Physical field prediction method and equipment based on gradient identification parameter tuning and medium

Abstract

The invention relates to the technical field of physical field prediction, in particular to a physical field prediction method and device based on gradient recognition parameter tuning and a medium, and the method comprises the steps: determining a space-time computational domain based on a physical problem, and determining a control equation, an initial condition constraint and a boundary condition constraint of the physical problem; constructing a training sample data set; initializing parameters of the neural network, and pre-training the neural network; obtaining pre-trained neural network parameters, and identifying high-contribution neural blocks; on the basis of the high-contribution-degree nerve blocks, parameter fine tuning iteration is carried out on the weights of the combination points of the neural network, and a physical field prediction model is obtained; and inputting the space-time coordinates of a to-be-solved point into the physical field prediction model to obtain a physical field prediction value of the point. The adaptive algorithm framework and the staged training strategy provided by the method enable the model to adapt to different partial differential equations and gradient distribution characteristics, thereby reducing the use threshold of the physical information neural network.

Description

Technical Field

[0001] This invention relates to the field of physical field prediction technology, and in particular to physical field prediction methods, devices and media based on gradient identification parameter tuning. Background Technology

[0002] In the fields of scientific computing and engineering simulation, physics-based neural networks (PINNs) have become an important method for solving complex partial differential equations (PDEs). The core idea of ​​this method is to embed the PDEs describing physical laws as constraints into the loss function of the neural network, driving the network to learn solution functions that satisfy the physical laws through an optimization process. Due to their characteristic of not requiring large amounts of labeled data, PINNs exhibit unique advantages in modeling complex physical fields in fields such as computational fluid dynamics, acoustic analysis, and aerospace.

[0003] Traditional PINN methods typically employ fully connected neural networks (FNNs) as their underlying architecture. However, the standard FNN architecture faces challenges when dealing with PDEs whose solution functions exhibit rapidly changing characteristics such as shock waves and wavefronts in the spatiotemporal domain. To improve the performance of PINNs in complex problems, various improvement schemes have been proposed, but all have certain drawbacks, which are as follows: Limitations of the adaptive sampling strategy: This strategy is essentially a passive optimization at the data level, and it cannot change the structural limitations of the network itself. Its sampling effectiveness heavily depends on the network state at the beginning of training; if high-gradient regions are not effectively identified in the initial stage, subsequent sampling may fail. Furthermore, for regions with extremely drastic gradient changes, simply increasing the number of sampling points is often insufficient to compensate for the network's limited expressive power, resulting in limited improvement.

[0004] Limitations of adaptive adjustment of sampling point weights: This method introduces new hyperparameters (such as weight calculation functions and update frequencies), which may lead to drastic oscillations or even divergence during training. Furthermore, this strategy forces the network to excessively concentrate its limited model resources on high-weight regions, thus affecting the accuracy and consistency of the global solution. More importantly, it does not enhance the network's expressive power and is highly sensitive to random states and noise in the early stages of training, making it difficult to serve as a reliable general solution.

[0005] Limitations of the domain decomposition method: This method comes at the cost of system simplicity and computational efficiency. First, determining how to reasonably divide the subdomains is itself a challenge. Second, complex interface conditions must be designed to ensure the continuity and smoothness of solutions between subdomains, which significantly increases the algorithm's complexity and implementation difficulty. Parallel training and coordination of multiple subnetworks also introduces additional computational overhead and management costs.

[0006] Limitations of network structure improvements: The performance of Fourier feature PINN heavily depends on the selection of Fourier mapping parameters (such as frequency bandwidth). These parameters typically require tedious tuning for specific problems and lack universality. Inappropriate parameter selection can worsen the solution performance and result in poor robustness. The binary structure network, while enhancing local feature capture, sacrifices effective global feature learning. When high gradients and smooth regions coexist in the solution domain, this network struggles to achieve consistently high accuracy globally, making it unsuitable for solving complex, multi-scale scenarios.

