Mechanical parameter optimization method based on physical information neural network

Abstract

The invention discloses a mechanical parameter optimization method based on a physical information neural network, and belongs to the technical field of mechanical constitutive theory and machine learning, and the method comprises the steps: constructing a constitutive model, designing a mechanical experiment, obtaining related data of a material, carrying out the normalization processing, and constructing a feedforward neural network model. Gradually optimizing the neural network through three times of pre-training to obtain a material hardening parameter optimization value, a stress prediction curve and a slip resistance prediction curve; and performing fourth formal training by taking the constitutive model as a loss function to obtain a final stress-strain curve graph. By the adoption of the mechanical parameter optimization method based on the physical information neural network, the defects that a traditional method is large in processing magnitude difference, high in parameter sensitivity and lack of clear labels are overcome, the problems of gradient explosion and unstable numerical values caused by exponential terms are solved, and the mechanical parameter optimization method based on the physical information neural network is suitable for large-scale popularization and application. It is guaranteed that output meets the physical constitutive relation and boundary conditions, and high-precision reverse solving of the elastic-plastic constitutive parameters is achieved under the multiple working conditions.

Description

Technical Field

[0001] The present invention relates to the technical fields of mechanical constitutive theory and machine learning, and in particular to a mechanical parameter optimization method based on a physics-informed neural network. Background Art

[0002] A physics-informed neural network (PINN) is a method that directly embeds physical laws into the 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 the data but also follow physical laws during the training process, thereby improving the accuracy and generalization ability of predictions. Compared with traditional numerical methods, PINN shows advantages in dealing with high-dimensional problems and complex geometries. In recent years, PINN has been widely applied in fields such as fluid mechanics, heat transfer, and solid mechanics, and various improved schemes have been continuously developed, such as combining Bayesian methods for uncertainty quantification and optimizing the model structure through neural architecture search, etc., to enhance its performance and scope of application. Currently, the inverse parameter calculation using the PINN method is mainly used for differential equation problems with relatively clear and simple structures such as fluid mechanics and heat transfer equations. Such equations usually have a clear mathematical structure and fewer parameters, and the parameter positions are fixed or the variation rules are relatively simple. Therefore, PINN can relatively effectively inverse these parameters through its embedded physical constraints.

[0003] However, when using PINN to handle some partial differential equations with sensitive parameter positions or high complexity, for cases where the parameters in the equation are highly coupled or highly sensitive to the solution, PINN may be difficult to accurately capture these parameters through the traditional loss function design. For some inverse problems, especially those involving highly nonlinear or multi-parameter fitting, PINN is prone to having multiple possible solutions, resulting in difficult convergence during training or the obtained solutions lacking physical meaning. For complex parameter distributions or highly sensitive equations, higher-order network architectures and more complex regularization methods may be required, and at the same time, the requirements for the depth and width of the network also increase significantly. Therefore, although PINN performs well in differential equations with clear structures, it still faces challenges when dealing with complex physical systems and requires further development and improvement of technologies.

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

[0005] Magnitude difference problem: There are significant differences in the physical quantities (such as stress, slip resistance, etc.) and parameter magnitudes involved in the model. For example, the stress data magnitude is about 10 3 while the magnitude of the slip resistance S may be only 10 -3 .

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

[0007] Missing labeled data: Some physical quantities (such as slip resistance S) cannot be directly measured in experiments and can only have their reasonable ranges determined based on physical meanings, which poses challenges to traditional data-driven parameter inverse calculation methods. Summary of the Invention

[0008] The objective of the present invention is to provide a mechanical parameter optimization method based on a physics-informed neural network. By means of step-by-step pre-training, introduction of physical residuals, and normalization processing, it overcomes the deficiencies of traditional methods in dealing with large magnitude differences, high parameter sensitivity, and lack of clear labels, effectively alleviates the gradient explosion and numerical instability problems caused by exponential terms, ensures that the model output satisfies 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 objective, the present invention provides a mechanical parameter optimization method based on a physics-informed neural network, including the following steps:

[0010] S1. Construct a constitutive model, design a mechanical experiment with typical characteristic 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 stress output value in the first pre-training, enable the feedforward neural network model to first fit the stress result and optimize the parameters of the feedforward neural network model for the first time;

