential equation through the trained neural network model, and construct a field model corresponding to the field type to be modeled based on the equation solution. It can automatically analyze user needs, generate model configurations, schedule computing resources, and complete high-precision modeling and prediction, achieving efficient and automated solutions to corresponding partial differential equations. It significantly improves the automation level and efficiency of physical information neural networks in solving partial differential equations, and provides efficient and reliable technical support for engineering applications in complex electromagnetic fields, flow fields, thermal fields and other environments.

[0017] In order to make the above-mentioned objectives, features and advantages of the present disclosure more obvious and easy to understand, preferred embodiments are given below and described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the following briefly introduces the drawings required for use in the embodiments. The drawings herein are incorporated into and constitute a part of the specification. These drawings illustrate embodiments consistent with the present disclosure and, together with the specification, are used to illustrate the technical solutions of the present disclosure. It should be understood that the following drawings only illustrate certain embodiments of the present disclosure and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without inventive effort.

[0019] Figure 1 A flow chart of a physical field modeling method provided by an embodiment of the present disclosure is shown; Figure 2 A flowchart of another physical field modeling method provided by an embodiment of the present disclosure is shown; Figure 3 A schematic diagram of a physical field modeling device provided by an embodiment of the present disclosure is shown; Figure 4 A schematic diagram of an electronic device provided by an embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0020] In order to make the purpose, technical solutions and advantages of the embodiments of the present disclosure clearer, the technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the embodiments of the present disclosure. Obviously, the described embodiments are only part of the embodiments of the present disclosure, not all of the embodiments. The components of the embodiments of the present disclosure generally described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present disclosure provided in the drawings is not intended to limit the scope of the disclosure for which protection is sought, but merely represents selected embodiments of the present disclosure. Based on the embodiments of the present disclosure, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present disclosure.

[0021] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0022] The term "and / or" herein simply describes an association relationship, indicating that three relationships can exist. For example, A and / or B can represent the existence of A alone, the simultaneous existence of A and B, and the existence of B alone. In addition, the term "at least one" herein refers to any combination of at least two of any one or more of a plurality of items. For example, "at least one of A, B, and C" can represent any one or more elements selected from the set consisting of A, B, and C.

[0023] Research has shown that in recent years, physics-informed neural networks (PINNs) have become an important alternative to traditional numerical methods due to their ability to directly embed partial differential constraints into neural network training. Their advantages include modeling physical constraints through automatic differentiation, supporting meshless solutions and data fusion, and have demonstrated their potential in various scientific fields. However, the application threshold of PINNs remains high. Key reasons include: the neural network structure and loss function design require manual coding, relying heavily on expert experience; poor adaptability to diverse equations, boundary conditions, and sampling regions; high parameter tuning costs, and a lack of intelligent collaborative tuning mechanisms during the training process.

[0024] Based on the above research, the present disclosure provides a physical field modeling method, device, electronic device and storage medium, which obtain the field type and modeling parameters to be modeled, determine the modeling partial differential equation corresponding to the field type to be modeled, and generate a modeling parameter code block corresponding to the modeling parameters; generate a loss function code block embedded in the modeling partial differential equation and a training algorithm code block corresponding to the training algorithm selected by the user, and construct a neural network model based on the modeling parameter code block, the loss function code block and the training algorithm code block; generate an initial hyperparameter group according to a preset optimization target and a historical hyperparameter group corresponding to the field type to be modeled, use the initial hyperparameter group to train the neural network model and record the corresponding loss function value; dynamically adjust the initial hyperparameter group according to the change of the loss function value until the neural network model meets the optimization target, calculate the equation solution corresponding to the modeling partial differential equation through the trained neural network model, and construct a field model corresponding to the field type to be modeled according to the equation solution. It can automatically analyze user needs, generate model configurations, schedule computing resources, and complete high-precision modeling and prediction, achieving efficient and automated solutions to corresponding partial differential equations. It significantly improves the automation level and efficiency of physical information neural networks in solving partial differential equations, and provides efficient and reliable technical support for engineering applications in complex electromagnetic fields, flow fields, thermal fields and other environments.

[0025] To facilitate understanding of this embodiment, a physical field modeling method disclosed in an embodiment of the present disclosure is first introduced in detail. The execution subject of the physical field modeling method provided in the embodiment of the present disclosure is generally a computer device with certain computing capabilities. The computer device includes, for example, a terminal device or a server or other processing device. The terminal device can be a user equipment (UE), a mobile device, a user terminal, a terminal, a cellular phone, a cordless phone, a personal digital assistant (PDA), a handheld device, a computing device, an in-vehicle device, a wearable device, etc. In some possible implementations, the physical field modeling method can be implemented by a processor calling computer-readable instructions stored in a memory.

