Method for identifying mechanical properties of heterogeneous materials based on physical information neural networks

Abstract

The application provides a heterogeneous material mechanical property identification method based on a physical information neural network, comprising: obtaining full-field strain data of a to-be-tested heterogeneous material under mechanical load, and constructing a training data set; constructing a physical information neural network, taking spatial coordinates as input, and outputting displacement field and material parameter field of the to-be-tested heterogeneous material; a total loss function adopted comprises a data loss term and a physical equation loss term; in the training process of the physical information neural network, the weight coefficients of the loss terms in the total loss function are dynamically adjusted, and the adjustment mode is: calculating the gradient norm of each loss term on the network trainable parameters, and updating the corresponding weight coefficient according to the deviation of the gradient norm of each loss term and the target gradient; using the training data set, taking the total loss function with the dynamically adjusted weight as an optimization target, training the physical information neural network; and outputting the mechanical property identification result of the to-be-tested heterogeneous material through the trained physical information neural network.

Description

Technical Field

[0001] This invention belongs to the fields of computational mechanics and artificial intelligence, specifically relating to a method for identifying the mechanical properties of heterogeneous materials based on physical information neural networks. Background Technology

[0002] Heterogeneous materials are widely found in many key fields such as engineering construction, aerospace, and biomedicine. They include soil and rock masses, composite laminated structures, functionally graded materials, and biological soft tissues. The spatial distribution of their internal mechanical parameters is significantly heterogeneous. Accurately identifying the mechanical properties and parameter distribution of these materials is the core foundation for engineering and medical applications such as slope stability assessment in geotechnical engineering, support design of underground structures, non-destructive testing and fatigue life prediction of aerospace composite components, non-invasive diagnosis of soft tissue tumors, and pathological analysis of cardiovascular diseases. It directly determines the safety of structural design, the reliability of test results, and the accuracy of disease diagnosis.

[0003] Traditional methods for identifying mechanical parameters of heterogeneous materials mainly rely on finite element model updates and iterative optimizations. This requires repeatedly solving forward mechanical problems, resulting in extremely high computational costs. Furthermore, these methods are highly sensitive to initial parameter values ​​and easily get trapped in local optima, making them unsuitable for identifying parameters in complex heterogeneous distributions. While pure data-driven deep learning methods have emerged in recent years and possess powerful nonlinear fitting capabilities, they require a large amount of well-labeled experimental data for training. However, testing the mechanical properties of heterogeneous materials is costly and difficult to obtain samples, especially in special scenarios such as living biological tissues, where sufficient labeled data is almost impossible to acquire, severely limiting the practical application of these methods. The emergence of Physical Information Neural Networks (PINNs) offers a novel approach to resolving this contradiction. This method embeds the fundamental governing equations of solid mechanics as soft constraints into the training process of the neural network. By leveraging prior physical information, it significantly reduces the need for training data and maintains good fitting and prediction capabilities even in small-sample scenarios, making it a research hotspot in the field of identifying mechanical parameters of heterogeneous materials.

[0004] However, in practical engineering applications, existing physical information neural network methods still face many technical bottlenecks that urgently need to be addressed. First, the training optimization objective of PINN is usually composed of multiple loss terms, including data loss terms that fit the measured data and PDE residual loss terms that satisfy the mechanical control equations. The magnitudes of different loss terms often differ by several orders of magnitude. Most existing methods use fixed weights to sum the multiple loss terms. Improper weight settings can easily lead to training imbalance. The loss term with the dominant magnitude will completely dominate the optimization direction of the network, while the other loss terms will be ignored by the model. Ultimately, the network output may fit the measured strain data, but it may violate the basic mechanical laws, directly causing the material parameter identification results to be distorted. Manually adjusting the weights requires a lot of trial and error for different materials and working conditions, lacking a unified adaptation criterion, resulting in extremely poor engineering practicality. Secondly, the training process of PINN is a typical highly non-convex optimization problem, especially in the scenario of identifying parameters of heterogeneous materials. The spatial distribution of material parameters exhibits strong nonlinearity, and a training strategy with a fixed learning rate is prone to problems such as oscillation and non-convergence in the early stages of training and failure to converge to the global optimum in the later stages. Manually adjusting the learning rate requires operators to have experience in both deep learning and computational mechanics, and requires monitoring the entire training process, which is time-consuming and labor-intensive, and cannot meet the needs of automated and batch engineering inspection. In addition, the optimal training parameters of existing methods do not have cross-scenario adaptability. The loss weights and learning rates optimized for a specific material, specific geometry, and specific load condition often result in a significant drop in recognition accuracy or even complete failure to converge when applied to other application scenarios. This makes it unsuitable for the diverse types of heterogeneous materials and the complex and variable working conditions required in practical applications, severely limiting the large-scale deployment of this technology. Summary of the Invention

