A solid stress field prediction method, device, equipment and storage medium

Abstract

The application discloses a solid stress field prediction method and device, equipment and storage medium, and relates to the technical field of computers, which comprises the following steps: inputting material parameters of a target matrix material into a target physical information depth operator network, processing material space coordinates in the material parameters through a backbone network in the network to obtain a first network output, and processing attribute parameters in the material parameters through a branch network in the network to obtain a second network output; performing Hadamard product on the first network output and the second network output to obtain a target physical field corresponding to the target matrix material; determining a target solution of the material parameters satisfying a target boundary condition in the target physical information depth operator network, and determining a target distance output obtained by processing the material space coordinates by a target distance function; and determining a solid stress field corresponding to the target matrix material based on the target distance output and the target physical field. Thus, the efficiency and adaptability of stress field prediction can be improved.

Description

Technical Field

[0001] This invention relates to the field of computer technology, and in particular to a method, apparatus, device, and storage medium for predicting solid stress fields. Background Technology

[0002] Accurate prediction of solid stress fields is crucial for oil and gas reservoir development, recovery optimization, and geological preservation engineering. Traditional numerical methods, such as the finite element method, can solve stress fields with high accuracy, but their high computational cost makes them unsuitable for rapid analysis of multiple parameters and operating conditions. In recent years, Physically Informed Neural Networks (PINNs) have achieved unsupervised solutions by embedding physical governing equations into loss functions. However, PINN models deeply couple the computational domain with physical parameters, resulting in models that are only applicable to a fixed set of material properties, such as Lamé constants, and lacking generalization ability. This means that the model needs to be retrained for each new material parameter, leading to low computational efficiency.

[0003] In existing research, DeepONet, a deep operator network, has been proposed to learn the mapping from parametric functions to solution functions, demonstrating generalization potential. However, stress fields, as tensor fields, have complex governing equations and coupling relationships between components, making it difficult to guarantee accuracy when directly applying DeepONet. Furthermore, existing methods are mostly designed for scalar fields such as temperature and fluid fields, lacking dedicated optimization structures for high-dimensional stress field tensors. Therefore, a method for intelligent stress field prediction that balances generalization ability and high accuracy is needed. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method, apparatus, device, and storage medium for predicting solid stress fields. This method can rapidly process input material parameters through a trained neural network and output the corresponding stress field, effectively improving computational efficiency and cross-scenario adaptability. The specific solution is as follows: In a first aspect, this application discloses a method for predicting the stress field of a solid, including: The material parameters of the target matrix material are input into the target physical information depth operator network. The material space coordinates in the material parameters are processed by the backbone network of the target physical information depth operator network to obtain the first network output. The attribute parameters in the material parameters are processed by the branch network of the target physical information depth operator network to obtain the second network output. The first network output and the second network output are multiplied by a Hadamard product to obtain the target physical field corresponding to the target matrix material. Determine the target solution in the target physical information depth operator network that satisfies the target boundary conditions for the material parameters, and determine the target distance output obtained after processing the material spatial coordinates by the target distance function; The solid stress field corresponding to the target matrix material is determined based on the target distance output and the target physical field.

[0005] Optionally, before inputting the material parameters of the target matrix material into the target physical information depth operator network, processing the material space coordinates in the material parameters through the backbone network of the target physical information depth operator network to obtain a first network output, and processing the attribute parameters in the material parameters through the branch networks of the target physical information depth operator network to obtain a second network output, the method further includes: The training space coordinates are sampled in the preset solution region, and training material parameters are randomly generated to generate a training set based on the training space coordinates and the training material parameters. The first training parameters are randomly sampled from the training set to perform random sampling training on the preset initial network based on the first training parameters, so as to obtain the target physical information deep operator network. Alternatively, based on the training set, assign corresponding parameter ranges to several preset training stages, and randomly sample corresponding second training parameters from the parameter ranges for each training period corresponding to the preset training stage; perform random sampling training on the preset initial network based on the several preset training stages and the second training parameters to obtain the target physical information deep operator network; wherein, each training stage in the several preset training stages corresponds to several training periods.

[0006] Optionally, the step of processing the material space coordinates in the material parameters through the backbone network of the target physical information depth operator network to obtain the first network output includes: The material spatial coordinates in the material parameters are extracted by several backbone network neurons in the backbone network of the target physical information deep operator network to obtain the coordinate features corresponding to the material parameters. The coordinate features are converted into coordinate feature vectors corresponding to preset basis functions in the target physical information depth operator network, and the coordinate feature vectors are used as the output of the first network.

[0007] Optionally, the step of processing the property parameters in the material parameters through a branch network in the target physical information depth operator network to obtain the second network output includes: The property parameters in the material parameters are extracted by several branch network neurons in the branch network of the target physical information deep operator network to obtain the property features corresponding to the property parameters. The attribute features are converted into attribute feature vectors corresponding to preset basis functions in the target physical information deep operator network, and the attribute feature vectors are used as the output of the second network.