[0007] Therefore, it is necessary to provide physical field prediction methods, devices, and media based on gradient identification parameter tuning to solve the above-mentioned technical problems. Summary of the Invention

[0008] The purpose of this invention is to provide a method, device, and medium for predicting physical fields based on gradient identification parameter optimization. The specific technical solution is as follows: A physics field prediction method based on gradient identification and parameter tuning includes the following steps: S1: Determine the spatiotemporal computational domain based on the physical problem, and determine the governing equations, initial condition constraints, and boundary condition constraints of the physical problem; S2: Select initial points, boundary points, and internal residual points for calculating the residuals of partial differential equations within the spatiotemporal computation domain to construct a training sample dataset; S3: Initialize the parameters of the neural network, pre-train the neural network, and construct the training loss based on the initial condition constraints, boundary condition constraints, and residuals of the partial differential equations; S4: Obtain the parameters of the pre-trained neural network and identify high-contribution neural blocks; S5: Based on high-contribution neural blocks, the parameters of the neural network junction weights are fine-tuned iteratively to obtain the physical field prediction model. S6: Input the spatiotemporal coordinates of the point to be solved into the physics prediction model to obtain the predicted physics value of that point.

[0009] Specifically, in S3, the neural network uses a binary structure neural network. The neural network architecture includes multiple hidden layers and is set up with binary tree-like hierarchical blocks.

[0010] Specifically, in S3, the neural network is pre-trained using the Adam optimizer, with spatiotemporal coordinates as input and predicted physical field values ​​as output. The activation function is tanh, and the loss function is... The expression is as follows: ; in, This represents the initial condition mean squared error loss. This represents the mean squared error loss due to boundary conditions. This represents the root mean square error loss of the unweighted partial differential equation residuals. This represents the parameters of the neural network.

[0011] Specifically, in S3, during the pre-training of the neural network, the maximum number of iterations is set to 90% of the total number of iterations. During the pre-training process, after the number of iterations reaches the preset number, a statistical period is set every certain number of iterations to calculate the average loss function value of the most recent statistical period and monitor the relative improvement rate. The expression for calculating the relative improvement rate is as follows: ; in, Indicates the relative improvement rate. This represents the average loss function value of the previous statistical period. This represents the average loss function value for the current statistical period; When the relative improvement rate is less than the preset threshold, record the current iteration number and end the pre-training process early.

[0012] Specifically, in S4, the process of identifying high-contribution neural blocks includes: Obtain the pre-trained and updated neural network parameters, and compute the set of gradient norms for solving partial differential equations on the internal residual point set. , Residual point The gradient norm; Determine the threshold based on the preset high gradient ratio P. for The (1-P) quantile is used to identify the set of points in the high gradient region; Identifying high-gradient region point sets within the gradient norm set ,in, Represents the predictive model. This represents the input to the model. Indicates the preset threshold; For each neuron in the last hidden layer of the neural network, the contribution of each neuron on the set of high gradient points is calculated as follows: ; in, Indicates the contribution of a neural block. Indicates that the nerve block is in Activation value at that location, The parameter weight norm represents the neural block; The contribution of the neural block is normalized and calculated as follows: ; in, Indicates the normalized contribution. This indicates the number of neural blocks in the last hidden layer. Indicates nerve block Contribution .

[0013] Specifically, in S5, the parameters of the neural network binding point weights are fine-tuned iteratively, and the process includes: Select the top few neural blocks with the highest contribution to form a subset of adjustable parameters. And freeze the remaining neural network parameters so that the gradient of the frozen neural network parameters is zero in subsequent training and will no longer be updated; The Adam optimizer is used to fine-tune the parameters in the adjustable parameter subset until the total number of iterations is reached.

[0014] Specifically, in S5, the fine-tuning iteration process includes: Recalculate the gradient norm of all internal residual points under the current parameters to obtain the global maximum gradient norm. and global minimum gradient norm ; Based on each residual point The gradient norm is used to assign point weights, where: like Then the weight The calculation expression is: ,otherwise ; The residual loss of the weighted partial differential equation is calculated using the following expression: ; in, Point The residuals of the partial differential equations; The weighted partial differential equation residual loss is used to replace the unweighted partial differential equation residual mean square error loss, and the parameters of the adjustable parameter subset are updated by the total loss function constructed after the replacement.

[0015] Specifically, in S5, after completing the fine-tuning iterations, model accuracy evaluation is also included, and the process includes: Input all spatiotemporal data points used to test the model's accuracy. The model outputs fitted values ​​through a neural network. The accuracy of the model is evaluated using the relative L2 error between the ground truth data and the fitted values, as shown in the following expression: ; in, This represents the relative L2 error value. Represents true data. This represents the fitted value output by the neural network.

