A mechanical parameter optimization method based on a physical information neural network

Abstract

This invention discloses a mechanical parameter optimization method based on a physical information neural network, belonging to the fields of mechanical constitutive theory and machine learning technology. The method includes constructing a constitutive model, designing mechanical experiments, acquiring relevant material data and performing normalization processing, and constructing a feedforward neural network model. Through three pre-training iterations, the neural network is progressively optimized to obtain optimized values ​​for material hardening parameters, stress prediction curves, and slip resistance prediction curves. The constitutive model is then used as a loss function for a fourth formal training iteration to obtain the final stress-strain curve. This invention employs a mechanical parameter optimization method based on a physical information neural network, overcoming the shortcomings of traditional methods in handling large differences in magnitude, high parameter sensitivity, and the lack of clear labels. It alleviates the gradient explosion and numerical instability problems caused by exponential terms, ensures that the output satisfies physical constitutive relations and boundary conditions, and achieves high-precision inverse calculation of elastoplastic constitutive parameters under multiple working conditions.

Description

Technical Field

[0001] This invention relates to the fields of mechanical constitutive theory and machine learning technology, and in particular to a method for optimizing mechanical parameters based on a physical information neural network. Background Technology

[0002] Physical Information Neural Networks (PINNs) are a method that directly embeds physical laws into a neural network architecture to solve complex scientific and engineering problems involving partial differential equations. Its core lies in introducing physical constraints into the loss function, enabling the model to not only fit data during training but also follow physical laws, thereby improving prediction accuracy and generalization ability. Compared to traditional numerical methods, PINNs demonstrate advantages in handling high-dimensional problems and complex geometries. In recent years, PINNs have been widely applied in fluid mechanics, heat transfer, and solid mechanics, and various improvement schemes have been continuously developed, such as combining Bayesian methods for uncertainty quantification and optimizing model structure through neural architecture search to improve performance and applicability. Currently, the PINN method for inverse parameter retrieval is mainly used for differential equation problems with relatively clear and simple structures, such as those in fluid mechanics and heat transfer equations. These equations typically have a clear mathematical structure and few parameters, and the parameter positions are fixed or their variation patterns are relatively simple. Therefore, PINNs can effectively inversely retrieve these parameters through their embedded physical constraints.

[0003] However, when using PINN to handle some parameter-sensitive or highly complex partial differential equations, especially those with highly coupled parameters or those highly sensitive to the solution, PINN may struggle to accurately capture these parameters using traditional loss function design. For some inverse problems, particularly those involving highly nonlinear or multi-parameter fitting, PINN is prone to multiple possible solutions, leading to training difficulties or solutions lacking physical meaning. For equations with complex parameter distributions or high sensitivity, higher-order network architectures and more complex regularization methods may be required, significantly increasing the demand for network depth and width. Therefore, although PINN performs well in well-structured differential equations, it still faces challenges when dealing with complex physical systems, necessitating further development and improvement techniques.

[0004] Currently, the PINN method has the following problems in solving complex elastoplastic constitutive models:

[0005] The issue of magnitude differences: There are significant differences in the magnitudes of the physical quantities (such as stress, slip resistance, etc.) and parameters involved in the model. For example, the magnitude of stress data is approximately 10. 3 The magnitude of the slip resistance S may only be 10. -3 .

[0006] Parameter sensitivity issue: Some parameters (such as those related to plastic flow) appear in the exponential term, and small changes in these parameters may cause drastic fluctuations in the network output, leading to gradient explosion or non-convergence of the loss function during training.

[0007] Missing label data: Some physical quantities (such as sliding resistance S) cannot be directly measured in experiments and can only be determined based on their physical meaning. This poses a challenge to the traditional data-driven method of parameter inverse calculation. Summary of the Invention

[0008] The purpose of this invention is to provide a mechanical parameter optimization method based on physical information neural networks. By step-by-step pre-training, the introduction of physical residuals, and normalization processing, it overcomes the shortcomings of traditional methods in handling large differences in magnitude, high parameter sensitivity, and lack of clear labels. It effectively alleviates the gradient explosion and numerical instability caused by exponential terms, ensures that the model output satisfies the physical constitutive relations and boundary conditions, and can achieve high-precision inverse calculation of elastoplastic constitutive parameters under multiple working conditions.