[0008] Optionally, performing a Hadamard product on the first network output and the second network output to obtain the target physical field corresponding to the target matrix material includes: The vector elements in the first network output and the second network output are multiplied element by element to obtain the target vector; The vector elements in the target vector are summed to obtain the target physical field corresponding to the target matrix material.

[0009] Optionally, determining the target solution in the target physical information depth operator network that satisfies the target boundary conditions for the material parameters, and determining the target distance output obtained after processing the material space coordinates by the target distance function, includes: The target computation domain of the target physical information depth operator network is determined, and the maximum boundary value, minimum boundary value, and target boundary of the target physical information depth operator network are determined based on the target computation domain. Based on the target boundary, construct the target boundary conditions, and determine the target solution in the target physical information deep operator network that satisfies the target boundary conditions for the material parameters; A target distance function is constructed based on the maximum and minimum boundary values, and the target distance output corresponding to the material space coordinates is determined according to the target distance function.

[0010] Optionally, determining the solid stress field corresponding to the target matrix material based on the target distance output and the target physical field includes: The product of the target distance output and the target physical field is calculated to obtain the target product, and the sum of the target product and the target solution is taken as the solid stress field corresponding to the target matrix material.

[0011] Secondly, this application discloses a solid stress field prediction device, comprising: The network processing module is used to input the material parameters of the target matrix material into the target physical information depth operator network, so as to process the material space coordinates in the material parameters through the backbone network of the target physical information depth operator network to obtain a first network output, and process the attribute parameters in the material parameters through the branch network of the target physical information depth operator network to obtain a second network output; The physics field calculation module is used to perform a Hadamard product on the first network output and the second network output to obtain the target physics field corresponding to the target matrix material. The parameter determination module is used to determine the target solution in the target physical information depth operator network that satisfies the target boundary conditions of the material parameters, and to determine the target distance output obtained after the target distance function processes the material spatial coordinates; The stress field calculation module is used to determine the solid stress field corresponding to the target matrix material based on the target distance and the target physical field.

[0012] Thirdly, this application discloses an electronic device, including: Memory, used to store computer programs; A processor is used to execute the computer program to implement the solid stress field prediction method as described above.

[0013] Fourthly, this application discloses a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the aforementioned solid stress field prediction method.

[0014] Therefore, in this application, the material parameters of the target matrix material can be input into a target physical information depth operator network. The material spatial coordinates in the material parameters are processed by the backbone network of the target physical information depth operator network to obtain a first network output. The attribute parameters in the material parameters are processed by the branch networks of the target physical information depth operator network to obtain a second network output. The first network output and the second network output are multiplied by a Hadamard product to obtain the target physical field corresponding to the target matrix material. The target solution that satisfies the target boundary conditions of the material parameters in the target physical information depth operator network is determined, and the target distance output obtained after processing the material spatial coordinates by the target distance function is determined. Based on the target distance output and the target physical field, the solid stress field corresponding to the target matrix material is determined.

[0015] Therefore, the method of this application requires inputting the material parameters of the target matrix material into a target physical information deep operator network. The backbone network processes the material spatial coordinates of the material parameters to obtain a first network output, and the branch networks process the attribute parameters of the material parameters to obtain a second network output. The first and second network outputs are then multiplied by a Hadamard product to obtain the target physical field corresponding to the target matrix material. The target solution satisfying the target boundary conditions for the material parameters in the target physical information deep operator network is determined, and the target distance output obtained after processing the material spatial coordinates using the target distance function is determined. Based on the target distance output and the target physical field, the solid stress field corresponding to the target matrix material is determined. In this way, an end-to-end mapping relationship from material parameters to the stress field tensor can be established through a branch-backbone network structure, hard-constrained boundary conditions, and an adaptive training strategy. This algorithm enables the trained model to have zero-shot inference capability, allowing direct input of any new material parameters within the training distribution to quickly output the stress, strain, and displacement field distributions, significantly improving computational efficiency and cross-scenario adaptability, and providing real-time support for engineering decision-making. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0017] Figure 1 This is a flowchart of a solid stress field prediction method disclosed in this application; Figure 2 This is a schematic diagram of a target physical information deep operator network structure disclosed in this application; Figure 3 This is a schematic diagram of one parameter setting disclosed in this application; Figure 4 This is a schematic diagram illustrating the percentage of prediction error in a phased progressive training scenario (40×40) as disclosed in this application; Figure 5 This is a schematic diagram illustrating the percentage of prediction error during random sampling training in a (40×40) scenario disclosed in this application; Figure 6 This is a schematic diagram illustrating the percentage of prediction error during random sampling training in an 80×80 scenario as disclosed in this application; Figure 7 This is a schematic diagram illustrating the percentage of prediction error in a phased progressive training scenario (80×80) as disclosed in this application; Figure 8This is a schematic diagram comparing soft constraints, hard constraints, and finite element results disclosed in this application. Figure 9(a) is a normal stress prediction cloud map disclosed in this application; Figure 9(b) shows a shear stress and stress disclosed in this application. Oriented strain prediction contour map; Figure 9(c) shows one of the disclosures of this application. Contour plots for predicting directional normal strain and shear strain; Figure 9(d) is a displacement field prediction cloud map disclosed in this application; Figure 10 This is a schematic diagram of the structure of a solid stress field prediction device disclosed in this application; Figure 11 This is a structural diagram of an electronic device disclosed in this application. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Currently, the PINN model is commonly used to solve stress fields. However, the PINN model deeply couples the computational domain with physical parameters, resulting in a trained model that only applies to a fixed set of material properties, such as Lamé constants, and lacks generalization ability. Furthermore, DeepONet, a deep operator network, has been proposed to learn the mapping from parametric functions to solution functions, demonstrating generalization potential. However, the stress field, as a tensor field, has complex governing equations and coupling relationships between components, making it difficult to guarantee accuracy when directly applying DeepONet.