[0005] To address the shortcomings and deficiencies of existing technologies, this invention provides a method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network. This method addresses the core problems of existing physical information neural networks in identifying the mechanical parameters of heterogeneous materials, including multi-loss term training imbalance, difficulty in manually adjusting hyperparameters, poor training convergence stability, and insufficient identification accuracy in small sample scenarios. Based on the full-field strain data of heterogeneous materials under mechanical loads, a physical information neural network architecture capable of simultaneously outputting displacement and material parameter fields is constructed. The solid mechanics momentum balance equation is embedded as a physical constraint in the network training process. The core design is based on… The dynamic loss weight adaptive adjustment mechanism based on the gradient equality principle calculates the gradient norm of each loss term with respect to the trainable parameters of the network. Using the statistical mean of all gradient norms as the balancing target, it dynamically updates the corresponding weight coefficients based on the deviation between the gradient norm of each loss term and the target gradient. This automatically balances the optimization priorities of data fitting and physical constraints, fundamentally solving the industry pain point of imbalanced training with multiple loss terms. Simultaneously, a dynamic learning rate adjustment mechanism based on the loss convergence state is designed, adaptively adjusting the optimization step size according to changes in loss during training. This effectively avoids training getting trapped in local optima, significantly improving the stability and convergence efficiency of the training process. This method does not rely on manual adjustment of hyperparameters based on interdisciplinary experience, and can adapt to different types of heterogeneous materials and complex load conditions. Even with small data scenarios using only a single set of experimental samples, it can still achieve extremely high recognition accuracy. The relative errors of strain fitting and material parameter recognition are controlled at extremely low levels, demonstrating good engineering application value and promotion potential.

[0006] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0007] A method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network includes:

[0008] Acquire full-field strain data of the heterogeneous material under test under mechanical load, and construct a training dataset;

[0009] A physical information neural network is constructed: taking spatial coordinates as input, it outputs the displacement field and material parameter field of the heterogeneous material to be measured; the total loss function adopted includes a data loss term and a physical equation loss term; the data loss term is constructed based on the difference between the predicted strain derived from the displacement field and the full-field strain data, and the physical equation loss term is constructed based on the residual of the momentum balance equation;

[0010] During the training process of the physical information neural network, the weight coefficients of each loss term in the total loss function are dynamically adjusted. The adjustment method is as follows: calculate the gradient norm of each loss term with respect to the trainable parameters of the network, take the statistical mean of all gradient norms as the target gradient, and update the corresponding weight coefficients according to the deviation between the gradient norm of each loss term and the target gradient.

[0011] Using the training dataset, the physical information neural network is trained with the total loss function after dynamic weight adjustment as the optimization objective.

[0012] The trained physical information neural network outputs the mechanical property identification results of the heterogeneous material under test.

[0013] Furthermore, when dynamically adjusting the weight coefficients, the logarithmic weights corresponding to each loss term are first updated according to the deviation between the gradient norm and the target gradient, and then the logarithmic weights are converted into actual weight coefficients through the softmax normalization function.

[0014] The update formula for the logarithmic weights is as follows:

[0015]

[0016] In the formula, The logarithmic weight of the k-th loss term in the (t+1)-th iteration step. Let α be the logarithmic weight of the k-th loss term in the t-th iteration step, and let α be the weight update rate. Let be the gradient norm of the k-th loss term. Let ε be the target gradient, and let ε be a small constant to avoid division by zero.

[0017] Furthermore, the softmax normalization function controls the smoothness of the weight transformation through a temperature parameter; when dynamically adjusting the weight coefficients, the gradient norm of each loss term is calculated once every preset number of iterations.

[0018] Furthermore, when dynamically adjusting the weight coefficients, a stable phase control is set: a preset base weight is used in the initial training phase, and after a preset number of training steps, dynamic weight adjustment based on the deviation between the gradient norm and the target gradient is enabled.