[0012] S3. Conduct a second pre-training on the feedforward neural network model to obtain the initial curve value of the slip resistance, and simultaneously optimize the parameters of the feedforward neural network model for the second time;

[0013] S4. Solve the material hardening parameter, substitute the material hardening parameter, the stress result output in S3, and the slip resistance result into the feedforward neural network model after the second pre-training for the third pre-training to obtain the optimized value of the material hardening parameter, the stress prediction curve, and the slip resistance prediction curve, and simultaneously optimize the parameters of the feedforward neural network model for the third time;

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

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

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

[0017]

[0018]

[0019] Among them, is the strain rate of material deformation, σ is the stress, is the stress change rate, E(T) is the Young's modulus determined by temperature, is the reference plastic strain rate, is the equivalent plastic strain rate, h S is the material hardening parameter, S is the slip resistance, is the slip resistance change rate, T represents the absolute temperature under different working conditions, S0 and S sat are the initial value and saturation value of the slip resistance S respectively, k is the ideal gas constant, is the maximum plastic strain rate, F0 represents the Boltzmann activation free energy constant, τ0 is the critical resolved shear stress for plastic deformation, q1 and p1 are energy-related metal material constants; among them F0, k, T, τ0, q1 and p1 are plastic flow rule parameters, M S 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 strain ε, strain rate and absolute temperature T of the material and perform normalization processing. The normalization processing formula is:

[0021]

[0022] Among them, X represents the variable, X min represents the minimum value in the variable, X max represents the maximum value in the variable, represents the maximum value of the normalization range, represents the minimum value of the normalization range;

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

[0024] Preferably, in S2, the stress fitting result is controlled by the loss function L data1 Specifically:

[0025]

[0026] where N is the total number of data points, used to normalize the loss function so that the loss value is independent of the number of data points, and σ pred1 (i) is the predicted stress value of the i-th data point of 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 of the first pre-trained model.

[0027] Preferably, in S3, the second pre-training and obtaining the initial curve value of the slip resistance are specifically as follows:

[0028] S31. Normalize the initial value S0 and the saturation value S of the slip resistance S sat ;

[0029] S32. Perform second pre-training on the feedforward neural network model after the first pre-training of S1, and control the loss function L data2 to obtain the predicted result S of the slip resistance S pred2 and the predicted result of the stress σ. The loss function L data2 is:

[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 corresponding empirical data points where the slip resistance is at the maximum / minimum value, and σ pred2 (i) is the predicted stress value of the i-th data point of 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 of the second pre-trained model, and S pred2 (j) is the predicted slip resistance value of the j-th data point of the second pre-trained model, where j represents the input feature of the j-th data point, and S exp2 (j) is the true empirical value of the slip resistance of the j-th data point of the second pre-trained model.

[0032] Preferably, in S4, it is specifically as follows:

[0033] S41. Solve the material hardening parameter h according to the initial value S0 and the saturation value S of the slip resistance S sat ; S ;

[0034] S42. Substitute the material hardening parameter h S , the stress σ result and the slip resistance S result output by S3 into the feedforward neural network model after the second pre-training for the third pre-training. By setting the weights, control the comprehensive loss function L, and through L 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] Among them, N is the total number of data points, M is the number of data points corresponding to the empirical value of slip resistance, 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, σ exp3 (i) is the true stress value of the i-th data point in the third pre-training model, S pred3 (j) is the slip resistance prediction value of the j-th data point in the third pre-training model, where j represents the input feature of the j-th data point, S exp3 (j) is the true empirical value of the slip resistance of the j-th data point in the third pre-training model, is the predicted value of the slip resistance change rate of the i-th data point in the third pre-training model, S pred3 (r) is the predicted value of the slip resistance of the i-th data point in the third pre-training model, λ data3 and λ PDE3 respectively correspond to the weight values of the data-driven loss function and the physical equation loss function of the third pre-training model;

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

[0039] Preferably, in S5, specifically:

[0040] S51. Substitute the optimized value of the material hardening parameter h S obtained in S4, the predicted curve of the output stress σ and the predicted curve of the slip resistance S as the initial values into the feedforward neural network model optimized for the third time, and use the constitutive model 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] Among them, N is the total number of data points, M is the number of data points corresponding to the empirical value of slip resistance, σpred4 \(\sigma^{(i)}\) is the predicted stress value of the \(i\)-th data point in the fourth formal training model, where \(i\) represents the input features of the \(i\)-th data point, \(\sigma\) exp4 \(\sigma^{(i)}\) is the true stress value of the \(i\)-th data point in the fourth formal training model, \(S\) pred4 \(S^{(j)}\) is the predicted slip resistance value of the \(j\)-th data point in the fourth formal training model, where \(j\) represents the input features of the \(j\)-th data point, \(S\) exp4 \(S^{(j)}\) is the empirical true value of the slip resistance of the \(j\)-th data point in the fourth formal training model. In the constitutive model describing the slip resistance change rate, is the predicted value of the slip resistance change rate corresponding to the physical equation of the \(r\)-th data point in the fourth formal training model, \(S\) pred4 \(S^{(r)}\) is the predicted slip resistance value of the \(r\)-th data point in the fourth formal training model. In the constitutive model describing the plastic deformation rate, is the predicted value of the corresponding plastic deformation rate of the \(m\)-th data point in the fourth formal training model, \(\sigma\) pred4 \(\sigma^{(m)}\) is the predicted stress value in the physical equation of the \(m\)-th data point in the fourth formal training model, \(S\) pred4 \(S^{(m)}\) is the predicted slip resistance value in the physical equation of the \(m\)-th data point in the fourth formal training model, \(\lambda\) data4 and \(\lambda\) PDE4 respectively correspond to the weight values of the data-driven loss function and the physical equation loss function of the fourth formal training model.

[0044] Therefore, the present invention adopts the above-mentioned method for optimizing mechanical parameters based on a physics-informed neural network. Through step-by-step pre-training, introduction of physical residuals, and normalization processing, it overcomes the deficiencies of traditional methods in dealing with large magnitude differences, high parameter sensitivity, and lack of clear labels, effectively alleviates the problems of gradient explosion and numerical instability caused by exponential terms, ensures that the model output satisfies the physical constitutive relationship and boundary conditions, and can achieve high-precision inversion of elastoplastic constitutive parameters under multiple working conditions.

[0045] Next, through the accompanying drawings and embodiments, the technical solutions of the present invention will be further described in detail. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flowchart of an embodiment of the method for optimizing mechanical parameters based on a physics-informed neural network of the present invention;

[0047] Figure 2 is a schematic diagram of a feedforward neural network model of an embodiment of the method for optimizing mechanical parameters based on a physics-informed neural network of the present invention;

[0048] Figure 3It is 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 the physics-informed neural network of the present invention;

[0049] Figure 4 It is the stress-strain curve diagram obtained after the fourth formal training of an embodiment of the mechanical parameter optimization method based on the physics-informed neural network of the present invention. Detailed implementation manners

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

[0051] Unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs. The "first", "second" and similar terms used in the present invention do not denote any order, quantity or importance, but are only used to distinguish different components. The terms such as "including" or "comprising" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left", "right" are only used to represent relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0052] Embodiment 1

[0053] The present invention provides a mechanical parameter optimization method based on a physics-informed neural network, and its process is as Figure 1 shown, including the following steps:

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

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

[0056]

[0057] Wherein, is the strain rate of material deformation, σ is the stress, is the stress change rate, E(T) is the Young's modulus determined by temperature, is the reference plastic strain rate, equivalent plastic strain rate, h S is the material hardening parameter, S is the slip resistance, is the change rate of slip resistance, T represents the absolute temperature under different working conditions, S0 and S sat are the initial value and saturation value of the slip resistance S respectively, k is the ideal gas constant, is the maximum plastic strain rate, F0 represents the Boltzmann activation free energy constant, τ0 is the critical resolved shear stress for plastic deformation, q1 and p1 are energy-related metal material constants; among them F0, k, T, τ0, q1 and p1 are plastic flow rule parameters, M S is a constant; F0, h S 、τ0, q1 and p1 are unknowns.

[0058] Design a mechanical experiment with typical characteristic working conditions, and obtain the strain ε, strain rate and absolute temperature T of the material. In order to prevent problems such as overfitting and gradient explosion, normalize the above data so that it can also meet the overall model integrity requirements to a certain extent with less data volume. The normalization formula is:

[0059]

[0060] Among them, X represents the variable, X min represents the minimum value in the variable, X max represents the maximum value in the variable, represents the maximum value of the normalization range, represents the minimum value of the normalization range.