[0016] In addition, the present invention also provides a computer device, including a memory and a processor; The memory is used to store computer programs that can run on the processor; When the processor executes the computer program, it implements the steps of the physical field prediction method as described above.

[0017] In addition, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the physical field prediction method described above.

[0018] The application of the technical solution of the present invention has at least the following beneficial effects: This invention provides a physical field prediction method based on gradient identification parameter tuning. Through a gradient-aware mechanism, it automatically captures complex regions with high gradients in the physical field (such as shock waves and boundary layers). Using an adaptive point weight allocation strategy, it applies a larger penalty to the residuals in these key regions, forcing the network to prioritize fitting the drastically changing parts of the solution. Applying this invention overcomes the problems of low accuracy and numerical oscillations inherent in traditional PINN methods when dealing with complex gradient distributions.

[0019] The method of this invention significantly reduces the number of parameters that need to be optimized during the fine-tuning stage by identifying high-contribution neural blocks and freezing low-contribution parameters. This targeted parameter update strategy avoids invalid computations and mutual interference in full-parameter fine-tuning, and significantly reduces the number of iterations and time cost required for model convergence.

[0020] This invention shifts computational resources (computing power) from smooth regions of the physical field to complex, critical high-gradient regions. By combining parameter selection at the structural level with weighted sampling at the data level, it achieves spatially optimized allocation of training resources, improving computational efficiency without increasing hardware costs.

[0021] The unified adaptive algorithm framework and phased training strategy proposed in this invention enable the model to automatically adapt to different types of partial differential equations and different gradient distribution characteristics, without the need for manual design of complex sampling strategies or adjustment of network structure for specific problems. This lowers the threshold for using physical information neural networks and improves the generalization ability of the method.

[0022] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0024] Figure 1 This is a flowchart of the steps of the physical field prediction method in a preferred embodiment of the present invention. Detailed Implementation

[0025] This invention aims to address the accuracy and efficiency bottlenecks encountered in solving nonlinear partial differential equations with high gradient characteristics (such as shock waves and wavefronts) using neural networks in fields such as computational fluid dynamics, acoustics, and aerospace. Specifically, existing techniques suffer from inherent structural contradictions when dealing with highly non-uniform gradient distributions in the spatiotemporal domain. On the one hand, to ensure feature capture in high-gradient regions, more attention needs to be allocated to these regions, enhancing the network's ability to fit local conditions. However, this often leads to numerical oscillations in smooth low-gradient regions. On the other hand, if the network tends to fit a globally smooth trend, it cannot accurately analyze drastic changes in high-gradient regions, resulting in the loss of crucial physical information. This contradiction limits the practicality and reliability of neural network-based solution methods in complex engineering problems.

[0026] To address the aforementioned technical problems, this invention proposes a physical field prediction method based on gradient identification and parameter tuning. This method constructs a two-stage sequential collaboration framework and leverages the parameter isolation characteristics of BsNN. First, during the pre-training stage, a relatively accurate gradient distribution is obtained, gradient features are analyzed, and intelligent region partitioning of the solution domain is achieved accordingly. Subsequently, neural blocks that contribute significantly to high-gradient regions are calculated. After obtaining these high-contribution neural blocks, a point weight allocation strategy is used in the second stage to fine-tune the network parameters of these highly relevant neural blocks. This method employs a key identification strategy, solving the problem that a single network structure cannot simultaneously consider global and local characteristics, thereby significantly improving the accuracy, convergence speed, and computational efficiency of solving nonlinear wave propagation problems.

[0027] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0028] Example: like Figure 1 As shown, this embodiment provides a physical field prediction method based on gradient identification parameter tuning, including the following steps (S1 to S6): S1: Determine the spatiotemporal computational domain based on the physical problem, and determine the governing equations, initial condition constraints, and boundary condition constraints of the physical problem.