[0019] Furthermore, the training process of the physical information neural network also includes a dynamic learning rate adjustment step: real-time monitoring of the convergence state of the total loss function; when the number of iterations in which the loss has not been improved reaches a preset threshold, the learning rate is adjusted by reducing the learning rate according to a preset decay factor, and the learning rate is not lower than the preset minimum learning rate.

[0020] The formula for updating the learning rate is:

[0021]

[0022] In the formula, For the updated learning rate, The current learning rate, This is the learning rate decay factor. This is the preset minimum learning rate;

[0023] After the learning rate is adjusted, a cooling-off period of a preset number of steps begins. No new learning rate adjustments will be triggered during the cooling-off period.

[0024] Furthermore, when constructing the training dataset, all node strain values ​​of the full-field strain data are used as training data, without dividing the data into training set, validation set, and test set; after obtaining the full-field strain data, the data is preprocessed by normalization or standardization.

[0025] Furthermore, the physical information neural network includes a parallel displacement field prediction subnetwork and a material parameter field prediction subnetwork; the displacement field prediction subnetwork takes spatial coordinates as input and outputs displacement components in the x and y directions; the material parameter field prediction subnetwork takes spatial coordinates as input and outputs a material parameter field; the material parameter field includes at least one of an elastic modulus field and a shear modulus field.

[0026] Furthermore, the predicted strain is calculated from the displacement field using automatic differentiation techniques to obtain the Green-Lagrangian strain tensor; the residual of the loss term in the physical equation is calculated based on the components of the first Piola-Kirchhoff stress tensor, which is calculated based on a hyperelastic constitutive model, including at least one of the Neo-Hookean model and the Mooney-Rivlin model.

[0027] Furthermore, a system for identifying the mechanical properties of heterogeneous materials based on a physical information neural network includes: a data processing module, a network construction module, a weight dynamic adjustment module, a training execution module, and a recognition output module;

[0028] The data processing module is used to acquire full-field strain data of the heterogeneous material under test under mechanical load and construct a training dataset.

[0029] The network construction module is used to construct a physical information neural network. The physical information neural network takes spatial coordinates as input and outputs the displacement field and material parameter field of the heterogeneous material to be tested. The total loss function of the physical information neural network includes a data loss term and a physical equation loss term. The data loss term is constructed based on the difference between the predicted strain derived from the displacement field and the full-field strain data. The physical equation loss term is constructed based on the residual of the momentum balance equation.

[0030] The weight dynamic adjustment module is used to dynamically adjust the weight coefficients of each loss term in the total loss function during the training process of the physical information neural network. The adjustment method is as follows: calculate the gradient norm of each loss term with respect to the trainable parameters of the network, take the statistical mean of all gradient norms as the target gradient, and update the corresponding weight coefficients according to the deviation between the gradient norm of each loss term and the target gradient.

[0031] The training execution module is used to train the physical information neural network using the training dataset and with the total loss function after dynamic weight adjustment as the optimization objective.

[0032] The identification output module is used to output the mechanical property identification results of the heterogeneous material under test through a trained physical information neural network.

[0033] And a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described above.

[0034] Compared to existing technologies, this invention and its preferred embodiment introduce a dynamic loss weight adjustment mechanism based on the gradient equality principle. This mechanism automatically and in real-time balances the weight relationship between data loss terms and physical equation loss terms in the physical information neural network, effectively overcoming the training imbalance problem caused by relying on empirically set fixed weights in traditional methods. This improves the stability and convergence efficiency of network training. Combined with a dynamic learning rate adjustment strategy, the optimization step size can be adaptively adjusted according to the loss convergence state during training, avoiding getting trapped in local optima and enhancing the robustness of the training process. Furthermore, by using all nodes of the full-field strain data as training samples and employing a parallel sub-network architecture to predict the displacement field and material parameter field respectively, the information from limited experimental data is fully utilized, improving the ability to identify the spatial variation characteristics of heterogeneous materials. Overall, the dynamic adaptive physical information neural network training framework constructed in this invention achieves a deep integration of physical constraints and data-driven approaches, providing a more accurate, adaptable, and easier-to-implement solution for identifying the mechanical properties of complex heterogeneous materials. Attached Figure Description

[0035] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0036] Figure 1 This is a schematic diagram of the overall process of the method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network according to an embodiment of the present invention;