[0026] See also Figure 1 FIG. 1 is a flow chart of a physical field modeling method provided by an embodiment of the present disclosure, wherein the method includes steps S101 to S104, wherein: S101 , obtaining a field type to be modeled and modeling parameters, determining a modeling partial differential equation corresponding to the field type to be modeled, and generating a modeling parameter code block corresponding to the modeling parameters.

[0027] In practice, the system first obtains user-entered field modeling requirements, which include the type of physical field to be modeled and a set of modeling parameters relevant to that field. Specifically, users can enter the modeling field type, solution domain information, initial value conditions, and boundary conditions through a graphical modeling interface or natural language input.

[0028] Here, the field type information includes, for example, two-dimensional heat conduction problems, electromagnetic field propagation problems, fluid mechanics problems, etc.; the definition domain information includes, for example, the spatial range [0,1]×[0,1] and the time range [0,2]; the initial condition information includes, for example, the function expression of the field variable at the start of time; the boundary condition information includes, for example, Dirichlet boundary conditions, Neumann boundary conditions, or periodic boundary conditions; and other parameter information related to modeling, such as material constants, source term function forms, etc.

[0029] Specifically, the field modeling requirements input by the user are obtained, the field modeling requirements are parsed, and the field modeling requirements included therein are determined; the modeling partial differential equation that matches the field type to be modeled is retrieved from the preset partial differential equation library, and the equation parameters of the modeling partial differential equation are adjusted accordingly in response to the user's parameter adjustment operation; a corresponding domain code block is generated according to the domain information, a corresponding initial value condition code block is generated according to the initial value condition information, and a corresponding boundary condition code block is generated according to the boundary condition information; the domain code block, the initial value condition code block and the boundary condition code block are determined as modeling parameter code blocks.

[0030] Here, the system parses the user's input field modeling requirements, identifies the desired field type, and searches the pre-set partial differential equation (PDE) library for a matching partial differential equation modeling model. The PDE library pre-stores standard mathematical expressions for a variety of common physical modeling problems, such as the Helmholtz equation, Poisson's equation, Maxwell's equations, Burgers' equation, and thermodynamic equations. It also records the adjustable parameters of each partial differential equation and supports the subsequent addition of equations from various fields.

[0031] After determining the target partial differential equation model, the user-entered domain, initial conditions, boundary conditions, and other information are further parsed and converted into code representations. The domain information is converted into a domain code block; the initial condition information is converted into an initial value condition code block; and the boundary condition information is converted into a boundary condition code block.

[0032] S102. Generate a loss function code block embedded in the modeling partial differential equation and a training algorithm code block corresponding to the training algorithm selected by the user, and build a neural network model based on the modeling parameter code block, the loss function code block and the training algorithm code block.

[0033] In this step, after completing the generation of the modeling parameter code block, the loss function code block is further automatically constructed based on the modeling partial differential equation, and the training algorithm code block corresponding to the training algorithm selected by the user is generated, thereby realizing the automatic construction of the neural network model.

[0034] In practice, the mathematical form of the aforementioned partial differential equations is first analyzed to extract key elements such as their operator structure, variable dimensions, and boundary condition constraints. This is followed by a loss function expression suitable for neural network solutions. This loss function can include the following components: a physical residual loss term, which constrains the neural network output to satisfy the partial differential equation; an initial condition constraint loss term, which indicates that the model's output at the initial time point must satisfy initial value conditions; and a boundary condition constraint loss term, which forces the output to satisfy specific boundary constraints on the boundary.

[0035] For example, assume that the equation to be solved has the following general format:

[0036] Among them, the definition in , the boundary is , for represents the space-time coordinate vector, represents the solution of the partial differential equation, is the variable parameter of the partial differential equation, is a function that identifies the problem data, is a nonlinear differential operator.

[0037] Here, since the initial condition can actually be considered as a Dirichlet boundary condition in the space-time domain, we can is an operator representing any initial or boundary conditions relevant to the problem, Represents the boundary function. Based on the adjusted equation, the partial differential equation loss function is constructed and the corresponding code block is generated. The partial differential equation loss function can be expressed as follows:

[0038] At the same time, training algorithm code blocks are generated based on the training strategy preset by the user or selected in the neural network algorithm library. The neural network algorithm library stores a variety of neural network methods, such as gradient boosting-based neural network methods, neural tangent kernel-based neural network methods, and residual-based adaptive encryption-based neural network methods, and supports the addition of subsequent neural network methods.

[0039] Next, the system automatically constructs a neural network model based on the aforementioned modeling parameter, loss function, and training algorithm code blocks. The model structure automatically configures the number of network layers, number of neurons per layer, activation function type, and other parameters based on the field modeling task. For example, for a two-dimensional heat conduction problem, the system can automatically construct the following structure: input layer dimensions: (x, y, t); number of hidden layers: 35, 64,128 neurons per layer; activation function: such as tanh or ReLU; output layer dimensions: u(x, y, t).