[0020] To overcome the aforementioned technical problems, this application discloses a method, apparatus, device, and storage medium for predicting solid stress fields. It can quickly process input material parameters through a trained neural network and then output the corresponding stress field, which can effectively improve computational efficiency and cross-scenario adaptability.

[0021] See Figure 1 As shown, this embodiment of the invention discloses a method for predicting the stress field of a solid, including: Step S11: Input the material parameters of the target matrix material into the target physical information depth operator network, so that the material space coordinates in the material parameters are processed by the backbone network in the target physical information depth operator network to obtain the first network output, and the attribute parameters in the material parameters are processed by the branch network in the target physical information depth operator network to obtain the second network output.

[0022] In this embodiment, before processing the material parameters of the target matrix material using the PI-DeepONet target physical information deep operator network, the initial network needs to be trained first to obtain the target physical information deep operator network. Specifically, a training set for training the initial network needs to be generated first. This involves sampling training space coordinates within a preset solution region and randomly generating training material parameters to create the training set based on the training space coordinates and the training material parameters. It should be noted that the preset solution region is the PDE (Partial Differential Equation) solution region corresponding to the initial network, and sampling of training space coordinates needs to be done within the solution region. nl 1× ml Two internal points were sampled uniformly on the boundary. nl 1 and ml Two boundary points. Additionally, material parameter pairs are randomly generated in each training batch. The generated material parameter pairs are Lamé constants to simulate different physical scenarios.

[0023] Furthermore, in this embodiment, the initial network can be trained in two ways: the first is random sampling training, and the second is phased progressive training. In the case of random sampling training, first training parameters need to be randomly sampled from the training set. Based on these first training parameters, the preset initial network is randomly sampled for training to obtain the target physical information deep operator network. It should be noted that the random sampling training strategy adopts the traditional single-stage training mode. Throughout the training process, material parameters are uniformly and randomly sampled from the entire target domain. In each training batch, multiple combinations of material parameters are sampled from the preset training set. This approach allows the model to be trained on parameters across the entire parameter space from start to finish, guiding it to learn physical laws with broad applicability. This training process is concise and, when training data is sufficient, can fully utilize the global distribution characteristics of the parameter space, helping the model establish a comprehensive representation of physical laws. However, due to the complexity of physical laws, the convergence speed may be slow in the early stages of training, especially when the parameter space is large, requiring the model to take longer to coordinate physical constraints under different parameter configurations.

[0024] In another scenario, a phased progressive training method can be used to train the initial network. This involves allocating corresponding parameter ranges to several preset training stages based on the training set, and randomly sampling corresponding second training parameters from these parameter ranges for each training cycle corresponding to the preset training stages. The preset initial network is then randomly sampled and trained based on the preset training stages and the second training parameters to obtain the target physical information deep operator network. Each of the preset training stages corresponds to a number of training cycles. It should be noted that the phased progressive training method requires a phased and hierarchical parameter space expansion approach to gradually transfer the neural network from simple physical laws to complex global physical laws. In this embodiment, the training process can be divided into 5 stages, each containing an equal number of training weeks (a total of 50,000 epochs, with 10,000 epochs per stage). The initial stage uses fixed parameter values. This allows the network to quickly grasp fundamental physical laws. Subsequent stages gradually expand the parameter range, ultimately covering the entire target domain. Within each training cycle, multiple sets of parameters are randomly sampled from the current parameter range for training, ensuring the model is fully adapted to the current difficulty level. Let the total number of stages be... The current stage index is The formula for dynamically adjusting the parameter range is: ; ; in, and As the baseline parameter value, , This is the range expansion factor. It should be noted that the training process varies at each stage. Within, from the current parameter range The model employs a uniform sampling method for material parameter combinations. Specifically, multiple sets of parameters are generated for each training batch, the corresponding physical constraint loss is calculated, and the network weights are updated. Furthermore, this embodiment uses the AdamW optimizer to update the network weights. This optimizer, through decoupling the weight decay mechanism, helps improve the model's generalization ability. Model weights are saved every 1000 epochs. During training, the following performance metrics are continuously recorded: average loss per epoch, moving average loss per 100 epochs, and model performance is periodically evaluated on fixed test parameters.