[0061] S13. Construct a feedforward neural network model. The model is shown as Figure 2 shown. Conduct the first pre-training. The input layer includes strain ε, strain rate temperature T, and the output layer includes stress σ and slip resistance S. The activation function is the relu activation function. 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 stress output value of the first pre-training, make the feedforward neural network model first fit the stress result and optimize the parameters of the feedforward neural network model for the first time. The stress fitting result is controlled by the loss function L data1 Specifically:

[0063]

[0064] Among them, 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 of the first pre-training model, where i represents the input feature of the i-th data point, σexp1 σ(i) is the true stress value of the i-th data point of the first pre-trained model.

[0065] S3. Conduct the second pre-training on the feedforward neural network model to obtain the preliminary curve value of the slip resistance, and simultaneously optimize the parameters of the feedforward neural network model for the second time. Specifically:

[0066] S31. Normalize the initial value S0 and the saturation value S of the slip resistance S sat for processing.

[0067] S32. Conduct the second pre-training on the feedforward neural network model after the first pre-training of S1, and control the loss function L data2 to obtain the prediction result Ŝ of the slip resistance S pred2 and the prediction result of the stress σ. The loss function L data2 is:

[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 corresponding empirical data points where the slip resistance is at the maximum / minimum value, σ pred2 σ(i) is the predicted stress value of the i-th data point of the second pre-trained model, where i represents the input feature of the i-th data point, and σ exp2 σ(i) is the true stress value of the i-th data point of the second pre-trained model, and S pred2 Ŝ(j) is the predicted slip resistance value of the j-th data point of the second pre-trained model, where j represents the input feature of the j-th data point, and S exp2 Ŝ(j) is the true empirical value of the slip resistance of the j-th data point of the second pre-trained model.

[0070] S4. Solve the material hardening parameter, substitute the material hardening parameter, the stress result and the slip resistance result output by S3 into the feedforward neural network model after the end of the second pre-training for the third pre-training to obtain the optimized value of the material hardening parameter, the stress prediction curve and the slip resistance prediction curve, and simultaneously optimize the parameters of the feedforward neural network model for the third time. Specifically:

[0071] S41. Solve the material hardening parameter h sat according to the initial value S0 and the saturation value S of the slip resistance S S ;

[0072] S42. Substitute the material hardening parameter h S , the stress σ result and the slip resistance S result output by S3 into the feedforward neural network model after the second pre-training for the third pre-training, control the comprehensive loss function L by setting the weight, and through L 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, σ pred3 (i) is the stress prediction value of the i-th data point of the third pre-training model, where i represents the input feature of the i-th data point, σ exp3 (i) is the true stress value of the i-th data point of the third pre-training model, S pred3 (j) is the slip resistance prediction value of the j-th data point of the third pre-training model, where j represents the input feature of the j-th data point, S exp3 (j) is the true empirical value of the slip resistance of the j-th data point of the third pre-training model. In the constitutive model describing the slip resistance change rate is the predicted value of the slip resistance change rate corresponding to the physical equation of the i-th data point of the third pre-training model, S pred3 (r) is the predicted value of the slip resistance corresponding to the physical equation of the i-th data point of the third pre-training model, λ data3 and λ PDE3 respectively correspond to the weight values of the data-driven loss function and the physical equation loss function of the third pre-training model. In this embodiment, in this training, λ data3 and λ PDE3 take values of 0.7 and 0.3 respectively.

[0076] S43. Obtain the predicted curve of stress σ and the predicted curve of slip resistance S, and the results are as Figure 3 shown.

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

[0078] S51. Substitute the material hardening parameter h obtained from S4 SThe optimized values, the predicted stress σ curve and the predicted slip resistance S curve are substituted into the feedforward neural network model optimized for the third time as initial values, and the constitutive model is used as the loss function to further optimize the neural network model. The loss function is as follows:

[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 values of slip resistance, σ pred4 (i) is the predicted stress value of the i-th data point of the fourth formal training model, where i represents the input feature of the i-th data point, σ exp4 (i) is the true stress value of the i-th data point of the fourth formal training model, S pred4 (j) is the predicted slip resistance value of the j-th data point of the fourth formal training model, where j represents the input feature of the j-th data point, S exp4 (j) is the true empirical value of the slip resistance of the j-th data point of the fourth formal training model. In the constitutive model describing the slip resistance change rate, is the predicted value of the slip resistance change rate corresponding to the physical equation of the r-th data point of 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 of the fourth formal training model. In the constitutive model describing the plastic deformation rate, is the predicted value of the plastic deformation rate corresponding to the physical equation of the m-th data point 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 correspond to the weight values of the data-driven loss function and the physical equation loss function of the fourth formal training model respectively.

