Physical field stability prediction method based on PINN-WL
By integrating physical mechanisms and adjusting weights into a neural network model, the PINN-WL method was used to solve the problem of unstable physical field prediction in the structural design of airborne active phased array radar, achieving high-precision and efficient simulation results.
Patent Information
- Application Number
- CN202511522414.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-23
- Publication Date
- 2026-01-13
AI Technical Summary
Existing machine learning methods struggle to achieve accurate and stable prediction of physical fields in the structural design of airborne active phased array radars, especially in small-batch production modes where data acquisition is difficult and costly, and existing data and mechanism fusion methods suffer from instability in prediction.
The PINN-WL-based approach incorporates physical mechanisms as regularization terms into the loss function of the neural network model. The model weights are adjusted by calculating the variance of the prediction error, and the gradient descent optimization algorithm is used to minimize the loss function in order to search for the optimal parameters.
Stable prediction of physical fields in radar structure design has been achieved, improving the accuracy and efficiency of simulation and solving the problem of unstable prediction in existing technologies.
Smart Images
Figure CN121328322A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the field of electronic device structure design simulation and artificial intelligence, and particularly relates to a physical field stability prediction method based on PINN-WL. BACKGROUND
[0002] The structure design of an airborne active phased array radar is the key to ensure the high performance of the radar, and the accuracy, efficiency and stability of the prediction error of the structure design simulation, i.e., the physical field prediction, are the basis for realizing reasonable structure design.
[0003] Existing simulation software is based on the finite element / volume principle, and it is difficult to meet the needs of simulation efficiency and accuracy at the same time. Building a data-driven simulation surrogate model is a cutting-edge research direction, which uses machine learning and other data processing technologies to establish a complex mapping relationship between structure design variables and physical fields. However, existing surrogate models need a large number of training samples to build data-driven models, and it is difficult and costly to obtain radar structure data under the small-batch production mode, making it difficult to achieve accurate and stable physical field prediction.
[0004] The data and mechanism fusion method combines data-driven models with mechanism models, which is an effective means of physical field prediction in structure design. It has the advantages of both data-driven methods and mechanism modeling methods, and may also avoid their limitations. In the field of machine learning, Physics-informed Neural Network (PINN) is a general data and mechanism fusion paradigm that uses mechanism knowledge as a regularization term to constrain the solution space of the machine learning model. However, existing data and mechanism fusion methods represented by PINN still have the problem of unstable prediction, i.e., the potential advantages of PINN have not been fully utilized, especially when the mechanism model is inaccurate or the data is noisy. Inaccurate mechanism priors have an uncertain guiding effect on data-driven models. How to effectively utilize the information provided by both models is an urgent problem to be solved, and model weight balancing may be a potential effective way. In some research on weighting and balancing of two models in data and mechanism fusion methods, the mechanism model and the data-driven model are weighted according to specific problems or experimental verification results, but the empirical weighting method is difficult to obtain a set of optimal weights. In addition, some weighting methods train the weights of the model together with the parameters of the model, and finally converge to an optimal solution. The problem with this method is the lack of interpretability of the weights, and more importantly, the purpose of the research is not to ensure the stability of the prediction error of the model, but the convergence and prediction accuracy of the model. Therefore, a new data and mechanism fusion method is needed to make the information of the mechanism model and the data model be utilized as reasonably as possible to realize the stable prediction of the physical field in radar structure design. SUMMARY
[0005] To solve the above problems, the application provides a physical field stability prediction method based on PINN-WL, comprising:
[0006] Step 1: constructing a neural network model;
[0007] Step 2: fusing a physical mechanism as a regularization term into a loss function of the neural network model to become a mechanism model part of the loss function, so that the loss function contains the mechanism model part and a data-driven model part possessed by the device itself;
[0008] Step 3: training the neural network model, using a gradient descent optimization algorithm to minimize the loss function to search for optimal parameters .
[0009] Preferably, in step 3, during the training process, for each batch of training data, the variance of the prediction error of the data-driven model part and the variance of the prediction error of the mechanism model part are calculated respectively; the reciprocal of the variance of the prediction error of the data-driven model part is taken as the weight correction term of the data-driven model part, and the reciprocal of the variance of the prediction error of the mechanism model part is taken as the weight correction term of the mechanism model part, to obtain a modified loss function.
[0010] Preferably, a sample database is established before step 3, and the sample database includes input x collected by simulation software and physical field u data corresponding to the input x.
[0011] Preferably, the loss function of the data-driven model part is:
[0012] ;
[0013] wherein, is the predicted target output of the neural network for the input , and u is the true label of the data, .