[0025] Furthermore, the structure of the target physical information deep operator network PI-DeepONet obtained after training is as follows: Figure 2As shown, the material parameters of the target matrix material need to be input into the target physical information deep operator network so that the network can process the material parameters and obtain the stress field of the target matrix material. It should be noted that the target physical information deep operator network PI-DeepONet is based on operator approximation theory and learns the mapping from the parameter space to the solution space.

[0026] Specifically, the material spatial coordinates in the material parameters can be processed by the backbone network of the target physical information deep operator network to obtain the first network output. Specifically, several backbone network neurons in the target physical information deep operator network (Trunk Net) need to extract features from the material spatial coordinates in the material parameters to obtain the coordinate features corresponding to the material parameters. These coordinate features can then be converted into coordinate feature vectors corresponding to preset basis functions in the target physical information deep operator network, and these coordinate feature vectors are used as the first network output. It should be noted that the backbone network adopts a forward propagation fully connected neural network structure, specifically defined as follows: ; ; ; in, The final output vector of the backbone network (Trunk-Net) is used to represent the feature information corresponding to the material space coordinates; This is the total number of layers in the backbone network, and for The maximum value; As a layer index in the backbone network, satisfying ; Main backbone network The linear transformation output of layer neurons, i.e., the output before activation; Main backbone network The activation output of layer neurons; Main backbone network The output vector of the layer, and also as the first The layer's input vector; Main backbone network Layer weight matrix; Main backbone network Layer bias vector; Main backbone network The activation function used in the layer; superscript " " indicates the first in the corresponding network Layer; subscript " "" indicates that the parameter belongs to the trunk network.

[0027] Furthermore, the property parameters in the material parameters can be processed through a branch network in the target physical information deep operator network to obtain the output of the second network. Specifically, the property parameters in the material parameters need to be feature-extracted by several branch network neurons in the target physical information deep operator network to obtain the corresponding property features. Then, the property features are converted into property feature vectors corresponding to the preset basis functions in the target physical information deep operator network, and the property feature vectors are used as the output of the second network. It should be noted that the branch network is similar to the backbone network, and its definition is as follows: ; ; ; in, This is the final output vector of the Branch-Net, used to represent the feature information corresponding to the material property parameters; Let be the total number of layers in the branch network, and for The maximum value; For the layer index in the branch network, satisfying ; For the branch network Linear transformation output of layer neurons; For the branch network The activation output of layer neurons; For the branch network The output vector of the layer, and also as the first The layer's input vector; For the branch network Layer weight matrix; For the branch network Layer bias vector; For the branch network The activation function used in the layer; superscript " " indicates the first in the corresponding network Layer; subscript " "" indicates that the parameter belongs to a branch network.

[0028] Step S12: Perform a Hadamard product on the first network output and the second network output to obtain the target physical field corresponding to the target matrix material.

[0029] In this embodiment, the Hadamard product needs to be performed on the outputs of the first network and the second network to obtain the target physical field corresponding to the target matrix material. Specifically, when performing the Hadamard product, the vector elements in the first network output and the second network output need to be multiplied element-wise to obtain the target vector. Then, the vector elements in the target vector are summed to obtain the target physical field corresponding to the target matrix material. The Hadamard product used in the output of PI-DeepONet is represented as follows: ; Where B is the output of the second network, T is the output of the first network, and U(x,y) is the target physical field corresponding to the target matrix material.

[0030] In this way, the changing parameter functions can be encoded through the branch networks in the target physical information deep operator network, and the solution domain coordinates can be encoded through the backbone network. Finally, the outputs of the two are synthesized into a solution through forms such as Hadamard product. The goal of the training process is no longer to optimize the solution under a specific parameter, but to learn a general operator that can generate solutions. It is this operator learning framework that enables the network operator trained by PI-DeepONet to accept any new input function within the training distribution, such as new material parameters, and output the corresponding physical field on the spot, thereby effectively improving the network's cross-parameter generalization ability.

[0031] Step S13: Determine the target solution in the target physical information depth operator network that satisfies the target boundary conditions for the material parameters, and determine the target distance output obtained after processing the material spatial coordinates by the target distance function.

[0032] In this embodiment, it is necessary to determine the target solution in which the material parameters satisfy the target boundary conditions in the target physical information depth operator network, and to determine the target distance output obtained after the target distance function processes the material space coordinates.