[0037] Figure 2 This is a schematic diagram of the physical information neural network structure according to an embodiment of the present invention;

[0038] Figure 3 This is a schematic diagram comparing the network-predicted strain value with the actual strain value in an embodiment of the present invention;

[0039] Figure 4 This is a schematic diagram comparing the network-predicted elastic modulus value with the actual elastic modulus value in an embodiment of the present invention. Detailed Implementation

[0040] To make the features and advantages of the present invention more apparent and understandable, specific embodiments are described below in detail:

[0041] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0042] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0043] The purpose of this invention is to solve the problems of low model accuracy, difficulty in parameter adjustment, and poor numerical stability in existing neural networks when the sample size is limited. This invention provides a method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network, the implementation of which includes the following steps:

[0044] Step S1: Obtain the full-field strain data of the material to be tested and construct a dataset. The dataset contains the strain values ​​of all nodes, and all data points are used for network training.

[0045] Step S2: Construct a physical information neural network;

[0046] Step S3: Construct the dynamic loss weight module;

[0047] Step S4: Construct the dynamic learning rate module;

[0048] Step S5: Construct a complete dynamic adaptive physical information neural network;

[0049] Step S6: Design a dynamic adaptive total loss function;

[0050] Step S7: Train the dynamic adaptive physical information neural network and evaluate the network's performance.

[0051] In one embodiment of the present invention, in step S1, full-field strain data of the material under mechanical load is first obtained by digital image correlation, ultrasonic elastography or optical coherence tomography; then the data is normalized and standardized preprocessed; since there is usually only one experimental sample in the material parameter identification problem, all node data points are used as training points for network training, without the need to divide the training set, validation set and test set.

[0052] In one embodiment of the present invention, in step S2, the physical information neural network includes an input layer, a hidden layer and an output layer. The output layer outputs a displacement field and a material parameter field. The material includes one or more of biological tissue and rock and soil materials. The material parameter field includes one or more of elastic modulus and shear modulus.

[0053] In one embodiment of the present invention, step S2 is specifically implemented as follows:

[0054] Step S21: Construct a displacement field prediction subnetwork: First, use a fully connected layer to extract features from the input coordinates; then, learn the spatial distribution of the displacement field through multi-layer nonlinear transformation; finally, output the displacement components. and ;

[0055] Step S22: Construct a material parameter field prediction sub-network: First, use independent fully connected layers to extract features from the input coordinates; then, learn the spatial distribution of material parameters through multi-layer nonlinear transformations; finally, output the material parameter field. .

[0056] In one embodiment of the present invention, step S3 is specifically implemented as follows:

[0057] Step S31: Construct a gradient calculation module: Calculate the gradient of each loss term with respect to the network parameters to obtain the gradient norm set. ,in This represents the total number of loss functions;

[0058] Step S32: Construct the target gradient calculation module: Calculate the mean of each gradient norm as the target gradient. The specific expression is as follows:

[0059]

[0060] Step S33: Construct the logarithmic weight update module: Update the logarithmic weights based on the deviation between the gradient norm and the target gradient. The specific expression is as follows:

[0061]

[0062] Among them The update rate, with a value ranging from 0.01 to 0.1, To avoid dividing by zero for small constants;

[0063] Step S34: Construct a weight normalization module: Convert the logarithmic weights into actual weights using the softmax function. The specific expression is shown below:

[0064]

[0065] Among them Temperature parameters control the smoothness of the weights;

[0066] Step S35: Construct a stabilization mechanism: Use preset base weights in the initial training phase, and enable dynamic adjustment after a preset number of steps.

[0067] In one embodiment of the present invention, the loss term includes data loss and physical loss. The data loss is based on the mean square error between the predicted strain and the actual strain, and the physical loss includes the residuals of the momentum balance equations in the x and y directions.

[0068] Data loss The specific expression is:

[0069]

[0070] in The total number of training data points, For the network in the first Green-Lagrangian strain tensor components predicted by each node For the first The true strain tensor components of each node. This represents the L2 norm of a vector.

[0071] Directional momentum loss The specific expression is:

[0072]

[0073] in and This is a common property of the first Piola-Kirchhoff stress tensor. express Spatial coordinates The partial derivatives, express Spatial coordinates The partial derivatives of .

[0074] Directional momentum loss The specific expression is:

[0075]

[0076] in and These are the components of the first Piola-Kichhoff stress tensor. express Spatial coordinates The partial derivatives, express Spatial coordinates The partial derivatives of .