[0009] To achieve the above objectives, this invention provides a method for optimizing mechanical parameters based on a physical information neural network, comprising the following steps:

[0010] S1. Construct a constitutive model, design a mechanical experiment with typical working conditions, obtain the strain data and temperature of the material and perform normalization processing, and construct a feedforward neural network model.

[0011] S2. By controlling the loss function result of the first pre-training stress output value, the feedforward neural network model is first fitted to the stress result, and the parameters of the feedforward neural network model are optimized for the first time.

[0012] S3. Perform a second pre-training on the feedforward neural network model to obtain the initial curve values ​​of the sliding resistance, and simultaneously optimize the parameters of the feedforward neural network model for the second time.

[0013] S4. Solve for the material hardening parameters. Substitute the material hardening parameters, the stress results and the slip resistance results output by S3 into the feedforward neural network model after the second pre-training to perform the third pre-training. Obtain the optimized values ​​of the material hardening parameters, the stress prediction curve and the slip resistance prediction curve. At the same time, optimize the parameters of the feedforward neural network model for the third time.

[0014] S5. Substitute the output of S4 as the initial value into the feedforward neural network model after the third optimization, and use the constitutive model as the loss function to perform the fourth formal training on the feedforward neural network model after the third optimization, so as to obtain the final stress-strain curve and the predicted values ​​of unknown parameters.

[0015] Preferably, S1 specifically includes the following steps:

[0016] S11. Construct the constitutive model as follows:

[0017]

[0018]

[0019] in, Let σ be the strain rate of the material deformation, and σ be the stress. E(T) is the rate of change of stress, and E(T) is the Young's modulus, which is determined by temperature. For reference plastic strain rate, Equivalent plastic strain rate, h S Here, S represents the material hardening parameter, and S represents the slip resistance. S0 represents the rate of change of sliding resistance, T represents the absolute temperature under different operating conditions, and S0 ... represent the values ​​of the two values. sat Let S be the initial and saturation values ​​of the slip resistance S, respectively, and k be the ideal gas constant. The maximum plastic strain rate is given by F0, where F0 represents the Holtzmann activation free energy constant, τ0 is the critical shear stress for plastic deformation, and q1 and p1 are energy-dependent metal material constants. F0, k, T, τ0, q1, and p1 are the regular parameters for plastic flow, and M... S It is a constant; F0, h S τ0, q1, and p1 are unknowns;

[0020] S12. Design a mechanical experiment with typical characteristic working conditions to obtain the material's strain ε and strain rate. The absolute temperature T is then normalized using the following formula:

[0021]

[0022] Where X represents a variable, X min X represents the minimum value among the variables. max This represents the maximum value among the variables. This represents the maximum value within the normalization range. This represents the minimum value within the normalization range;

[0023] S13. Construct a feedforward neural network model and perform the first pre-training. The input layer includes strain ε and strain rate. The temperature is T, the output layer includes stress σ and slip resistance S, and the activation function is the ReLU activation function.

[0024] Preferably, in S2, the stress fitting result is obtained through the loss function L data1 Control, specifically:

[0025]

[0026] Where N is the total number of data points, used to normalize the loss function so that the loss value does not depend on the number of data points, σ pred1 (i) is the stress prediction value of the i-th data point in the first pre-trained model, where i represents the input feature of the i-th data point, and σ exp1 (i) is the true stress value of the i-th data point in the first pre-trained model.

[0027] Preferably, in S3, the second pre-training and acquisition of the preliminary curve values ​​of the slip resistance are as follows:

[0028] S31. Initial value S0 and saturation value S of the slip resistance S. sat Perform normalization processing;

[0029] S32. Perform a second pre-training on the feedforward neural network model after the first pre-training in S1, controlling the loss function L. data2 Obtain the predicted result S of the slip resistance S pred2 And the stress σ prediction results, loss function L data2 for:

[0030]

[0031] Where N is the total number of data points, M is the number of data points corresponding to the empirical value of the slip resistance, that is, the empirical data points corresponding to the maximum / minimum value of the slip resistance, and σ pred2 (i) is the stress prediction value of the i-th data point in the second pre-trained model, where i represents the input feature of the i-th data point, and σ exp2 (i) is the true stress value of the i-th data point in the second pre-trained model, S pred2 (j) is the predicted slip resistance value for the j-th data point in the second pre-trained model, where j represents the input feature of the j-th data point, S exp2 (j) is the empirical true value of the slip resistance at the j-th data point in the second pre-trained model.