[0040] Ultimately, the constructed neural network model will serve as an approximate solver of the partial differential equation, and its parameters can be subsequently optimized through a training process so that its output satisfies physical constraints and user goals.

[0041] S103. Generate an initial hyperparameter group according to a preset optimization target and a historical hyperparameter group corresponding to the type of field to be modeled, use the initial hyperparameter group to train the neural network model and record the corresponding loss function value.

[0042] In this step, after the neural network model is built, in order to improve the model training efficiency and accelerate the convergence process, an initial hyperparameter group generation mechanism based on historical experience and goal-driven is further introduced to intelligently set the training starting configuration of the neural network, and accordingly start the training process and record the change trend of the loss function.

[0043] In practice, the system first uses a user-defined optimization objective, such as minimum residual error, minimum number of training rounds, maximum convergence rate, or high-precision fitting boundary values, along with the type of domain being modeled (e.g., two-dimensional steady-state heat conduction, fluid dynamics, or Maxwell equations modeling), to retrieve matching historical hyperparameter configurations from a pre-set hyperparameter history database. This optimization objective defines the training termination point for the neural network architecture, which involves multiple constraints on model accuracy, training time, and the number of hyperparameter iterations.

[0044] Specifically, the preset optimization objectives and the modeled partial differential equations are input into the preset large language model, the parameter characteristics corresponding to the modeled partial differential equations are analyzed by the large language model, and the initial hyperparameter group is generated in combination with the historical hyperparameter group; the large language model is pre-trained with the hyperparameters described in natural language and the corresponding meanings as prior knowledge, and the hyperparameters include at least the number of initial boundary values, the number of configuration points, the number of network layers, the number of neurons, the number of optimization steps and the learning rate; the neural network model is trained according to the initial hyperparameter group, and the loss function value corresponding to the initial hyperparameter group is monitored and recorded in real time.

[0045] To further improve parameter matching accuracy and modeling intelligence during the generation of the initial hyperparameter set, an intelligent analysis mechanism based on a Large Language Model (LLM) was introduced. This mechanism, combined with the user-specified optimization objective and the modeling partial differential equation, enables automated hyperparameter recommendation and initialization. Training is initiated by using the LLM to generate the first set of hyperparameters based on the initial information from the thought chain. During training, changes in the loss function are monitored in real time, and the initial hyperparameter combinations and their corresponding loss values are recorded as a real-time feedback array.

[0046] The large language model is pre-trained using a corpus of data containing natural language descriptions of hyperparameters and modeling background knowledge. This enables it to interpret the structure and physical meaning of various partial differential equations and to infer and recommend hyperparameters based on this information. The hyperparameter set includes the number of initial boundary values, the number of collocation points, the number of network layers, the number of neurons, the number of Adam optimization steps, and the learning rate. The large language model is then fed with natural language prompts, combined with its rich prior theoretical knowledge acquired through pre-training, to enhance its understanding of the hyperparameters to be optimized. This provides the large language model with a basic understanding of the hyperparameters to be optimized, including their names and meanings. Furthermore, a hyperparameter range is specified to constrain the language model's search space.

[0047] It should be noted that the large language model conducts in-depth thinking based on the constructed thinking chain, which includes rich prior theoretical knowledge formed based on pre-training, historical training experience, historical feedback arrays consisting of hyperparameter groups and corresponding loss function values, and model information and optimization goals of the neural network model.

[0048] The number of initial and boundary values refers to the number of data points sampled at the initial conditions and boundary conditions when solving the electromagnetic equations, ensuring that the initial and boundary conditions are met. The number of collocation points refers to the number of data points sampled within the domain of definition when solving the electromagnetic equations, ensuring that the model conforms to the physical laws of the electromagnetic equations. The number of network layers refers to the number of hidden layers in a neural network. The number of neurons refers to the number of neurons in each layer. The number of optimization steps refers to the number of iterations used in the optimization algorithm for training. The number of optimization steps determines the number of times the network parameters are updated during training. The learning rate is a hyperparameter used in the optimization algorithm to control the parameter update step size. The amount of network parameter update in each iteration is proportional to the learning rate.

[0049] In this way, historical training experience records the optimal hyperparameter information accumulated during previous model training. When faced with a new problem, the large language model analyzes the parameter characteristics of the newly introduced partial differential equation and combines it with historical experience of similar problems to ensure that it can generate an optimal initial hyperparameter set with zero training samples.

[0050] For example, the structure of the hyperparameter group can be: {"Equation ID": "Helmholtz equation","Variable parameter k": 0.5,"Number of initial boundary values": 2048,"Number of configuration points": 10000,"Number of network layers and neurons": "2+5*

[30] +2","Number of optimization steps": 8000,"Learning rate": 0.001}.