[0077] The stress components mentioned above are calculated based on the Neo-Hookean hyperelastic constitutive model, and the calculation formula is as follows:

[0078]

[0079] in Let the deformation gradient tensor be defined as follows: , For Kronecker notation, For displacement components; The determinant of the deformation gradient; It is the inverse matrix of the transpose of the deformed gradient; and Let Lame's constant be the constant, and its relationship with the elastic modulus and Poisson's ratio be:

[0080]

[0081] In one embodiment of the present invention, step S4 is specifically implemented as follows:

[0082] Step S41: Construct a loss monitoring module: Record the loss value of each iteration step and compare it with the historical best loss, and count the number of iteration steps in which the loss has not improved continuously;

[0083] Step S42: Construct the plateau detection module: when the loss is continuous The number of iterations did not decrease beyond the threshold. When this is triggered, the learning rate is adjusted, where The value range is 50-200. The value range is 0.01-0.05;

[0084] Step S43: Construct the learning rate update module: according to the preset factor Reduce the learning rate:

[0085]

[0086] in The value range is 0.1-0.5. This is the preset minimum learning rate.

[0087] Step S44: Construct a cooling-off period mechanism: After the learning rate is adjusted, a cooling-off period begins. No new adjustments are triggered during the cooling-off period. The number of steps in the cooling-off period ranges from 20 to 100.

[0088] In one embodiment of the present invention, step S5 is specifically implemented as follows:

[0089] Step S51: First, connect the physical information neural network with the dynamic loss weight module to realize the dynamic adjustment of the loss weight;

[0090] Step S52: Then, embed the dynamic learning rate module into the training process to achieve dynamic adjustment of the learning rate;

[0091] Step S53: Set network hyperparameters, including the number of hidden layers, the number of neurons, and the type of activation function;

[0092] Step S54: Initialize network weights using the Xavier or He method and configure the optimizer.

[0093] In one embodiment of the present invention, the specific expression of the dynamic adaptive total loss function in step S6 is as follows:

[0094]

[0095] in For data loss, and They are respectively direction and Momentum loss in the direction of motion. , and These are the weight coefficients that are dynamically adjusted by the dynamic loss weight module, with initial values ​​set to 100, 1, and 1 respectively.

[0096] In one embodiment of the present invention, in step S7, the network is first trained using a dataset. During the training process, the dynamic loss weight module dynamically balances each loss term based on the gradient equality principle, and the dynamic learning rate module dynamically adjusts the optimizer parameters based on loss plateau detection. The network performance is evaluated by comparing the error between the strain value predicted by the network and the true value, and calculating the root mean square error and L2 relative error. If there is a true value for the material parameter, the error between the material parameter value predicted by the network and the true value is compared, and the root mean square error and L2 relative error are calculated to evaluate the accuracy of material parameter identification.

[0097] Compared to existing technologies, this invention addresses the challenges of determining loss weights, manually adjusting learning rates, and requiring large amounts of data in identifying the mechanical properties of heterogeneous materials. It proposes a method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network. In this method, the physical information neural network outputs a displacement field. Automatic differentiation is used to calculate the strain and stress fields from the displacement field, and the residual of the momentum balance equation is constructed as the physical loss. A dynamic loss weight module uses the gradient norm of the loss function as a dynamic adjustment index, dynamically adjusting the weights of data loss and momentum loss in both directions based on the principle of gradient equality, achieving automatic balance of multi-objective losses and avoiding the tedious process of manual parameter tuning. A dynamic learning rate module dynamically adjusts the optimizer parameters based on loss plateau detection, accelerating convergence and improving stability. This invention offers significant advantages over existing methods in identifying parameters of heterogeneous materials, exhibiting lower dependence on sample data, higher accuracy, and good potential for engineering applications.

[0098] The implementation process of this solution will be further demonstrated and introduced below with reference to the accompanying drawings through more specific embodiments:

[0099] like Figure 1 As shown in the figure, this embodiment provides the design process of a method for identifying the mechanical properties of heterogeneous materials based on physical information neural networks, including the following steps:

[0100] First, full-field strain data of the composite laminate under biaxial tensile load was obtained using digital image correlation technology. The strain data included... , Three components. In this embodiment, the total strain data includes strain values ​​from 5041 nodes, with each node providing a set of strain data ( , Then, the strain data is normalized to map the data range to the [-1,1] interval. Since there is only one experimental sample in the material parameter identification problem, all 5041 node data points are used as training points for network training, without the need to divide the data into training, validation, and test sets.