[0029] In this embodiment, the physical problem is the prediction of abnormal waves in near-shore port channels. In this physical scenario, the evolution of nonlinear waves in shallow water areas can be accurately described by the classic Korteweg–de Vries (KdV) equation in fluid mechanics. This equation characterizes the dynamic balance between nonlinear wave steepness and frequency dispersion effects. The solitary wave phenomenon corresponding to its solution is the theoretical model of abnormal waves (freak waves) that may suddenly appear in the channel, characterized by steep crests and concentrated energy. The solution field of such waves exhibits the typical characteristics of the coexistence of local extremely high gradient regions (dangerous wave crests) and vast smooth water areas. Accurate prediction of their evolution is crucial for navigation safety.

[0030] Furthermore, the governing equations for the above physical problem are as follows: ; in, Represents wave height; , is the coefficient of the nonlinear term, used to control the steepening effect of the waveform; , where is the dispersion coefficient, used to suppress excessive steepness and oscillation.

[0031] Furthermore, the boundary conditions for the above physical problem are as follows: ; Furthermore, the initial condition for the above physical problem is as follows: using a smooth cosine pulse, this condition will evolve over time, spontaneously decomposing into multiple solitons with steep peaks, accompanied by dispersive oscillations, as expressed below: ; In this embodiment, the model will be further verified to require ground truth data. The process for generating ground truth data for the aforementioned physical problem is as follows: High-precision spectral methods (such as pseudospectral methods, 512 Fourier modes, and fourth-order Runge-Kutta time integration) are employed. Generate a reference solution as an evaluation benchmark.

[0032] S2: Select initial points, boundary points, and internal residual points for calculating the residuals of partial differential equations within the spatiotemporal computation domain to construct a training sample dataset.

[0033] In this embodiment, the training sample dataset is constructed as follows: At least one of the following methods is used: uniform sampling, random sampling, or Latin hypercube sampling. Training points are selected in the computational domain, and N0=500 is chosen as the initial point to constrain the initial conditions. B =500, used to constrain boundary conditions, N L =10000 is used as the residual point to minimize the residual of the governing equation, and the total number of training points is N=11000.

[0034] S3: Initialize the parameters of the neural network and pre-train the neural network. The training loss is constructed based on the initial condition constraints, boundary condition constraints, and residuals of the partial differential equations.

[0035] The neural network adopts a binary structure neural network, and the architecture of the neural network includes multiple hidden layers, which are set up in a binary tree-like hierarchical block configuration.

[0036] Specifically, in this embodiment, the neural network adopts a binary structure neural network. The neural network architecture includes four hidden layers, which are set up in a binary tree-like hierarchical block configuration. The first layer includes at least one neural block, which includes at least 64 neurons; the second layer includes two neural blocks, each of which includes at least 32 neurons; the third layer includes at least four neural blocks, each of which includes at least 16 neurons; and the fourth layer includes at least eight neural blocks, each of which includes at least eight neurons.

[0037] The neural network architecture design in this embodiment progressively enhances the ability to extract refined and structured features of local mutations (such as isolated peaks in the KdV equation).

[0038] Furthermore, the neural network is pre-trained using the Adam optimizer (the initial learning rate during pre-training can be set to 0.001), with spatiotemporal coordinates as input and predicted physical field values ​​as output. The activation function is tanh, and the loss function is... The expression is as follows: ; in, This represents the initial condition mean squared error loss. This represents the mean squared error loss due to boundary conditions. This represents the root mean square error loss of the unweighted partial differential equation residuals. This represents the parameters of the neural network.

[0039] Specifically, in S3, during the pre-training of the neural network, the maximum number of iterations is set to 90% of the total number of iterations. In this embodiment, the total number of iterations is set to... It is 30,000; During pre-training, after 200 iterations, the average loss function value of the most recent 100 iterations is calculated every 100 iterations, and the relative improvement rate is monitored. The expression for calculating the relative improvement rate is as follows: ; in, Indicates the relative improvement rate. This represents the average loss function value of the most recent 100 iterations. This represents the average loss function value over the most recent 100 iterations; when At this point, the current iteration number is recorded, and pre-training is terminated early. In this embodiment, pre-training typically reaches the early stopping condition within 8000–12000 iterations.

[0040] S4: Obtain the parameters of the pre-trained neural network and identify high-contribution neural blocks.