[0032] Preferably, in S4, specifically:

[0033] S41. Based on the initial value S0 and saturation value S of the sliding resistance S. sat Solve for the material hardening parameter h S ;

[0034] S42, Set the material hardening parameter h S The stress σ and slip resistance S results output by S3 are substituted into the feedforward neural network model after the second pre-training for the third pre-training. The comprehensive loss function L is controlled by setting weights. data3 L PDE3Obtain the slip resistance S and the material hardening parameter h S Optimized value, loss function L data3 L PDE3 And L are respectively:

[0035]

[0036] L=λ data3 L data3 +λ PDE3 L PDE3 ;

[0037] Where N is the total number of data points, M is the number of data points corresponding to the empirical value of slip resistance, and σ pred3 (i) is the stress prediction value of the i-th data point in the third pre-training, where i represents the input feature of the i-th data point, and σ exp3 (i) is the true stress value of the i-th data point in the third pre-trained model, S pred3 (j) is the predicted slip resistance value for the j-th data point in the third pre-trained model, where j represents the input feature of the j-th data point, and S exp3 (j) is the empirical true value of the slip resistance at the j-th data point in the third pre-trained model. This is the predicted rate of change of slip resistance for the i-th data point in the third pre-trained model, S. pred3 (r) is the predicted slip resistance value for the i-th data point in the third pre-trained model, λ data3 and λ PDE3 These correspond to the weight values ​​of the data-driven loss function and the physical equation loss function of the third pre-trained model, respectively;

[0038] S43. Obtain the stress σ prediction curve and the slip resistance S prediction curve.

[0039] Preferably, in S5, specifically:

[0040] S51, Apply the material hardening parameter h obtained in S4 S The optimized values, the output stress σ prediction curve, and the slip resistance S prediction curve are used as initial values ​​and substituted into the feedforward neural network model after the third optimization. The constitutive model is used as the loss function to further optimize the neural network model. The loss function is:

[0041]

[0042] L=λ data4 L data4 +λ PDE4 L PDE4 ;

[0043] Where N is the total number of data points, M is the number of data points corresponding to the empirical value of slip resistance, and σpred4 (i) is the stress prediction value of the i-th data point in the fourth formal training model, where i represents the input feature of the i-th data point, and σ exp4 (i) is the true stress value of the i-th data point in the fourth formal training model, S pred4 (j) is the predicted slip resistance value for the j-th data point in the fourth formal training model, where j represents the input feature of the j-th data point, S exp4 (j) is the empirical true value of the slip resistance at the j-th data point in the fourth formal training model. In the constitutive model describing the rate of change of slip resistance, This is the predicted rate of change of slip drag corresponding to the physical equation of the r-th data point in the fourth formal training model, S. pred4 (r) is the predicted slip resistance value for the r-th data point in the fourth formal training model. In the constitutive model describing the plastic deformation rate, This is the predicted value of the plastic deformation rate corresponding to the m-th data point in the fourth formal training model, σ. pred4 (m) is the predicted stress value in the physical equation of the m-th data point of the fourth formal training model, S pred4 (m) is the predicted slip resistance value in the physical equation of the m-th data point of the fourth formal training model, λ data4 and λ PDE4 These correspond to the weights of the data-driven loss function and the physical equation loss function of the fourth formal training model, respectively.

[0044] Therefore, this invention adopts the above-mentioned mechanical parameter optimization method based on physical information neural network. Through step-by-step pre-training, introduction of physical residuals and normalization processing, it overcomes the shortcomings of traditional methods in handling large differences in magnitude, high parameter sensitivity and lack of clear labels. It effectively alleviates the gradient explosion and numerical instability caused by exponential terms, ensures that the model output satisfies the physical constitutive relation and boundary conditions, and can achieve high-precision inverse calculation of elastoplastic constitutive parameters under multiple working conditions.