[0101] Step S2: Construct a physical information neural network: such as Figure 2 As shown, the physical information neural network comprises two parallel branches: a displacement field prediction subnetwork and a material parameter field prediction subnetwork. The displacement field prediction subnetwork takes spatial coordinates (x, y) as input and outputs displacement components. and The material parameter field prediction subnetwork takes spatial coordinates (x, y) as input and outputs the material parameter field. Both subnetworks contain 5 fully connected hidden layers, each with 75 neurons, and the activation function used is Swish.

[0102] As a further preferred embodiment, when constructing the loss function based on the output of the physical information neural network, the deformation gradient is calculated from the displacement components output by the displacement field prediction subnetwork using automatic differentiation techniques. The deformation gradient is defined as follows: ,in For Kronecker notation, The displacement components are used; then, the Green-Lagrangian strain tensor is calculated based on the deformation gradient, using the following formula: Simultaneously, based on the material parameters output by the deformation gradient and material parameter field prediction subnetwork, the first Piola-Kirchhoff stress tensor is calculated using the Neo-Hookean hyperelastic constitutive model. The calculation formula is as follows: ,in The determinant of the deformation gradient, The inverse matrix of the transpose of the deformed gradient. and Let be the Lamé constant, and let its relationship with the elastic modulus E and Poisson's ratio v be: .

[0103] Step S3: Construct the dynamic loss weight module:

[0104] The dynamic loss weight module uses the gradient norm of the loss function as a dynamic adjustment index, and dynamically adjusts the data loss based on the principle of gradient equality. Directional momentum loss and The weight of directional momentum loss. In this embodiment, the total loss includes three loss items: data loss. , Directional momentum loss , Directional momentum loss ,therefore .

[0105] Step S31: Calculate the gradient of each loss term with respect to the network parameters every 50 iterations to obtain the gradient norm. , and ;

[0106] Step S32: Calculate the target gradient norm As a balancing objective;

[0107] Step S33: Update the logarithmic weights based on the deviation between the gradient norm and the target gradient, updating the rate. :

[0108] ;

[0109] Step S34: Convert the logarithmic weights into actual weights using the softmax function, temperature parameter. :

[0110] ,

[0111] Step S35: Set up a stabilization period mechanism; use the basic weights for the first 200 iterations. , , Then, dynamic adjustment will be enabled.

[0112] Step S4: Construct the dynamic learning rate module: The dynamic learning rate module consists of a loss monitoring module, a plateau detection module, a learning rate update module, and a cooldown mechanism, specifically including the following steps:

[0113] Step S41: Construct a loss monitoring module: Record the loss value of each iteration step and compare it with the historical best loss, and count the number of iteration steps in which the loss has not improved continuously.

[0114] Step S42: Construct the plateau detection module: When the loss does not decrease by more than 1% for 100 consecutive iterations, trigger the learning rate adjustment.

[0115] Step S43: Construct the learning rate update module: by factor Reduce the learning rate, and set the minimum learning rate to [value missing]. :

[0116]

[0117] Step S44: Establish a cooldown mechanism: After the learning rate is adjusted, a 50-step cooldown period begins, during which no new adjustments are triggered.

[0118] Step S5: Construct a complete dynamic adaptive physical information neural network: The dynamic adaptive physical information neural network is composed of the above modules connected in sequence, specifically including the following steps:

[0119] Step S51: First, connect the physical information neural network with the dynamic loss weight module to realize the dynamic adjustment of the loss weight.

[0120] Step S52: Then embed the dynamic learning rate module into the training process to achieve dynamic adjustment of the learning rate.

[0121] Step S53: Set network hyperparameters: 5 hidden layers, 75 neurons per layer, and Swish activation function.

[0122] Step S54: Initialize network weights using the Xavier method, configure the Adam optimizer, and set the initial learning rate to [value missing]. .

[0123] As a further preferred implementation, when building a dynamic adaptive physical information neural network, the dynamic loss weight module and the dynamic learning rate module are synchronously embedded into the network's training process. During training, the dynamic loss weight module updates the weight of the loss term once every preset iteration step, and the dynamic learning rate module monitors the loss convergence status in real time and adjusts the learning rate synchronously. The two modules work together to optimize the network's training process, improving convergence stability and recognition accuracy.