[0041] In this embodiment, the process of identifying high-contribution neural blocks includes: Obtain the updated parameters of the pre-trained neural network Compute the solution of the partial differential equation on the internal residual point set. The set of gradient norms , Residual point The gradient norm; Set the high gradient ratio P=0.2 and determine the threshold. for The 80th percentile (i.e., (1-P) quantile) is used to identify high gradient region point sets; Identifying high-gradient region point sets within the gradient norm set ,in, Represents the predictive model. This represents the input to the model. Indicates the preset threshold; For each neuron in the last hidden layer of the neural network, the contribution of each neuron on the set of high gradient points is calculated as follows: ; in, Indicates the contribution of a neural block. Indicates that the nerve block is in Activation value at that location, The parameter weight norm represents the neural block; The contribution of the neural block is normalized and calculated as follows: ; in, Indicates the normalized contribution. This indicates the number of neural blocks in the last hidden layer. Indicates nerve block Contribution .

[0042] S5: Based on high-contribution neural blocks, the parameters of the neural network junction weights are fine-tuned iteratively to obtain the physical field prediction model.

[0043] The process of fine-tuning the parameters of the weights at the junctions of the neural network includes: Select the top 30% of neurons with the highest contribution to form a subset of adjustable parameters. And freeze the remaining neural network parameters so that the gradient of the frozen neural network parameters is zero in subsequent training and will no longer be updated; The Adam optimizer (with the learning rate reduced to 0.0001 during the fine-tuning iteration phase) is used to fine-tune the parameters in the adjustable parameter subset until the total number of iterations is reached.

[0044] Specifically, in S5, the fine-tuning iteration process includes: Recalculate the gradient norm of all internal residual points under the current parameters to obtain the global maximum gradient norm. and global minimum gradient norm ; Based on each residual point The gradient norm is used to assign point weights, where: like Then the weight The calculation expression is: ,otherwise ; The residual loss of the weighted partial differential equation is calculated using the following expression: ; in, Point The residuals of the partial differential equations; The weighted partial differential equation residual loss is used to replace the unweighted partial differential equation residual mean square error loss, and the parameters of the adjustable parameter subset are updated by the total loss function constructed after the replacement.

[0045] Specifically, in S5, after completing the fine-tuning iterations, model accuracy evaluation is also included, and the process includes: Input all spatiotemporal data points used to test the model's accuracy. The model outputs fitted values ​​through a neural network. The accuracy of the model is evaluated using the relative L2 error between the ground truth data and the fitted values, as shown in the following expression: ; in, This represents the relative L2 error value. Represents true data. This represents the fitted value output by the neural network.

[0046] S6: Input the spatiotemporal coordinates of the point to be solved into the physics prediction model to obtain the predicted physics value of that point.

[0047] In addition, this embodiment also provides a computer device, including a memory and a processor; The memory is used to store computer programs that can run on the processor; When the processor executes the computer program, it implements the steps of the physical field prediction method as described above.

[0048] It should be noted that computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof. These programming languages ​​include object-oriented programming languages—such as Java, Smalltalk, and C++—as well as conventional procedural programming languages—such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a Local Area Network (LAN) or a Wide Area Network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0049] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0050] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the functionality of the unit itself.

[0051] In addition, this embodiment also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the physical field prediction method described above.

[0052] The readable storage medium provided in this application is a computer-readable storage medium, which stores computer-readable program instructions (i.e., a computer program) for performing the above-described physical field prediction method. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as the beneficial effects of the physical field prediction method provided in the above embodiments, and will not be repeated here.

[0053] The above description is only a preferred embodiment of the present invention and does not limit the scope of the present invention. All equivalent structural transformations made under the inventive concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the protection scope of the present invention.

Claims

1. A physical field prediction method based on gradient identification parameter tuning, characterized in that, Includes the following steps: S1: Determine the spatiotemporal computational domain based on the physical problem, and determine the governing equations, initial condition constraints, and boundary condition constraints of the physical problem; S2: Select initial points, boundary points, and internal residual points for calculating the residuals of partial differential equations within the spatiotemporal computation domain to construct a training sample dataset; S3: Initialize the parameters of the neural network, pre-train the neural network, and construct the training loss based on the initial condition constraints, boundary condition constraints, and residuals of the partial differential equations; S4: Obtain the parameters of the pre-trained neural network and identify high-contribution neural blocks; S5: Based on high-contribution neural blocks, the parameters of the neural network junction weights are fine-tuned iteratively to obtain the physical field prediction model. S6: Input the spatiotemporal coordinates of the point to be solved into the physics prediction model to obtain the predicted physics value of that point.