[0051] S104. Dynamically adjust the initial hyperparameter group according to the change of the loss function value until the neural network model meets the optimization goal, calculate the solution of the modeling partial differential equation through the trained neural network model, and construct the field model corresponding to the field type to be modeled according to the solution of the equation.

[0052] In this step, after training the neural network model and obtaining the initial loss function value, in order to make the model better approximate the analytical solution or numerical solution of the partial differential equation, a dynamic hyperparameter adjustment mechanism based on loss feedback is further provided to achieve iterative optimization of the hyperparameter group and ultimately generate a physical field model with satisfactory accuracy.

[0053] In practice, the loss function is continuously monitored during training. Based on the deviation between the current training loss and the preset optimization target (e.g., total loss less than 1e-4), the system determines whether the currently used hyperparameter set needs to be updated. If the current model training effect does not meet the optimization target, the system triggers the hyperparameter adjustment process.

[0054] Here, the adjustment process is driven by a preset large language model, which uses the current hyperparameter group, its corresponding loss function value, and historical training records as context input. The large language model performs a comprehensive analysis and generates a new round of hyperparameter group recommendations. For example, based on the slow decrease in "loss_pde", the large language model can recommend increasing the number of configuration points or the number of neural network layers. Based on the updated hyperparameter group, the neural network model training is restarted, and the changes in the loss function during training are recorded again to form a second round of real-time feedback array. This real-time feedback array will be compared with the historical feedback array to extract the loss change trend, such as whether it has converged, whether it is oscillating, whether it is overfitting, etc., as an important basis for the next round of update strategies.

[0055] Among them, the hyperparameter adjustment process can be carried out in multiple rounds of iterations. The system records the correspondence between the hyperparameter group and the loss function in each round of update until the loss function value meets the preset optimization goal.

[0056] Furthermore, once model training is complete and convergence is achieved, the trained neural network model is used as a solver for the partial differential equation to be modeled. After inputting spatial or spatiotemporal sampling points within the domain, the network's predictions are output through a forward propagation process, resulting in a numerical solution to the partial differential equation. Ultimately, the system constructs a physical field model based on this solution (including the distribution of state variables within the domain, such as temperature, pressure, and electric field intensity). This field model can be used for visualization, simulation, or further engineering applications, such as multi-physics coupling analysis, structural optimization design, or boundary control decision-making.

[0057] As a possible implementation, the dynamic adjustment of the hyperparameter group can be achieved through the following steps 1 to 5: Step 1: Mark the initial hyperparameter group and the corresponding loss function value as the first real-time feedback array.

[0058] Step 2: Analyze the changes in the loss function value and prior knowledge through the large language model, update the initial hyperparameter group to the first updated hyperparameter group, train the neural network model with the first updated hyperparameter group, and record the corresponding loss function value; Step 3. Mark the first updated hyperparameter group and the corresponding loss function value as the second real-time feedback array, use the first real-time feedback array as the historical feedback array, and update the first updated hyperparameter group to the second updated hyperparameter group according to the change trend between the historical feedback array and the corresponding loss function value of the second real-time feedback array.

[0059] Step 4: Train the neural network model with the second updated hyperparameter set, record the corresponding loss function value, and mark the second updated hyperparameter set and the corresponding loss function value as a third real-time feedback array.

[0060] Step 5: Add the second real-time feedback array to the historical feedback array, repeat the steps of updating the hyperparameter group according to the change trend between the corresponding loss function values in the historical feedback array and the real-time feedback array, and train the neural network model with the updated hyperparameter group until the neural network model meets the optimization goal.

[0061] In the specific implementation, after the neural network model completes the first training based on the initial hyperparameter group and records the corresponding loss function value, in order to further improve the model training efficiency and accuracy, a multi-round hyperparameter optimization method driven by a large language model is provided to achieve adaptive evolutionary updates of the neural network training parameters.

[0062] Specifically, the initial hyperparameter group is first paired with its corresponding loss function value and marked as the first real-time feedback array. Subsequently, the first real-time feedback array and the prior knowledge are input into the pre-trained large language model. The prior knowledge includes information such as the meaning, common functions, and empirical tuning rules of various hyperparameters. The large language model analyzes the numerical performance of the current loss function in combination with the prior rules to identify the shortcomings of the current parameter configuration. For example, if the loss value in the initial training phase decreases slowly, the large language model may recommend increasing the number of configuration points or adjusting the learning rate. The neural network model is reconstructed based on the first updated hyperparameter group and retrained. After the training is completed, the corresponding loss function value is recorded, and the pairing result consisting of the updated hyperparameter group and its loss function value is marked as the second real-time feedback array.