[0033] Specifically, the target computational domain of the target physical information depth operator network can be determined, and the maximum and minimum boundary values ​​within the target computational domain, as well as the target boundary of the target physical information depth operator network, can be determined based on the target boundary. Target boundary conditions are then constructed based on the target boundary, and the target solution where the material parameters satisfy the target boundary conditions in the target physical information depth operator network is determined. It should be noted that, in order to effectively and accurately embed the initial and boundary conditions of the partial differential equations, a hard constraint method can be used to construct a special network output structure, so that the solution function automatically satisfies the given initial and boundary conditions, thereby transforming the original constrained optimization problem into an unconstrained optimization problem. The network structure output after adding hard constraints is as follows: ; in This is the output of the original PI-DeepONet; A special function that satisfies the Dirichlet boundary conditions; It is a distance function that takes a value of 0 on the Dirichlet boundary.

[0034] Under normal circumstances, It is not easy to construct because, in this problem, the Dirichlet boundary values ​​are constant functions. It is set as a particular solution that satisfies the boundary conditions. Distance function ( d Ideally, an index function would be used; however, the index function is discontinuous and non-differentiable at the boundaries, making it impossible to perform effective gradient calculation on the neural network output. Therefore, a smooth distance function needs to be constructed that satisfies: ; in, Let distance be a function defined on the computational domain; For two-dimensional space coordinate variables; Dirichlet boundary; For the computational domain; symbol " " indicates "for any"; the symbol " The symbol "" indicates the set difference operation, which means "remove" or "exclude". This represents the region in the computational domain excluding the Dirichlet boundary.

[0035] The distance function is ,in, and These represent the maximum and minimum boundary values ​​of the computational domain, respectively.

[0036] Therefore, a target distance function can be constructed based on the maximum and minimum boundary values, and the target distance output corresponding to the material space coordinates can be determined according to the target distance function.

[0037] Step S14: Determine the solid stress field corresponding to the target matrix material based on the target distance output and the target physical field.

[0038] In this embodiment, based on the network structure output after adding hard constraints in step S13, it is known that it is necessary to calculate the product of the target distance output and the target physical field to obtain the target product, and use the sum of the target product and the target solution as the solid stress field corresponding to the target matrix material.

[0039] In this embodiment, the material parameters of the target matrix material are input into the target physical information deep operator network. The backbone network processes the material space coordinates of the material parameters to obtain a first network output, and the branch networks process the attribute parameters of the material parameters to obtain a second network output. The first and second network outputs are then multiplied by a Hadamard product to obtain the target physical field corresponding to the target matrix material. The target solution satisfying the target boundary conditions in the target physical information deep operator network is determined, and the target distance output obtained after processing the material space coordinates by the target distance function is determined. Based on the target distance output and the target physical field, the solid stress field corresponding to the target matrix material is determined. In this way, an end-to-end mapping relationship from material parameters to the stress field tensor can be established through a branch-backbone network structure, hard-constrained boundary conditions, and an adaptive training strategy. This algorithm enables the trained model to have zero-shot inference capability, allowing direct input of any new material parameters within the training distribution to quickly output the stress, strain, and displacement field distributions, significantly improving computational efficiency and cross-scenario adaptability, and providing real-time support for engineering decision-making.

[0040] As a preferred embodiment, this embodiment uses a specific set of data to illustrate the solid stress field prediction method of this application. The case settings are as follows: Figure 3 As shown, the solution domain is a 2m × 2m square, and the material parameter range is... , Test parameters are taken , In the training configuration, the physical space discretization uses a 40×40 sparse grid and an 80×80 dense grid for comparison, the optimizer is AdamW, and the learning rate is 0.001.

[0041] A phased progressive training strategy was applied using a sparse 40×40 grid. The training process consisted of 50,000 rounds, divided into 5 phases. The initial phase had fixed parameters. This allows the model to quickly grasp fundamental physical laws; subsequent stages gradually expand the parameter range, with expansion coefficients at each stage. , After training, the model is tested with the following parameters. , The prediction error is as follows Figure 4 As shown, the error distribution is uniform, with an average error of 0.361%, which is lower than that of the random strategy. Figure 5 The 0.345% was slightly higher, but the training time decreased from 1813 minutes to 1258 minutes, resulting in an efficiency improvement of approximately 30.6%.

[0042] Under a dense 80×80 grid, the random sampling training strategy performs better. Parameters are uniformly sampled from the entire range, and training is conducted for 50,000 epochs. The results are as follows: Figure 6As shown, the average prediction error decreased to 0.106%, significantly lower than the 0.282% of the staged strategy, as... Figure 7 As shown, the accuracy improvement is approximately 62.4%. This indicates that, with sufficient data, the global exploration capability of the stochastic strategy is more conducive to generalization. The effectiveness of the hard constraint mechanism is demonstrated through... Figure 8 Verification of strain components in the x-direction The results of hard constraints are highly consistent with the finite element solution, while the results of soft constraints show significant deviations, which confirms the advantage of hard constraints in eliminating physical paradoxes.