[0014] Preferably, the loss function of the mechanism model part is:
[0015] ;
[0016] wherein, is a general form of a differential equation parameterized by , the solution of the differential equation is , and is defined in the number domain ; for time series problems, time t is considered as a special component of , and contains the time domain.
[0017] Preferably, the formulas for calculating the variance of the prediction error of the data-driven model part and the variance of the prediction error of the mechanistic model part are as follows:
[0018] ;
[0019] This is the current prediction error of the model. It is the expected prediction error of the model.
[0020] Preferably, the corrected loss function is:
[0021] ;
[0022] in and These are the mean square error (MSE) of the predictions for the data-driven model and the mechanistic model, respectively. and These represent the variances of the prediction errors of the two models, respectively. This is the current predicted output value of the data-driven model. These are data labels. This is the current predicted output value of the mechanistic model.
[0023] (1) This invention solves the problem of poor stability of physical field simulation in the structural design of active phased array radar by establishing a physical field stability prediction model based on PINN-WL, and can ensure the accuracy and efficiency of simulation.
[0024] (2) This invention is a general simulation technology with the ability to solve common simulation problems and can be promoted and applied in the field of electronic equipment structure design in aerospace. Attached Figure Description
[0025] Figure 1 This is the overall framework diagram of PINN based on weight correction. Detailed Implementation
[0026] For the purposes of making the objects, technical solutions and advantages of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the drawings in the embodiments of the present application. Identical or similar reference numerals are used to represent identical or similar elements or elements having identical or similar functions throughout the drawings. The described embodiments are part of the embodiments of the present application, rather than all the embodiments of the present application. The embodiments described below with reference to the drawings are exemplary and are intended to explain the present application, and cannot be understood as a limitation of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the scope of protection of the present application. The embodiments of the present application will be described in detail below with reference to the drawings. A physical field stable prediction method based on PINN-WL, characterized in that: the solution of a differential equation is expressed as a neural network through PINN, the solving process of the differential equation is converted into the training process of the neural network, a multi-physical field partial differential equation is introduced as a regularization term of a loss function, weights are assigned to a multi-physical field model loss function and a data model loss function based on uncertainty evaluation, the solution space of the neural network is jointly constrained, and finally the differential equation is solved through PINN-WL, the prediction error stability is improved, and stable prediction of the physical field is realized.
[0027] A physical field stable prediction method based on PINN-WL, characterized in that: the definition of the physical field prediction error stability is that, given training data and test data , a physical field prediction model f is trained on and tested on , for the regression problem of physical field prediction, given a test sample i in the test data , the test error of the test sample i refers to the gap between the output of the prediction model for the sample i and the true label of the sample i, which can be measured by the absolute error (AE):
[0028] (1)
[0029] wherein and are the output of the prediction model f for the test sample i and the true label of the test sample i, respectively. For all test samples in the test data , their test errors can be expressed as a vector , wherein d is the number of test samples.
[0030] The prediction accuracy of the physical field prediction model can be represented by the average absolute error of all test samples:
[0031] (2)
[0032] The prediction error stability of the physical field prediction model can be represented by the variance of all test sample errors:
[0033] (3)
[0034] The PINN construction method is to consider a general form of parameterized differential equations, the solution of the differential equation is , and is defined in the number field :
[0035] (4)
[0036] For time series problems, time t is considered as a special component of , containing the time domain.
[0037] In the physical field prediction problem of radar structure design, a neural network is constructed to establish the mapping relationship between the input (such as Euclidean space coordinates and time t) and the predicted target output u (such as stress, flow rate, pressure, temperature, etc. Physical quantity). is the set of all weight matrices in the neural network . Therefore, the loss function of the data-driven model can be set as the mean square error loss:
[0038] (5)
[0039] Where is the predicted target output of the neural network for the input , and u is the true label of the data. In order to constrain the solution space of the neural network, the physical mechanism (such as heat conduction mechanism) is fused into the loss function of the neural network model as a regularization term:
[0040] (6)
[0041] The loss function weight correction strategy of the mechanism model and the data model is that the uncertainty of the mechanism model and the data-driven model is quantified by the variance of the prediction error of the two models. For each batch of training data, calculate the variance of the neural network model prediction error and the variance of the mechanism model prediction error:
[0042] (7)
[0043] Where is the current prediction error of the model, is the expected prediction error of the model. The inverse of the prediction error variance is taken as the weight, which is assigned to the loss function of the mechanism model part and the data-driven model part:
[0044] (8)
[0045] where and are the prediction mean square error (MSE) of the data-driven model part and the mechanism model part, respectively, and are the variances of the prediction error of the two models, respectively, is the current prediction output value of the data-driven model part, is the label of the data, is the current prediction output value of the mechanism model part.