[0063] Furthermore, to further optimize training performance, the first real-time feedback array is used as the historical feedback array. The changing trends between the loss function values in the second real-time feedback array and the corresponding items in the historical feedback array are analyzed. Based on the analysis results, the large language model further adjusts the first updated hyperparameter set to generate a second updated hyperparameter set. For example, if the loss value decreases rapidly but stabilizes later, the large language model may recommend reducing the number of optimization steps or adjusting the number of network layers. If the loss value fluctuates significantly, the large language model may recommend reducing the learning rate or increasing the number of initial boundary values.

[0064] Afterwards, the neural network model is trained with the second updated hyperparameter set, the corresponding loss function value is recorded, and the updated result is marked as the third real-time feedback array. The second real-time feedback array is added to the historical feedback array, and the changing trend between the loss function value in the third real-time feedback array and the corresponding item in the historical feedback array is further analyzed. Based on the analysis results, the large language model adjusts the second updated hyperparameter set to generate a third updated hyperparameter set. The neural network model is trained based on the third updated hyperparameter set, and its loss function value is recorded and compared with the historical feedback array again for analysis. This iterative optimization process will continue until the system detects that the current loss function value meets the preset optimization target conditions.

[0065] It should be noted that during training, changes in loss are monitored in real time, and termination is determined based on multiple constraints, including optimization objectives such as model accuracy, training time, and the number of hyperparameter iterations. For example, when the loss reaches a preset threshold or the training time exceeds a limit, iterations are terminated and the final hyperparameter combination and solution are output. The hyperparameter combination and loss value of the last iteration are recorded in real time. The optimal hyperparameter combination and its corresponding loss value for this training are stored in a memory module for reference in future optimization processes.

[0066] See also Figure 2 FIG. 2 is a flow chart of another physical field modeling method provided by an embodiment of the present disclosure, wherein the method includes steps S201 to S204, wherein: S201. Obtain and store model weight checkpoints corresponding to the neural network model, each of the model weight checkpoints including at least model weight information, training progress information, and timestamp information.

[0067] S202. Storing the model weight checkpoint in a preset model library for the user to call when selecting the training algorithm, wherein the model library pre-stores a variety of neural network algorithms.

[0068] S203. When the neural network model needs to be optimized, the optimal model weight checkpoint is selected based on historical training records and current task requirements.

[0069] S204. Determine the training progress information corresponding to the model weight checkpoint, and use the current number of training steps, the loss function value, and the hyperparameter group indicated by the training progress information as the starting point of a new round of training.

[0070] In the specific implementation, in order to improve the training efficiency and cross-task reuse capability of the neural network model, a checkpoint storage and calling mechanism for the model weights during the neural network training process is further provided, which can be used for breakpoint resumption of training, model migration or parameter reuse scenarios.

[0071] Specifically, during neural network model training, the system periodically acquires and stores weight checkpoints of the current neural network model. Each model weight checkpoint includes at least model weight information, training progress information, and a timestamp. Model weight information contains the parameter state of the neural network at a specific training stage. Training progress includes the current number of training steps, loss value, and hyperparameter combination. The timestamp indicates the time the checkpoint was generated and is used for version management and backtracking.

[0072] Here, the above-mentioned model weight checkpoints are stored in a preset model library. The model library is a centralized management structure, which pre-stores various types of neural network methods, such as gradient enhancement-based neural network methods, neural tangent kernel-based neural network methods, residual-based adaptive encryption-based neural network methods, etc., and supports fast indexing and calling based on task type or modeling objectives.

[0073] In actual applications, after the user configures a new modeling task and selects a training algorithm, the optimal model weight checkpoint is automatically selected based on the current task's field type, PDE structure, optimization objectives, and other required information, combined with historical training records. If the current task is highly similar to a previous task in terms of PDE structure, boundary condition configuration, or network structure, the weight checkpoint at the final training round of that previous task is prioritized. If the current task is only fine-tuning, incremental training, or a local boundary condition change, the weight checkpoint at the intermediate step where the loss function has not yet converged but the change trend is positive can be prioritized. Combined with the analysis suggestions of the large language model, the performance of multiple candidate checkpoints can be further integrated to select the optimal one.

[0074] Here, after determining the selected weight checkpoint, the training progress information contained in the checkpoint is extracted, and the subsequent training process of the neural network model is continued with the number of training steps, loss function value and corresponding hyperparameter group indicated in the information as the starting point.

[0075] In this way, the existing model knowledge is used for rapid initialization, computing resources are saved, multiple rounds of breakpoint resumption and task migration are supported to enhance the robustness of the training process, cross-task model generalization and transfer learning are promoted, and support is provided for multiple PDE scenarios. At the same time, the training convergence efficiency is improved, and unnecessary hyperparameter search and weight cold start are avoided.