[0043] Compared with the traditional PINN method, PINN has the advantage of fixed parameters. The calculation results are shown in Figure 9. Figure 9(a) is the predicted normal stress contour map, where the horizontal axis represents the dimensionless coordinates along the model's length direction. The directional coordinates range from 0 to 1; the ordinate represents the dimensionless coordinates in the model's height direction, i.e. Direction coordinates, ranging from 0 to 1. The color contour plot in the image represents the predicted distribution of the normal stress components, including... and The colors, from blue to red, represent stress values ​​from low to high, with blue areas indicating lower stress values ​​and red areas indicating higher stress values. Figure 9(b) shows the relationship between shear stress and stress. The directional strain prediction contour plot, whose horizontal axis represents the dimensionless coordinates along the model's length direction, i.e. The directional coordinates range from 0 to 1; the ordinate represents the dimensionless coordinates in the model's height direction, i.e. Direction coordinates, ranging from 0 to 1. The left image of the color cloud represents... Directional shear stress components The predicted distribution, represented in the right figure. Directional strain components The predicted distribution is shown in Figure 9(c). Color changes represent the magnitude and sign of the corresponding physical quantity values; red areas indicate higher values, and blue areas indicate lower values. The predicted contour plots for directional normal strain and shear strain have their horizontal axes representing dimensionless coordinates along the model's length direction. The directional coordinates range from 0 to 1; the ordinate represents the dimensionless coordinate in the height direction of the model, i.e. Direction coordinates, ranging from 0 to 1. The left image of the color cloud represents... Directional strain components The predicted distribution, represented in the right figure. Directional shear strain components The predicted distribution of the strain field is shown in Figure 9(d). The color-coded cloud map reflects the spatial distribution of the strain field within the computational domain; red indicates larger positive values, and blue indicates smaller or negative values. The horizontal axis represents the dimensionless coordinates along the model's length direction. The directional coordinates range from 0 to 1; the ordinate represents the dimensionless coordinate in the height direction of the model, i.e. Direction coordinates, ranging from 0 to 1. The color cloud in the figure represents the predicted distribution of displacement components, including... Directional displacement and Directional displacement The left figure shows the displacement field. The right figure shows the displacement field. The color change from blue to red indicates a shift in displacement value from low to high, reflecting the deformation trend of the structure in different directions. Therefore, it can be seen that INN, with fixed parameters... Although the calculated results under the previous method agree well with the finite element solution with an average error of 1.82%, they cannot be generalized to new parameters. However, the method of this application achieves zero-sample inference with an error of less than 1% under the above experimental data, demonstrating its high efficiency and reliability in multi-condition stress field prediction.

[0044] See Figure 10 As shown, an embodiment of the present invention discloses a solid stress field prediction device, comprising: The network processing module 11 is used to input the material parameters of the target matrix material into the target physical information depth operator network, so as to process the material space coordinates in the material parameters through the backbone network in the target physical information depth operator network to obtain a first network output, and process the attribute parameters in the material parameters through the branch network in the target physical information depth operator network to obtain a second network output. The physics field calculation module 12 is used to perform a Hadamard product on the first network output and the second network output to obtain the target physics field corresponding to the target matrix material. The parameter determination module 13 is used to determine the target solution in the target physical information depth operator network that satisfies the target boundary conditions of the material parameters, and to determine the target distance output obtained after the target distance function processes the material spatial coordinates; The stress field calculation module 14 is used to determine the solid stress field corresponding to the target matrix material based on the target distance output and the target physical field.

[0045] In this embodiment, the material parameters of the target matrix material are input into the target physical information deep operator network. The backbone network processes the material space coordinates of the material parameters to obtain a first network output, and the branch networks process the attribute parameters of the material parameters to obtain a second network output. The first and second network outputs are then multiplied by a Hadamard product to obtain the target physical field corresponding to the target matrix material. The target solution satisfying the target boundary conditions in the target physical information deep operator network is determined, and the target distance output obtained after processing the material space coordinates by the target distance function is determined. Based on the target distance output and the target physical field, the solid stress field corresponding to the target matrix material is determined. In this way, an end-to-end mapping relationship from material parameters to the stress field tensor can be established through a branch-backbone network structure, hard-constrained boundary conditions, and an adaptive training strategy. This algorithm enables the trained model to have zero-shot inference capability, allowing direct input of any new material parameters within the training distribution to quickly output the stress, strain, and displacement field distributions, significantly improving computational efficiency and cross-scenario adaptability, and providing real-time support for engineering decision-making.