[0082] In this embodiment, in the fourth formal training, λ data4 and λ PDE4 are respectively taken as 0.4 and 0.6, and finally the stress-strain curve diagram as shown in Figure 4 is generated. The root mean square error RMSE is calculated for the statistical points of the existing experimental data, and the fitting degree of the model is quantified and controlled. After the overall training process, the size of RMSE approaches 0, ensuring the sufficient fitting degree of the model. In addition, the results of the other unknown parameters are shown in Table 1:

[0083] Table 1 generates corresponding prediction parameters through the PINN network after deep learning

[0084]

[0085] Therefore, the present invention adopts the above-mentioned mechanical parameter optimization method based on the physics-informed neural network. Through step-by-step pre-training, physical residual introduction, and normalization processing, it overcomes the deficiencies of traditional methods in dealing with large magnitude differences, high parameter sensitivity, and lack of clear labels, effectively alleviates the gradient explosion and numerical instability problems caused by exponential terms, ensures that the model output satisfies the physical constitutive relationship and boundary conditions, and can achieve high-precision inverse solution 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 are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A mechanical parameter optimization method based on a physics-informed neural network, characterized in that Including the following steps: S1. Construct a constitutive model, design a mechanical experiment with typical characteristic working conditions, obtain the strain data and temperature of the material and perform normalization processing, and construct a feedforward neural network model; S2. By controlling the loss function result of the first pre-training stress output value, make the feedforward neural network model first fit the stress result, and optimize the parameters of the feedforward neural network model for the first time; S3. Conduct a second pre-training on the feedforward neural network model, obtain the preliminary curve value of the slip resistance, and optimize the parameters of the feedforward neural network model for the second time; S4. Solve the material hardening parameter, substitute the material hardening parameter, the stress result and the slip resistance result output by S3 into the feedforward neural network model after the end of the second pre-training for the third pre-training, obtain the optimized value of the material hardening parameter, the stress prediction curve and the slip resistance prediction curve, and optimize the parameters of the feedforward neural network model for the third time; S5. Substitute the output result of S4 as the initial value into the feedforward neural network model optimized for the third time, use the constitutive model as the loss function to conduct the fourth formal training on the feedforward neural network model optimized for the third time, and obtain the final stress-strain curve graph and the predicted values of unknown parameters.

2. The mechanical parameter optimization method based on a physics-informed neural network according to claim 1, wherein: In S1, it specifically includes the following steps: S11. Construct the constitutive model as follows: Among them, is the material deformation strain rate, σ is the stress, is the stress change rate, E(T) is the Young's modulus determined by temperature, is the reference plastic strain rate, equivalent plastic strain rate, h S is the material hardening parameter, S is the slip resistance, is the slip resistance change rate, T represents the absolute temperature under different working conditions, S0 and S sat are respectively the initial value and the saturation value of the slip resistance S, k is the ideal gas constant, is the maximum plastic strain rate, F0 represents the Boltzmann activation free energy constant, τ0 is the critical resolved shear stress for plastic deformation, q1 and p1 are energy-related metal material constants; among them F0, k, T, τ0, q1 and p1 are plastic flow rule parameters, M S is a constant; F0, h S 、τ0, q1 and p1 are unknowns; S12. Design a mechanical experiment with typical characteristic working conditions to obtain the strain ε, strain rate and absolute temperature T of the material, and perform normalization processing. The normalization processing formula is as follows: Among them, X represents a variable, and X min represents the minimum value among the variables, and X max represents the maximum value among the variables, represents the maximum value of the normalization range, represents the minimum value of the normalization range; S13. Construct a feedforward neural network model and conduct the first pre-training. The input layer includes strain ε, strain rate temperature T, and the output layer includes stress σ and slip resistance S. The activation function is the relu activation function.