[0124] Step S6: Design the dynamic adaptive total loss function: The specific expression of the dynamic adaptive total loss function is as follows:

[0125]

[0126] in For data loss, and They are respectively direction and Momentum loss in the direction of motion. , and These are the weight coefficients that are dynamically adjusted by the dynamic loss weight module, with initial values ​​set to 100, 1, and 1 respectively.

[0127] Step S7: Train the dynamic adaptive physical information neural network and evaluate its performance: First, train the network using the dataset, iterating 100,000 times. During training, the dynamic loss weight module updates the weights every 50 steps, and the dynamic learning rate module dynamically adjusts the learning rate based on the loss plateau.

[0128] The network performance is evaluated in the following ways: First, the error between the strain value predicted by the network and the actual input strain value is compared, and the root mean square error and L2 relative error are calculated. Second, since this embodiment uses finite element simulation to generate data, there are actual values ​​of material parameters. The error between the material parameter values ​​predicted by the network and the actual values ​​is compared, and the root mean square error and L2 relative error are calculated.

[0129] The effectiveness of this method is illustrated by the following experiments. In this embodiment, training data containing a heterogeneous elastic modulus distribution is generated through finite element simulation. The dataset contains full-field strain data with 5041 nodes, each node containing spatial coordinates and the corresponding strain value. The material parameter field is a preset heterogeneous elastic modulus distribution.

[0130] The adaptive physical information neural network method proposed in this invention can accurately fit the full-field strain distribution of a material, and the comparison results between the predicted strain value and the true value are as follows: Figure 3As shown, the calculated L2 errors of strain fitting along the x-axis and y-axis are 0.55% and 0.46%, respectively, proving that the displacement field and strain field output by the network have extremely high fitting accuracy.

[0131] Meanwhile, this method can accurately identify the spatial distribution of the elastic modulus of heterogeneous materials, and the comparison results between the predicted elastic modulus value and the true value are as follows: Figure 4 As shown, the L2 error for elastic modulus identification is only 1.17%; after training, the momentum loss in both directions converges to 10. -3 The magnitude indicates that the network prediction results simultaneously meet the requirements of fitting the measured data and the constraints of the physical laws of solid mechanics, verifying the accuracy and reliability of this method.

[0132] This embodiment also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it can implement all the steps of the above-described method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network. This computer device can be implemented as a general-purpose computing device, including but not limited to industrial control computers, personal computers, servers, cloud computing nodes, etc. Internally, it can be connected to basic structures such as processors, memory, communication interfaces, and input / output units via a system bus to meet the computing and deployment requirements of this solution.

[0133] This embodiment also provides a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements all the steps of the method described above in this embodiment. The computer-readable storage medium may include volatile and non-volatile memory, including but not limited to random access memory (RAM), read-only memory (ROM), flash memory, hard disk drive (HDD), solid-state drive (SSD), etc., and can be used to store the computer program instructions and related data of this solution, providing a stable storage medium for the implementation of the method.

[0134] This invention is not limited to the above-described preferred embodiments. Anyone inspired by this invention can derive other various forms of methods for identifying the mechanical properties of heterogeneous materials based on physical information neural networks. All equivalent changes and modifications made within the scope of the claims of this invention should be included in the scope of this invention.

Claims

1. A method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network, characterized in that, include: Acquire full-field strain data of the heterogeneous material under test under mechanical load, and construct a training dataset; A physical information neural network is constructed: taking spatial coordinates as input, it outputs the displacement field and material parameter field of the heterogeneous material to be measured; the total loss function adopted includes a data loss term and a physical equation loss term; the data loss term is constructed based on the difference between the predicted strain derived from the displacement field and the full-field strain data, and the physical equation loss term is constructed based on the residual of the momentum balance equation; During the training process of the physical information neural network, the weight coefficients of each loss term in the total loss function are dynamically adjusted. The adjustment method is as follows: calculate the gradient norm of each loss term with respect to the trainable parameters of the network, take the statistical mean of all gradient norms as the target gradient, and update the corresponding weight coefficients according to the deviation between the gradient norm of each loss term and the target gradient. Using the training dataset, the physical information neural network is trained with the total loss function after dynamic weight adjustment as the optimization objective. The trained physical information neural network outputs the mechanical property identification results of the heterogeneous material under test.