2. The physical field prediction method as described in claim 1, characterized in that, In S3, the neural network uses a binary structure neural network. The neural network architecture includes multiple hidden layers and is set up with binary tree-like hierarchical blocks.

3. The physical field prediction method as described in claim 1, characterized in that, In S3, the neural network is pre-trained using the Adam optimizer. The input is spatiotemporal coordinates, and the output is the predicted physical field value. The activation function is tanh, and the loss function is... The expression is as follows: ； in, This represents the initial condition mean squared error loss. This represents the mean squared error loss due to boundary conditions. This represents the root mean square error loss of the unweighted partial differential equation residuals. This represents the parameters of the neural network.

4. The physical field prediction method as described in claim 1, characterized in that, In S3, during the pre-training of the neural network, the maximum number of iterations is set to 90% of the total number of iterations; During pre-training, after the preset number of iterations is reached, a statistical period is set every certain number of iterations. The average loss function value of the most recent statistical period is calculated, and the relative improvement rate is monitored. The formula for calculating the relative improvement rate is as follows: ； in, Indicates the relative improvement rate. This represents the average loss function value of the previous statistical period. This represents the average loss function value for the current statistical period; When the relative improvement rate is less than the preset threshold, record the current iteration number and end the pre-training process early.

5. The physical field prediction method as described in claim 4, characterized in that, In S4, the process of identifying high-contribution neural blocks includes: Obtain the pre-trained and updated neural network parameters, and compute the set of gradient norms for solving partial differential equations on the internal residual point set. , Residual point The gradient norm; Determine the threshold based on the preset high gradient ratio P. for The (1-P) quantile is used to identify the set of points in the high gradient region; Identifying high-gradient region point sets within the gradient norm set. ,in, Represents the predictive model. This represents the input to the model. Indicates the preset threshold; For each neuron in the last hidden layer of the neural network, the contribution of each neuron on the set of high gradient points is calculated as follows: ； in, Indicates the contribution of a neural block. Indicates nerve block in Activation value at that location, The parameter weight norm represents the neural block; The contribution of the neural block is normalized and calculated as follows: ； in, Indicates the normalized contribution. This indicates the number of neural blocks in the last hidden layer. Indicates nerve block Contribution .

6. The physical field prediction method as described in claim 5, characterized in that, In S5, the parameters of the neural network binding point weights are fine-tuned iteratively, and the process includes: Select the top few neural blocks with the highest contribution to form a subset of adjustable parameters. And freeze the remaining neural network parameters so that the gradient of the frozen neural network parameters is zero in subsequent training and will no longer be updated; The Adam optimizer is used to fine-tune the parameters in the adjustable parameter subset until the total number of iterations is reached.

7. The physical field prediction method as described in claim 6, characterized in that, In S5, the fine-tuning iteration process includes: Recalculate the gradient norm of all internal residual points under the current parameters to obtain the global maximum gradient norm. and global minimum gradient norm ; Based on each residual point The gradient norm is used to assign point weights, where: like Then the weight The calculation expression is: ,otherwise ; The residual loss of the weighted partial differential equation is calculated using the following expression: ； in, Point The residuals of the partial differential equations; The weighted partial differential equation residual loss is used to replace the unweighted partial differential equation residual mean square error loss, and the parameters of the adjustable parameter subset are updated by the total loss function constructed after the replacement.

8. The physical field prediction method as described in claim 7, characterized in that, In S5, after completing the fine-tuning iterations, model accuracy evaluation is also included, and the process includes: Input all spatiotemporal data points used to test the model's accuracy. The model outputs fitted values ​​through a neural network. The accuracy of the model is evaluated using the relative L2 error between the ground truth data and the fitted values, as shown in the following expression: ； in, This represents the relative L2 error value. Represents true data. This represents the fitted value output by the neural network.

9. A computer device, characterized in that, Including memory and processor; The memory is used to store computer programs that can run on the processor; When the processor executes the computer program, it implements the steps of the physical field prediction method as described in any one of claims 1 to 8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the physical field prediction method as described in any one of claims 1 to 8.

Images