[0076] A physical field modeling method provided by an embodiment of the present disclosure obtains a field type to be modeled and modeling parameters, determines a modeling partial differential equation corresponding to the field type to be modeled, and generates a modeling parameter code block corresponding to the modeling parameters; generates a loss function code block embedded in the modeling partial differential equation and a training algorithm code block corresponding to the training algorithm selected by a user, and constructs a neural network model based on the modeling parameter code block, the loss function code block, and the training algorithm code block; generates an initial hyperparameter group based on a preset optimization target and a historical hyperparameter group corresponding to the field type to be modeled, trains the neural network model using the initial hyperparameter group and records the corresponding loss function value; dynamically adjusts the initial hyperparameter group based on changes in the loss function value until the neural network model meets the optimization target, calculates the equation solution corresponding to the modeling partial differential equation through the trained neural network model, and constructs a field model corresponding to the field type to be modeled based on the equation solution. It can automatically analyze user needs, generate model configurations, schedule computing resources, and complete high-precision modeling and prediction, achieving efficient and automated solutions to corresponding partial differential equations. It significantly improves the automation level and efficiency of physical information neural networks in solving partial differential equations, and provides efficient and reliable technical support for engineering applications in complex electromagnetic fields, flow fields, thermal fields and other environments.

[0077] Those skilled in the art will understand that in the above-mentioned method of the specific implementation method, the writing order of each step does not mean a strict execution order and does not constitute any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

[0078] Based on the same inventive concept, a physical field modeling device corresponding to the physical field modeling method is also provided in the embodiment of the present disclosure. Since the principle of solving the problem by the device in the embodiment of the present disclosure is similar to the above-mentioned physical field modeling method in the embodiment of the present disclosure, the implementation of the device can refer to the implementation of the method, and the repeated parts will not be repeated.

[0079] See also Figure 3 , Figure 3 Schematic diagram of a physical field modeling device provided in an embodiment of the present disclosure. Figure 3 As shown in , the physical field modeling device 300 provided by the embodiment of the present disclosure includes: The partial differential equation determination module 310 is used to obtain the type of field to be modeled and modeling parameters, determine the modeling partial differential equation corresponding to the type of field to be modeled, and generate a modeling parameter code block corresponding to the modeling parameters.

[0080] The neural network model construction module 320 is used to generate a loss function code block embedded in the modeling partial differential equation and a training algorithm code block corresponding to the training algorithm selected by the user, and to construct a neural network model based on the modeling parameter code block, the loss function code block and the training algorithm code block.

[0081] The initial training module 330 is used to generate an initial hyperparameter group according to a preset optimization target and a historical hyperparameter group corresponding to the field type to be modeled, use the initial hyperparameter group to train the neural network model and record the corresponding loss function value.

[0082] The hyperparameter update module 340 is used to dynamically adjust the initial hyperparameter group according to the change of the loss function value until the neural network model meets the optimization goal, calculate the solution of the modeling partial differential equation through the trained neural network model, and construct the field model corresponding to the field type to be modeled according to the solution of the equation.

[0083] For descriptions of the processing flow of each module in the device and the interaction flow between each module, reference can be made to the relevant descriptions in the above method embodiment, which will not be described in detail here.

[0084] A physical field modeling device provided by an embodiment of the present disclosure obtains a field type to be modeled and modeling parameters, determines a modeling partial differential equation corresponding to the field type to be modeled, and generates a modeling parameter code block corresponding to the modeling parameters; generates a loss function code block embedded in the modeling partial differential equation and a training algorithm code block corresponding to a training algorithm selected by a user, and constructs a neural network model based on the modeling parameter code block, the loss function code block, and the training algorithm code block; generates an initial hyperparameter group based on a preset optimization target and a historical hyperparameter group corresponding to the field type to be modeled, trains the neural network model using the initial hyperparameter group and records the corresponding loss function value; dynamically adjusts the initial hyperparameter group based on changes in the loss function value until the neural network model meets the optimization target, calculates the equation solution corresponding to the modeling partial differential equation through the trained neural network model, and constructs a field model corresponding to the field type to be modeled based on the equation solution. It can automatically analyze user needs, generate model configurations, schedule computing resources, and complete high-precision modeling and prediction, achieving efficient and automated solutions to corresponding partial differential equations. It significantly improves the automation level and efficiency of physical information neural networks in solving partial differential equations, and provides efficient and reliable technical support for engineering applications in complex electromagnetic fields, flow fields, thermal fields and other environments.

[0085] Corresponding to Figure 1 and Figure 2 The physical field modeling method in the present disclosure also provides an electronic device 400, such as Figure 4 FIG. 4 is a schematic diagram of the structure of an electronic device 400 provided in an embodiment of the present disclosure, including: Processor 41, memory 42, and bus 43; memory 42 is used to store execution instructions, including memory 421 and external memory 422; the memory 421 here is also called internal memory, which is used to temporarily store the operation data in the processor 41 and the data exchanged with the external memory 422 such as the hard disk. The processor 41 exchanges data with the external memory 422 through the memory 421. When the electronic device 400 is running, the processor 41 and the memory 42 communicate through the bus 43, so that the processor 41 executes Figure 1 and Figure 2 The steps of the physical field modeling method in .