[0045] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0046] Figure 1 This is a flowchart of an embodiment of a mechanical parameter optimization method based on a physical information neural network according to the present invention;

[0047] Figure 2 This is a schematic diagram of a feedforward neural network model, representing an embodiment of a mechanical parameter optimization method based on a physical information neural network according to the present invention.

[0048] Figure 3These are the stress σ prediction curve and the slip resistance S prediction curve obtained after the third pre-training of an embodiment of the mechanical parameter optimization method based on physical information neural network of the present invention.

[0049] Figure 4 This is the stress-strain curve obtained after the fourth formal training of an embodiment of the mechanical parameter optimization method based on physical information neural network of the present invention. Detailed Implementation

[0050] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0051] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0052] Example 1

[0053] This invention provides a method for optimizing mechanical parameters based on a physical information neural network, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0054] S1. Construct a constitutive model and design a mechanical experiment with typical working conditions. The experiment conducted in this embodiment is a uniaxial tensile test of metal. Obtain the strain data and temperature of the material and perform normalization processing to construct a feedforward neural network model.

[0055] S11. Construct the constitutive model as follows:

[0056]

[0057] in, Let σ be the strain rate of the material deformation, and σ be the stress. E(T) is the rate of change of stress, and E(T) is the Young's modulus, which is determined by temperature. For reference plastic strain rate, Equivalent plastic strain rate, h S Here, S represents the material hardening parameter, and S represents the slip resistance. S0 represents the rate of change of sliding resistance, T represents the absolute temperature under different operating conditions, and S0 ... represent the values ​​of the two values. sat Let S be the initial and saturation values ​​of the slip resistance S, respectively, and k be the ideal gas constant. The maximum plastic strain rate is given by F0, where F0 represents the Holtzmann activation free energy constant, τ0 is the critical shear stress for plastic deformation, and q1 and p1 are energy-dependent metal material constants. F0, k, T, τ0, q1, and p1 are the regular parameters for plastic flow, and M... S It is a constant; F0, h S τ0, q1 and p1 are unknowns.

[0058] S12. Design a mechanical experiment with typical characteristic working conditions to obtain the material's strain ε and strain rate. In addition to the absolute temperature T, to prevent overfitting, gradient explosion, and other problems, the above data are normalized so that they can still meet the overall model integrity requirements to a certain extent with a relatively small amount of data. The normalization formula is:

[0059]

[0060] Where X represents a variable, X min X represents the minimum value among the variables. max This represents the maximum value among the variables. This represents the maximum value within the normalization range. This represents the minimum value within the normalization range.

[0061] S13. Construct a feedforward neural network model, as shown in the diagram below. Figure 2 As shown, the first pre-training is performed, and the input layer includes strain ε and strain rate. The temperature is T, the output layer includes stress σ and slip resistance S, the activation function is the ReLU activation function, and in this embodiment, the hidden layer is set to 5 layers, with 50 nodes in each layer.

[0062] S2. By controlling the loss function result of the first pre-trained stress output value, the feedforward neural network model is first fitted with the stress result, thus optimizing the feedforward neural network model parameters for the first time. The stress fitting result is then processed by the loss function L. data1 Control, specifically:

[0063]

[0064] Where N is the total number of data points, used to normalize the loss function so that the loss value does not depend on the number of data points, σ pred1 (i) is the stress prediction value of the i-th data point in the first pre-trained model, where i represents the input feature of the i-th data point, and σexp1 (i) is the true stress value of the i-th data point in the first pre-trained model.

[0065] S3. Perform a second pre-training of the feedforward neural network model to obtain preliminary curve values ​​of slip resistance. Simultaneously, optimize the parameters of the feedforward neural network model for the second time, specifically as follows:

[0066] S31. Initial value S0 and saturation value S of the slip resistance S. sat Normalization is performed.

[0067] S32. Perform a second pre-training on the feedforward neural network model after the first pre-training in S1, controlling the loss function L. data2 Obtain the predicted result S of the slip resistance S pred2 And the stress σ prediction results, loss function L data2 for:

[0068]

[0069] Where N is the total number of data points, M is the number of data points corresponding to the empirical value of the slip resistance, that is, the empirical data points corresponding to the maximum / minimum value of the slip resistance, and σ pred2 (i) is the stress prediction value of the i-th data point in the second pre-trained model, where i represents the input feature of the i-th data point, and σ exp2 (i) is the true stress value of the i-th data point in the second pre-trained model, S pred2 (j) is the predicted slip resistance value for the j-th data point in the second pre-trained model, where j represents the input feature of the j-th data point, S exp2 (j) is the empirical true value of the slip resistance at the j-th data point in the second pre-trained model.