2. The method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network according to claim 1, characterized in that: When dynamically adjusting the weight coefficients, the logarithmic weights corresponding to each loss term are first updated according to the deviation between the gradient norm and the target gradient, and then the logarithmic weights are converted into actual weight coefficients through the softmax normalization function. The update formula for the logarithmic weights is as follows: In the formula, The logarithmic weight of the k-th loss term in the (t+1)-th iteration step. Let α be the logarithmic weight of the k-th loss term in the t-th iteration step, and let α be the weight update rate. Let be the gradient norm of the k-th loss term. Let ε be the target gradient, and let ε be a small constant to avoid division by zero.

3. The method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network according to claim 2, characterized in that: The softmax normalization function controls the smoothness of the weight transformation through a temperature parameter; when dynamically adjusting the weight coefficients, the gradient norm of each loss term is calculated once every preset number of iterations.

4. The method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network according to claim 2, characterized in that: When dynamically adjusting the weight coefficients, a stable phase control is set: a preset base weight is used in the initial training phase, and after a preset number of training steps, dynamic weight adjustment based on the deviation between the gradient norm and the target gradient is enabled.

5. The method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network according to claim 1, characterized in that: The training process of the physical information neural network also includes a dynamic learning rate adjustment step: real-time monitoring of the convergence state of the total loss function; when the number of iterations in which the loss has not been improved reaches a preset threshold, the learning rate is adjusted by reducing the learning rate according to a preset decay factor, and the learning rate is not lower than the preset minimum learning rate. The formula for updating the learning rate is: In the formula, For the updated learning rate, The current learning rate, This is the learning rate decay factor. This is the preset minimum learning rate; After the learning rate is adjusted, a cooling-off period of a preset number of steps begins. No new learning rate adjustments will be triggered during the cooling-off period.

6. The method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network according to claim 1, characterized in that: When constructing the training dataset, all node strain values ​​of the full-field strain data are used as training data, without dividing the data into training set, validation set and test set; after obtaining the full-field strain data, the data is preprocessed by normalization or standardization.

7. The method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network according to claim 1, characterized in that: The physical information neural network includes a parallel displacement field prediction subnetwork and a material parameter field prediction subnetwork; the displacement field prediction subnetwork takes spatial coordinates as input and outputs displacement components in the x and y directions; the material parameter field prediction subnetwork takes spatial coordinates as input and outputs a material parameter field; the material parameter field includes at least one of an elastic modulus field and a shear modulus field.

8. The method for identifying the mechanical properties of heterogeneous materials based on a physical information neural network according to claim 1, characterized in that: The predicted strain is calculated from the displacement field using an automatic differentiation technique to obtain the Green-Lagrangian strain tensor; the residual of the loss term in the physical equation is calculated based on the components of the first Piola-Kirchhoff stress tensor, which is calculated based on a hyperelastic constitutive model, including at least one of the Neo-Hookean model and the Mooney-Rivlin model.

9. A system for identifying the mechanical properties of heterogeneous materials based on a physical information neural network, characterized in that, include: The module comprises a data processing module, a network construction module, a dynamic weight adjustment module, a training execution module, and a recognition output module. The data processing module is used to acquire full-field strain data of the heterogeneous material under test under mechanical load and construct a training dataset. The network construction module is used to construct a physical information neural network. The physical information neural network takes spatial coordinates as input and outputs the displacement field and material parameter field of the heterogeneous material to be tested. The total loss function of the physical information neural network includes a data loss term and a physical equation loss term. The data loss term is constructed based on the difference between the predicted strain derived from the displacement field and the full-field strain data. The physical equation loss term is constructed based on the residual of the momentum balance equation. The weight dynamic adjustment module is used to dynamically adjust the weight coefficients of each loss term in the total loss function during the training process of the physical information neural network. The adjustment method is as follows: calculate the gradient norm of each loss term with respect to the trainable parameters of the network, take the statistical mean of all gradient norms as the target gradient, and update the corresponding weight coefficients according to the deviation between the gradient norm of each loss term and the target gradient. The training execution module is used to train the physical information neural network using the training dataset and with the total loss function after dynamic weight adjustment as the optimization objective. The identification output module is used to output the mechanical property identification results of the heterogeneous material under test through a trained physical information neural network.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 8.

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