3. The mechanical parameter optimization method based on a physics-informed neural network according to claim 2, characterized in that: In S2, the stress fitting result is controlled by the loss function L data1 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, and σ pred1 (i) is the predicted stress value of the i-th data point of 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 of the first pre-trained model.

4. The mechanical parameter optimization method based on a physics-informed neural network according to claim 3, characterized in that: In S3, the second pre-training and obtaining the preliminary curve value of the slip resistance are specifically as follows: S31. Normalize the initial value S0 and the saturation value S of the slip resistance S sat ; S32. Perform a second pre-training on the feedforward neural network model after the first pre-training of S1, and control the loss function L data2 Obtain the prediction result Ŝ of the slip resistance S pred2 And the prediction result of the stress σ, the loss function L data2 is: 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 corresponding empirical data points where the slip resistance is at the maximum / minimum value, σ pred2 (i) is the predicted stress value of the i-th data point of the second pre-trained model, where i represents the input feature of the i-th data point, σ exp2 (i) is the true stress value of the i-th data point of the second pre-trained model, S pred2 (j) is the predicted slip resistance value of the j-th data point of the second pre-trained model, where j represents the input feature of the j-th data point, S exp2 (j) is the true empirical value of the slip resistance of the j-th data point of the second pre-trained model.

5. The mechanical parameter optimization method based on the physics-informed neural network according to claim 4, wherein: In S4, it is specifically as follows: S41. Solve for the material hardening parameter h according to the initial value S0 and the saturation value S of the slip resistance S sat S ;​ S42. Substitute the material hardening parameter h S , the stress σ result and the slip resistance S result output by S3 into the feedforward neural network model after the second pre-training for the third pre-training. Control the comprehensive loss function L by setting the weights. Through L data3 , L PDE3 Obtain the optimized values of the slip resistance S and the material hardening parameter h S . The loss functions L data3 , L PDE3 And L are respectively: L = λ data3 L data3 + λ PDE3 L PDE3 ; 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, 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, σ exp3 (i) is the true stress value of the i-th data point in the third pre-training model, S pred3 (j) is the predicted slip resistance value of the j-th data point in the third pre-training model, where j represents the input feature of the j-th data point, S exp3 (j) is the true empirical slip resistance value of the j-th data point in the third pre-training model, is the predicted slip resistance change rate value of the i-th data point in the third pre-training model, S pred3 (r) is the predicted slip resistance value of the i-th data point in the third pre-training model, λ data3 and λ PDE3 correspond to the weight values of the data-driven loss function and the physical equation loss function of the third pre-training model, respectively; S43. Obtain the stress σ prediction curve and the slip resistance S prediction curve.

6. The mechanical parameter optimization method based on the physics-informed neural network according to claim 5, characterized in that: In S5, it is specifically as follows: S51. Substitute the material hardening parameter h obtained in S4 S The optimized value, the predicted stress σ curve and the predicted slip resistance S curve are used as the initial values and substituted into the feedforward neural network model optimized for the third time. The constitutive model is used as the loss function to further optimize the neural network model. The loss function is as follows: L = λ data4 L data4 + λ PDE4 L PDE4 ; where N is the total number of data points, M is the number of data points corresponding to the empirical value of slip resistance, σ pred4 (i) is the predicted stress value of the i-th data point in the fourth official training model, where i represents the input feature of the i-th data point, σ exp4 (i) is the true stress value of the i-th data point in the fourth official training model, S pred4 (j) is the predicted slip resistance value of the j-th data point in the fourth official training model, where j represents the input feature of the j-th data point, S exp4 (j) is the true empirical slip resistance value of the j-th data point in the fourth official training model. In the constitutive model describing the slip resistance change rate, is the predicted slip resistance change rate corresponding to the physical equation of the r-th data point in the fourth official training model, S pred4 (r) is the predicted slip resistance value of the r-th data point in the fourth official training model. In the constitutive model describing the plastic deformation rate, is the predicted value of the corresponding plastic deformation rate of the m-th data point in the fourth official training model, σ pred4 (m) is the predicted stress value in the physical equation of the m-th data point in the fourth official training model, S pred4 (m) is the predicted slip resistance value in the physical equation of the m-th data point in the fourth official training model, λ data4 and λ PDE4 correspond to the weight values of the data-driven loss function and the physical equation loss function of the fourth official training model, respectively.

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