[0046] In some embodiments, the solid stress field prediction device may further include: The training set generation unit is used to sample training space coordinates in a preset solution region and randomly generate training material parameters to generate a training set based on the training space coordinates and the training material parameters. The first network training unit is used to randomly sample first training parameters from the training set, and to perform random sampling training on a preset initial network based on the first training parameters to obtain the target physical information deep operator network. The second network training unit is used to allocate corresponding parameter ranges to several preset training stages based on the training set, and randomly sample corresponding second training parameters from the parameter range for each training period corresponding to the preset training stage; and randomly sample and train the preset initial network based on the several preset training stages and the second training parameters to obtain the target physical information deep operator network; wherein, each training stage in the several preset training stages corresponds to several training periods.

[0047] In some embodiments, the network processing module 11 may specifically include: The coordinate feature extraction unit is used to extract the material space coordinates in the material parameters through several backbone network neurons in the backbone network of the target physical information depth operator network, so as to obtain the coordinate features corresponding to the material parameters. The first network output determination unit is used to convert the coordinate features into coordinate feature vectors corresponding to preset basis functions in the target physical information depth operator network, and to use the coordinate feature vectors as the first network output.

[0048] In some embodiments, the network processing module 11 may specifically include: The attribute feature extraction unit is used to extract the attribute parameters in the material parameters through several branch network neurons in the branch network of the target physical information deep operator network, so as to obtain the attribute features corresponding to the attribute parameters. The second network output determination unit is used to convert the attribute features into attribute feature vectors corresponding to preset basis functions in the target physical information deep operator network, and to use the attribute feature vectors as the output of the second network.

[0049] In some embodiments, the physics field calculation module 12 may specifically include: The vector elements in the first network output and the second network output are multiplied element by element to obtain the target vector; The vector elements in the target vector are summed to obtain the target physical field corresponding to the target matrix material.

[0050] In some embodiments, the parameter determination module 13 may specifically include: The boundary parameter determination unit is used to determine the target computation domain of the target physical information depth operator network, and to determine the maximum boundary value, minimum boundary value and target boundary of the target physical information depth operator network in the target computation domain based on the target computation domain. The target solution determination unit is used to construct target boundary conditions based on the target boundary and determine the target solution in the target physical information depth operator network that satisfies the target boundary conditions. The distance output determination unit is used to construct a target distance function based on the maximum boundary value and the minimum boundary value, and to determine the target distance output corresponding to the material space coordinates according to the target distance function.

[0051] In some embodiments, the stress field calculation module 14 may specifically include: The stress field calculation unit is used to calculate the product of the target distance output and the target physical field to obtain the target product, and the sum of the target product and the target solution is used as the solid stress field corresponding to the target matrix material.

[0052] Furthermore, embodiments of this application also disclose an electronic device, Figure 11This is a structural diagram of an electronic device 20 according to an exemplary embodiment. The content of the diagram should not be construed as limiting the scope of this application.

[0053] Figure 11 This is a schematic diagram of the structure of an electronic device 20 provided in an embodiment of this application. Specifically, the electronic device 20 may include: at least one processor 21, at least one memory 22, a power supply 23, a communication interface 24, an input / output interface 25, and a communication bus 26. The memory 22 stores a computer program, which is loaded and executed by the processor 21 to implement the relevant steps in the solid stress field prediction method disclosed in any of the foregoing embodiments. Furthermore, the electronic device 20 in this embodiment may specifically be an electronic computer.

[0054] In this embodiment, the power supply 23 is used to provide operating voltage for each hardware device on the electronic device 20; the communication interface 24 can create a data transmission channel between the electronic device 20 and external devices, and the communication protocol it follows can be any communication protocol applicable to the technical solution of this application, and is not specifically limited here; the input / output interface 25 is used to acquire external input data or output data to the outside world, and its specific interface type can be selected according to specific application needs, and is not specifically limited here.

[0055] In addition, the memory 22, as a carrier for resource storage, can be a read-only memory, random access memory, disk or optical disk, etc. The resources stored thereon can include operating system 221, computer program 222, etc., and the storage method can be temporary storage or permanent storage.

[0056] The operating system 221 is used to manage and control the various hardware devices on the electronic device 20 and the computer program 222, which may be Windows Server, Netware, Unix, Linux, etc. In addition to including a computer program capable of performing the solid stress field prediction method executed by the electronic device 20 as disclosed in any of the foregoing embodiments, the computer program 222 may further include computer programs capable of performing other specific tasks.

[0057] Furthermore, this application also discloses a computer-readable storage medium for storing a computer program; wherein, when the computer program is executed by a processor, it implements the aforementioned disclosed method for predicting solid stress fields. Specific steps of this method can be found in the corresponding content disclosed in the foregoing embodiments, and will not be repeated here.

[0058] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to in the method section.