[0070] S4. Solve for the material hardening parameters. Substitute the material hardening parameters, the stress results output from S3, and the slip resistance results into the feedforward neural network model after the second pre-training for a third pre-training. Obtain the optimized values ​​of the material hardening parameters, the stress prediction curve, and the slip resistance prediction curve. Simultaneously, optimize the feedforward neural network model parameters for the third time. Specifically:

[0071] S41. Based on the initial value S0 and saturation value S of the sliding resistance S. sat Solve for the material hardening parameter h S ;

[0072] S42, Set the material hardening parameter h S The stress σ and slip resistance S results output by S3 are substituted into the feedforward neural network model after the second pre-training for the third pre-training. The comprehensive loss function L is controlled by setting weights. data3 LPDE3 Obtain the slip resistance S and the material hardening parameter h S Optimized value, loss function L data3 L PDE3 And L are respectively:

[0073]

[0074] L=λ data3 L data3 +λ PDE3 L PDE3 ;

[0075] Where N is the total number of data points, M is the number of data points corresponding to the empirical value of slip resistance, and σ pred3 (i) is the stress prediction value of the i-th data point in the third pre-trained model, where i represents the input feature of the i-th data point, and σ exp3 (i) is the true stress value of the i-th data point in the third pre-trained model, S pred3 (j) is the predicted slip resistance value for the j-th data point in the third pre-trained model, where j represents the input feature of the j-th data point, and S exp3 (j) is the empirical true value of the slip resistance at the j-th data point in the third pre-trained model, in the constitutive model describing the rate of change of slip resistance. This is the predicted rate of change of slip drag corresponding to the physical equation of the i-th data point in the third pre-trained model, S. pred3 (r) is the predicted slip resistance value corresponding to the physical equation of the i-th data point in the third pre-trained model, λ data3 and λ PDE3 These correspond to the weights of the data-driven loss function and the physical equation loss function in the third pre-training model, respectively. In this embodiment, λ in this training... data3 and λ PDE3 The values ​​are 0.7 and 0.3 respectively.

[0076] S43. Obtain the stress σ prediction curve and the slip resistance S prediction curve. The results are as follows: Figure 3 As shown.

[0077] S5. Substitute the output of S4 as the initial value into the feedforward neural network model after the third optimization, and use the constitutive model as the loss function to perform the fourth formal training on the feedforward neural network model after the third optimization, to obtain the final stress-strain curve and the predicted values ​​of unknown parameters. Specifically:

[0078] S51, Apply the material hardening parameter h obtained in S4 SThe optimized values, the output stress σ prediction curve, and the slip resistance S prediction curve are used as initial values ​​and substituted into the feedforward neural network model after the third optimization. The constitutive model is used as the loss function to further optimize the neural network model. The loss function is:

[0079]

[0080] L=λ data4 L data4 +λ PDE4 L PDE4 ;

[0081] Where N is the total number of data points, M is the number of data points corresponding to the empirical value of slip resistance, and σ pred4 (i) is the stress prediction value of the i-th data point in the fourth formal training model, where i represents the input feature of the i-th data point, and σ exp4 (i) is the true stress value of the i-th data point in the fourth formal training model, S pred4 (j) is the predicted slip resistance value for the j-th data point in the fourth formal training model, where j represents the input feature of the j-th data point, S exp4 (j) is the empirical true value of the slip resistance at the j-th data point in the fourth formal training model. In the constitutive model describing the rate of change of slip resistance, This is the predicted rate of change of slip drag corresponding to the physical equation of the r-th data point in the fourth formal training model, S. pred4 (r) is the predicted slip resistance value corresponding to the physical equation of the r-th data point in the fourth formal training model. In the constitutive model describing the plastic deformation rate, This is the predicted value of the plastic deformation rate corresponding to the m-th data point in the physical equation of the fourth formal training model, σ. pred4 (m) is the predicted stress value in the physical equation of the m-th data point of the fourth formal training model, S pred4 (m) is the predicted slip resistance value in the physical equation of the m-th data point of the fourth formal training model, λ data4 and λ PDE4 These correspond to the weights of the data-driven loss function and the physical equation loss function of the fourth formal training model, respectively.