[0046] The training method of the PINN-WL is to minimize the loss function using the gradient descent optimization algorithm to search for the optimal parameters .
[0047] With the aid of the accompanying drawings, including as shown in Figure 1 the following specific steps are included:
[0048] Step 1: Construct a neural network to establish the mapping relationship between the input and the predicted target output u, such as in temperature field prediction, x is the vector of Euclidean space coordinates and time t, and u is the temperature field.
[0049] Step 2: To constrain the solution space of the neural network, the physical mechanism is integrated into the loss function of the neural network model as a regularization term, such as in thermal simulation, the heat conduction equation is used as the loss function of the mechanism model:
[0050]
[0051] Step 3: Training sample database establishment; collect the physical field u data corresponding to the input x through simulation software as training data, such as in thermal simulation, collect the temperature field data corresponding to the coordinates and time through Comsol software.
[0052] Step 4: Training of PINN-WL; minimize the loss function using the gradient descent optimization algorithm to search for the optimal parameters The PINN-WL model is trained. Meanwhile, for each batch of training data, the variance of the prediction error of the neural network model and the variance of the prediction error of the mechanism model are calculated, and the inverse of the variance of the prediction error is taken as a weight correction term and distributed to the loss functions of the mechanism model part and the data-driven model part.
[0053] The parameters of the overall structure of the model are studied, including the stacking depth of the neural network model, the number of neurons of each layer, the selection of the activation function, etc. The single control variable method is used for experiments to quantitatively analyze the influence of different parameters on the overall performance of the model, and the optimal value of each parameter is selected for the final thermal simulation.
[0054] Taking a thermal simulation case as an example, the structure and hyperparameters of the neural network model are as follows: the network has 5 layers, of which 3 are hidden layers; the input node is 4, the node of each hidden layer is 50, and the output is 1 node, i.e., the temperature of the current time and coordinate point.
[0055] Step 6: Physical field stability prediction based on PINN-WL; in the physical field prediction process, the newly acquired x is taken as the input of the PINN-WL model trained in the above steps, and the physical quantity u corresponding to the current input x can be output, and the physical quantities corresponding to all x are calculated to obtain the current physical field.
[0056] The above is only a specific embodiment of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.
Claims
1. A PINN-WL-based physical field stability prediction method, characterized in that, The method comprises the following steps: Step 1: constructing a neural network model; Step 2: fusing a physical mechanism as a regularization term into a loss function of the neural network model to become a mechanism model part of the loss function, and the loss function comprises the mechanism model part and a data-driven model part possessed by the device itself; Step 3: Train the neural network model using an optimization algorithm such as gradient descent to minimize the loss function and search for the optimal parameters .
2. The PINN-WL based physical field stable prediction method of claim 1, wherein, The method comprises the following steps: In step 3, in the training process, for each batch of training data, the variance of the prediction error of the data-driven model part and the variance of the prediction error of the mechanism model part are calculated respectively; The reciprocal of the variance of the prediction error of the data-driven model part is taken as a weight correction term of the data-driven model part, and the reciprocal of the variance of the prediction error of the mechanism model part is taken as a weight correction term of the mechanism model part to obtain a modified loss function.
3. The PINN-WL based physical field stabilization prediction method of claim 1, wherein, Before step 3, a sample database is established, and the sample database comprises input x collected by simulation software and physical field u data corresponding to the input x.
4. The PINN-WL based physical field stabilization prediction method of claim 1, wherein, The loss function of the data-driven model part is: ； wherein, is the predicted target output of the neural network for input u is the true label of the data, is.
5. The PINN-WL based physical field stabilization prediction method of claim 1, wherein, The loss function of the mechanism model part is: ； wherein, is a general form of a parameterized differential equation, the solution of the differential equation is , and , and is defined on the number field ; for a time series problem, time t is considered as a special component of , and contains the time domain.
6. The PINN-WL based physical field stabilization prediction method of claim 1, wherein, The formula for calculating the variance of the prediction error of the data-driven model part and the variance of the prediction error of the mechanism model part is: ； is the model's current prediction error, is the model's expected prediction error.
7. The PINN-WL based physical field stabilization prediction method of claim 1, wherein, The modified loss function is: ； wherein and are the prediction Mean Square Error (MSE) of the data-driven model part and the mechanistic model part, respectively, and are the variances of the prediction errors of the two models, respectively, is the current prediction output value of the data-driven model part, is the label of the data, is the current prediction output value of the mechanistic model part.