[0086] The present disclosure also provides a computer-readable storage medium having a computer program stored thereon. When executed by a processor, the computer program executes the steps of the physical field modeling method described in the above method embodiment. The storage medium may be a volatile or non-volatile computer-readable storage medium.

[0087] The embodiments of the present disclosure also provide a computer program product, which includes computer instructions. When the computer instructions are executed by a processor, the steps of the physical field modeling method described in the above method embodiment can be executed. For details, please refer to the above method embodiment, which will not be repeated here.

[0088] The computer program product may be implemented in hardware, software, or a combination thereof. In one embodiment, the computer program product is implemented as a computer storage medium. In another embodiment, the computer program product is implemented as a software product, such as a software development kit (SDK).

[0089] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the device described above can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here. In the several embodiments provided in the present disclosure, it should be understood that the disclosed device and method can be implemented in other ways. The device embodiments described above are merely schematic. For example, the division of the units is only a logical function division. There may be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some communication interfaces, and the indirect coupling or communication connection of the device or unit can be electrical, mechanical or other forms.

[0090] The units described as separate components may or may not be physically separate, and 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 these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0091] In addition, each functional unit in each embodiment of the present disclosure may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0092] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a non-volatile computer-readable storage medium that is executable by a processor. Based on this understanding, the technical solution of the present disclosure, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present disclosure. The aforementioned storage medium includes: various media that can store program code, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0093] Finally, it should be noted that the above-described embodiments are only specific implementation methods of the present disclosure, which are used to illustrate the technical solutions of the present disclosure, rather than to limit them. The scope of protection of the present disclosure is not limited thereto. Although the present disclosure has been described in detail with reference to the above-described embodiments, those skilled in the art should understand that any person skilled in the art can modify or easily conceive of changes to the technical solutions described in the above-described embodiments within the technical scope disclosed in the present disclosure, or replace some of the technical features therein with equivalents. Such modifications, changes, or replacements do not deviate from the spirit and scope of the technical solutions of the embodiments of the present disclosure, and should be included in the scope of protection of the present disclosure. Therefore, the scope of protection of the present disclosure shall be subject to the scope of protection of the claims.

Claims

1. A physical field modeling method, characterized in that: include: Acquire the type of the field to be modeled and modeling parameters, determine the modeling partial differential equation corresponding to the type of the field to be modeled, and generate a modeling parameter code block corresponding to the modeling parameters; Generate a loss function code block embedded in the modeling partial differential equation and a training algorithm code block corresponding to the training algorithm selected by the user, and build a neural network model based on the modeling parameter code block, the loss function code block and the training algorithm code block; Generate an initial hyperparameter group according to a preset optimization target and a historical hyperparameter group corresponding to the type of field to be modeled, train the neural network model using the initial hyperparameter group and record the corresponding loss function value; The initial hyperparameter group is dynamically adjusted according to the change of the loss function value until the neural network model meets the optimization goal, the solution of the modeling partial differential equation is calculated through the trained neural network model, and the field model corresponding to the field type to be modeled is constructed according to the solution of the equation.

2. The method according to claim 1, characterized in that Obtaining the type of field to be modeled and modeling parameters, determining the modeling partial differential equation corresponding to the field type to be modeled, and generating a modeling parameter code block corresponding to the modeling parameters, specifically including: Obtaining a field modeling requirement input by a user, parsing the field modeling requirement, and determining the field type to be modeled, domain information, initial value condition information, and boundary condition information included therein; Retrieving the modeling partial differential equation that matches the type of the field to be modeled from a preset partial differential equation library, and adjusting equation parameters of the modeling partial differential equation accordingly in response to a parameter adjustment operation by a user; Generate a corresponding domain code block according to the domain information, generate a corresponding initial value condition code block according to the initial value condition information, and generate a corresponding boundary condition code block according to the boundary condition information; The definition domain code block, the initial value condition code block and the boundary condition code block are determined as the modeling parameter code block.

3. The method according to claim 1, characterized in that Generate an initial hyperparameter group according to a preset optimization target and a historical hyperparameter group corresponding to the type of field to be modeled, train the neural network model using the initial hyperparameter group, and record the corresponding loss function value, specifically including: Inputting the preset optimization target and the modeling partial differential equation into a preset large language model, analyzing parameter features corresponding to the modeling partial differential equation through the large language model, and generating the initial hyperparameter group in combination with the historical hyperparameter group; The large language model is pre-trained using hyperparameters and corresponding meanings described in natural language as prior knowledge, wherein the hyperparameters include at least the number of initial boundary values, the number of configuration points, the number of network layers, the number of neurons, the number of optimization steps, and the learning rate; The neural network model is trained according to the initial hyperparameter group, and the loss function value corresponding to the initial hyperparameter group is monitored and recorded in real time.