[0082] In this embodiment, during the fourth formal training session, λ data4 and λ PDE4 Taking values ​​of 0.4 and 0.6 respectively, the final result is as follows: Figure 4 The stress-strain curve shown is used to calculate the root mean square error (RMSE) based on statistical points of existing experimental data. This quantitatively controls the model's fit, ensuring that the RMSE approaches zero after the overall training process, guaranteeing a good fit. The results for other unknown parameters are shown in Table 1.

[0083] Table 1 shows the corresponding prediction parameters generated by the PINN network after deep learning.

[0084]

[0085] Therefore, this invention adopts the above-mentioned mechanical parameter optimization method based on physical information neural network. Through step-by-step pre-training, introduction of physical residuals and normalization processing, it overcomes the shortcomings of traditional methods in handling large differences in magnitude, high parameter sensitivity and lack of clear labels. It effectively alleviates the gradient explosion and numerical instability caused by exponential terms, ensures that the model output satisfies the physical constitutive relation and boundary conditions, and can achieve high-precision inverse calculation of elastoplastic constitutive parameters under multiple working conditions.

[0086] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for optimizing mechanical parameters based on a physical information neural network, characterized in that, Includes the following steps: S1. Construct a constitutive model, design a mechanical experiment with typical working conditions, obtain material strain data and temperature and perform normalization processing, and construct a feedforward neural network model; specifically including the following steps: S11. Construct the constitutive model as follows: ； ； ； in, The strain rate of the material deformation. For stress, E(T) is the rate of change of stress, and E(T) is the Young's modulus, which is determined by temperature. For reference plastic strain rate, Equivalent plastic strain rate, h S Here, S represents the material hardening parameter, and S represents the slip resistance. S0 represents the rate of change of sliding resistance, T represents the absolute temperature under different operating conditions, and S0 ... represent the values ​​of the two values. sat Let S be the initial and saturation values ​​of the slip resistance S, respectively, and k be the ideal gas constant. The maximum plastic strain rate is given by F0, where F0 represents the Holtzmann activation free energy constant, τ0 is the critical shear stress for plastic deformation, and q1 and p1 are energy-dependent metal material constants. F0, k, T, τ0, q1, and p1 are the plastic flow rule parameters, and M... S It is a constant; F0, h S τ0, q1, and p1 are unknowns; S12. Design a mechanical experiment with typical working conditions to obtain the strain of the material. strain rate The absolute temperature T is then normalized using the following formula: ； Where X represents a variable, X min X represents the minimum value among the variables. max This represents the maximum value among the variables. This represents the maximum value within the normalization range. This represents the minimum value within the normalization range; S13. Construct a feedforward neural network model and perform the first pre-training. The input layer includes strain. strain rate Temperature T, the output layer includes stress σ and slip resistance S, and the activation function is the ReLU activation function; S2. By controlling the loss function result of the first pre-training stress output value, the feedforward neural network model is first fitted to the stress result, and the parameters of the feedforward neural network model are optimized for the first time. S3. Perform a second pre-training on the feedforward neural network model to obtain the initial curve values ​​of the sliding resistance, and simultaneously optimize the parameters of the feedforward neural network model for the second time. S4. Solve for the material hardening parameters. Substitute the material hardening parameters, the stress results and the slip resistance results output by S3 into the feedforward neural network model after the second pre-training to perform the third pre-training. Obtain the optimized values ​​of the material hardening parameters, the stress prediction curve and the slip resistance prediction curve. At the same time, optimize the parameters of the feedforward neural network model for the third time. S5. Substitute the output of S4 as the initial value into the feedforward neural network model after the third optimization, and use the constitutive model as the loss function to perform the fourth formal training on the feedforward neural network model after the third optimization, so as to obtain the final stress-strain curve and the predicted values ​​of unknown parameters.