[0059] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0060] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0061] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0062] The technical solutions provided in this application have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for predicting the stress field of a solid, characterized in that, include: The material parameters of the target matrix material are input into the target physical information depth operator network. The material space coordinates in the material parameters are processed by the backbone network of the target physical information depth operator network to obtain the first network output. The attribute parameters in the material parameters are processed by the branch network of the target physical information depth operator network to obtain the second network output. The first network output and the second network output are multiplied by a Hadamard product to obtain the target physical field corresponding to the target matrix material. Determine the target solution in the target physical information depth operator network that satisfies the target boundary conditions for the material parameters, and determine the target distance output obtained after processing the material spatial coordinates by the target distance function; The solid stress field corresponding to the target matrix material is determined based on the target distance output and the target physical field.

2. The method for predicting the stress field of a solid according to claim 1, characterized in that, Before the step of inputting the material parameters of the target matrix material into the target physical information depth operator network, processing the material space coordinates in the material parameters through the backbone network of the target physical information depth operator network to obtain a first network output, and processing the attribute parameters in the material parameters through the branch networks of the target physical information depth operator network to obtain a second network output, the method further includes: The training space coordinates are sampled in the preset solution region, and training material parameters are randomly generated to generate a training set based on the training space coordinates and the training material parameters. The first training parameters are randomly sampled from the training set to perform random sampling training on the preset initial network based on the first training parameters, so as to obtain the target physical information deep operator network. Alternatively, based on the training set, assign corresponding parameter ranges to several preset training stages, and randomly sample corresponding second training parameters from the parameter ranges for each training period corresponding to the preset training stage; perform random sampling training on the preset initial network based on the several preset training stages and the second training parameters to obtain the target physical information deep operator network; wherein, each training stage in the several preset training stages corresponds to several training periods.

3. The method for predicting the stress field of a solid according to claim 1, characterized in that, The step of processing the material space coordinates in the material parameters through the backbone network of the target physical information depth operator network to obtain the first network output includes: The material spatial coordinates in the material parameters are extracted by several backbone network neurons in the backbone network of the target physical information deep operator network to obtain the coordinate features corresponding to the material parameters. The coordinate features are converted into coordinate feature vectors corresponding to preset basis functions in the target physical information depth operator network, and the coordinate feature vectors are used as the output of the first network.

4. The method for predicting the stress field of a solid according to claim 1, characterized in that, The step of processing the property parameters in the material parameters through a branch network in the target physical information depth operator network to obtain the second network output includes: The property parameters in the material parameters are extracted by several branch network neurons in the branch network of the target physical information deep operator network to obtain the property features corresponding to the property parameters. The attribute features are converted into attribute feature vectors corresponding to preset basis functions in the target physical information deep operator network, and the attribute feature vectors are used as the output of the second network.

5. The method for predicting the stress field of a solid according to claim 1, characterized in that, The step of performing a Hadamard product on the first network output and the second network output to obtain the target physical field corresponding to the target matrix material includes: The vector elements in the first network output and the second network output are multiplied element by element to obtain the target vector; The vector elements in the target vector are summed to obtain the target physical field corresponding to the target matrix material.

6. The method for predicting the stress field of a solid according to claim 1, characterized in that, The process of determining the target solution in the target physical information depth operator network that satisfies the target boundary conditions for the material parameters, and determining the target distance output obtained after processing the material space coordinates by the target distance function, includes: The target computation domain of the target physical information depth operator network is determined, and the maximum boundary value, minimum boundary value, and target boundary of the target physical information depth operator network are determined based on the target computation domain. Based on the target boundary, construct the target boundary conditions, and determine the target solution in the target physical information deep operator network that satisfies the target boundary conditions for the material parameters; A target distance function is constructed based on the maximum and minimum boundary values, and the target distance output corresponding to the material space coordinates is determined according to the target distance function.

7. The method for predicting the stress field of a solid according to any one of claims 1 to 6, characterized in that, The step of determining the solid stress field corresponding to the target matrix material based on the target distance output and the target physical field includes: The product of the target distance output and the target physical field is calculated to obtain the target product, and the sum of the target product and the target solution is taken as the solid stress field corresponding to the target matrix material.

8. A solid stress field prediction device, characterized in that, include: The network processing module is used to input the material parameters of the target matrix material into the target physical information depth operator network, so as to process the material space coordinates in the material parameters through the backbone network of the target physical information depth operator network to obtain a first network output, and process the attribute parameters in the material parameters through the branch network of the target physical information depth operator network to obtain a second network output; The physics field calculation module is used to perform a Hadamard product on the first network output and the second network output to obtain the target physics field corresponding to the target matrix material. The parameter determination module is used to determine the target solution in the target physical information depth operator network that satisfies the target boundary conditions of the material parameters, and to determine the target distance output obtained after the target distance function processes the material spatial coordinates; The stress field calculation module is used to determine the solid stress field corresponding to the target matrix material based on the target distance and the target physical field.

9. An electronic device, characterized in that, include: Memory, used to store computer programs; A processor for executing the computer program to implement the solid stress field prediction method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the solid stress field prediction method as described in any one of claims 1 to 7.

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