4. The method according to claim 3, characterized in that Dynamically adjusting the initial hyperparameter set according to changes in the loss function value until the neural network model meets the optimization goal specifically includes: Mark the initial hyperparameter group and the corresponding loss function value as a first real-time feedback array; Analyzing, by the large language model, the change in the loss function value and the prior knowledge, updating the initial hyperparameter group to a first updated hyperparameter group, training the neural network model with the first updated hyperparameter group, and recording the corresponding loss function value; Marking the first updated hyperparameter group and the corresponding loss function value as a second real-time feedback array, using the first real-time feedback array as a historical feedback array, and updating the first updated hyperparameter group to a second updated hyperparameter group based on a change trend between the historical feedback array and the loss function value corresponding to the second real-time feedback array; Training the neural network model with the second updated hyperparameter set, recording the corresponding loss function value, and marking the second updated hyperparameter set and the corresponding loss function value as a third real-time feedback array; The second real-time feedback array is added to the historical feedback array, and the steps of updating the hyperparameter group according to the change trend between the corresponding loss function values in the historical feedback array and the real-time feedback array are repeated, and the neural network model is trained with the updated hyperparameter group until the neural network model meets the optimization objective.

5. The method according to claim 1, wherein When the neural network model is completed, the method further includes: Obtain and store model weight checkpoints corresponding to the neural network model, each of the model weight checkpoints including at least model weight information, training progress information, and timestamp information; The model weight checkpoint is stored in a preset model library for the user to call when selecting the training algorithm, wherein the model library pre-stores a variety of neural network algorithms.

6. The method according to claim 5, characterized in that When the neural network model needs to be optimized, the method further includes: Filter the optimal model weight checkpoint based on historical training records and current task requirements; Determine the training progress information corresponding to the model weight checkpoint, and use the current number of training steps, the loss function value, and the hyperparameter group indicated by the training progress information as the starting point of a new round of training.

7. A physical field modeling device, characterized in that: include: A partial differential equation determination module is used to obtain the type of field to be modeled and modeling parameters, determine the modeling partial differential equation corresponding to the type of field to be modeled, and generate a modeling parameter code block corresponding to the modeling parameters; A neural network model construction module is used to generate a loss function code block embedded in the modeling partial differential equation and a training algorithm code block corresponding to the training algorithm selected by the user, and to construct a neural network model based on the modeling parameter code block, the loss function code block, and the training algorithm code block; An initial training module is used to generate an initial hyperparameter group according to a preset optimization target and a historical hyperparameter group corresponding to the type of field to be modeled, train the neural network model using the initial hyperparameter group, and record the corresponding loss function value; A hyperparameter update module is used to dynamically adjust the initial hyperparameter group according to the change of the loss function value until the neural network model meets the optimization goal, calculate the solution of the modeling partial differential equation through the trained neural network model, and construct the field model corresponding to the field type to be modeled according to the solution of the equation.

8. The device according to claim 7, characterized in that The hyperparameter updating module is specifically used for: Mark the initial hyperparameter group and the corresponding loss function value as a first real-time feedback array; Analyzing the change in the loss function value and the prior knowledge using a preset large language model, updating the initial hyperparameter group to a first updated hyperparameter group, training the neural network model with the first updated hyperparameter group, and recording the corresponding loss function value; Marking the first updated hyperparameter group and the corresponding loss function value as a second real-time feedback array, using the first real-time feedback array as a historical feedback array, and updating the first updated hyperparameter group to a second updated hyperparameter group based on a change trend between the historical feedback array and the loss function value corresponding to the second real-time feedback array; Training the neural network model with the second updated hyperparameter set, recording the corresponding loss function value, and marking the second updated hyperparameter set and the corresponding loss function value as a third real-time feedback array; The second real-time feedback array is added to the historical feedback array, and the steps of updating the hyperparameter group according to the change trend between the corresponding loss function values in the historical feedback array and the real-time feedback array are repeated, and the neural network model is trained with the updated hyperparameter group until the neural network model meets the optimization objective.

9. An electronic device, characterized in that: include: A processor, a memory, and a bus, wherein the memory stores machine-readable instructions executable by the processor, and when the electronic device is running, the processor and the memory communicate via the bus, and when the machine-readable instructions are executed by the processor, the steps of the physical field modeling method according to any one of claims 1 to 6 are performed.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which, when executed by a processor, executes the steps of the physical field modeling method according to any one of claims 1 to 6.

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