2. The mechanical parameter optimization method based on a physical information neural network according to claim 1, characterized in that: In S2, the stress fitting result is obtained through the loss function L. data1 Control, specifically: ； Where N is the total number of data points, used to normalize the loss function so that the loss value does not depend on the number of data points. This is the stress prediction value for the i-th data point in the first pre-trained model, where i represents the input feature of the i-th data point. It is the true stress value of the i-th data point in the first pre-trained model.

3. The mechanical parameter optimization method based on a physical information neural network according to claim 2, characterized in that: In S3, the second pre-training and the acquisition of the initial curve values ​​for slip resistance are as follows: S31. Initial value S0 and saturation value S of the slip resistance S. sat Perform normalization processing; S32. Perform a second pre-training on the feedforward neural network model after the first pre-training in S1, controlling the loss function L. data2 Obtain the predicted result S of the slip resistance S pred2 And the stress σ prediction results, loss function L data2 for: ； Where N is the total number of data points, and M is the number of data points corresponding to the empirical value of the slip resistance, that is, the empirical data points corresponding to the maximum / minimum value of the slip resistance. This is the stress prediction value of the i-th data point in the second pre-trained model, where i represents the input feature of the i-th data point. This is the true stress value of the i-th data point in the second pre-trained model. This is the predicted slip resistance value for the j-th data point in the second pre-trained model, where j represents the input feature of the j-th data point. It is the empirical true value of the sliding resistance at the j-th data point of the second pre-trained model.

4. The mechanical parameter optimization method based on a physical information neural network according to claim 3, characterized in that: In S4, specifically: S41. Based on the initial value S0 and saturation value S of the sliding resistance S. sat Solve for the material hardening parameter h S ; S42, Set the material hardening parameter h S The stress σ and slip resistance S results output by S3 are substituted into the feedforward neural network model after the second pre-training for the third pre-training. The comprehensive loss function L is controlled by setting weights. data3 L PDE3 Obtain the slip resistance S and the material hardening parameter h S Optimized value, loss function L data3 L PDE3 And L are respectively: ； ； ； Where N is the total number of data points, and M is the number of data points corresponding to the empirical value of slip resistance. This is the stress prediction value of the i-th data point in the third pre-training, where i represents the input feature of the i-th data point. This is the true stress value of the i-th data point in the third pre-trained model. This is the predicted slip resistance value for the j-th data point in the third pre-trained model, where j represents the input feature of the j-th data point. It is the empirical true value of the slip resistance at the j-th data point in the third pre-trained model. This is the predicted rate of change of slip drag for the i-th data point in the third pre-trained model. This is the predicted slip resistance value for the i-th data point in the third pre-trained model. and These correspond to the weight values ​​of the data-driven loss function and the physical equation loss function of the third pre-trained model, respectively; S43. Obtain the stress σ prediction curve and the slip resistance S prediction curve.

5. The mechanical parameter optimization method based on a physical information neural network according to claim 4, characterized in that: In S5, specifically: S51, Apply the material hardening parameter h obtained in S4 S The optimized values, the output stress σ prediction curve, and the slip resistance S prediction curve are used as initial values ​​and substituted into the feedforward neural network model after the third optimization. The constitutive model is used as the loss function to further optimize the neural network model. The loss function is: ； ； ； Where N is the total number of data points, and M is the number of data points corresponding to the empirical value of slip resistance. This is the stress prediction value for the i-th data point in the fourth formal training model, where i represents the input feature of the i-th data point. This is the true stress value of the i-th data point in the fourth formal training of the model. This is the predicted sliding drag value for the j-th data point in the fourth formal training model, where j represents the input feature of the j-th data point. This is the empirical true value of the slip resistance at the j-th data point in the fourth formal training model. In the constitutive model describing the rate of change of slip resistance, This is the fourth time the model has been formally trained. r The physical equations for each data point correspond to the predicted rate of change of slip resistance. This is the fourth time the model has been formally trained. r The predicted slip resistance values ​​for each data point, in the constitutive model describing the plastic deformation rate, This is the predicted value of the plastic deformation rate corresponding to the m-th data point in the fourth formal training model. This is the predicted stress value in the physical equation of the m-th data point of the fourth formal training model. This is the predicted value of slip drag in the physical equation for the m-th data point of the fourth formal training model. and These correspond to the weights of the data-driven loss function and the physical equation loss function of the fourth formal training model, respectively.

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