Physics-based Information-driven model, method, and apparatus for predicting the strength of porous materials
By combining graph convolutional neural networks driven by physical information with physical laws, the problems of data dependence and physical consistency in the strength prediction of porous materials in traditional methods are solved, and high-precision, interpretable strength prediction is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HUAZHONG UNIV OF SCI & TECH
- Filing Date
- 2026-01-30
- Publication Date
- 2026-05-26
AI Technical Summary
Traditional methods rely on a large amount of experimental data to predict the strength of porous materials. The prediction results lack physical consistency and are difficult to effectively capture the complex mapping relationship between pore space topology and mechanical properties. Furthermore, existing data-driven methods are limited in application in scenarios where data is scarce.
We employ a graph convolutional neural network driven by physical information. By constructing a multi-layer local feature extraction module and a feature fusion and prediction module, and combining graph neural networks with physical laws, we establish a mapping relationship from microstructure to macroscopic intensity, and introduce a multi-task learning objective that combines data-driven loss and physical constraints.
It achieves high-precision and interpretable strength prediction of porous materials under limited data conditions, improving the accuracy and physical rationality of the prediction and enhancing the generalization ability of the model.
Smart Images
Figure CN122091035A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of mechanical property prediction and analysis of porous printed materials, and relates to a porous material strength prediction model, method and device based on physical information driven, and more specifically, to a porous material strength prediction model, training method, prediction method and device based on physical information driven graph convolutional neural network. Background Technology
[0002] 3D printed components, formed using powder bed fusion technology, inevitably introduce randomly distributed pore defects such as air bubbles and incomplete fusion during the manufacturing process. These defects act as stress concentration sources, constraining and determining the final component's mechanical properties. Due to the randomness of defect distribution, each component possesses a unique microstructure, making traditional destructive strength testing methods neither economical nor suitable for individualized assessment. Therefore, developing efficient non-destructive strength prediction methods has become an urgent need for industrial quality control.
[0003] Traditional techniques typically employ a "non-destructive testing + numerical simulation" approach. This involves obtaining a defect model through CT scans and then performing mechanical calculations using methods such as the finite element method (FEM) and discrete element method (DIM). However, this approach suffers from high computational costs and complex constitutive parameter calibration in numerical simulations, resulting in overall low efficiency and making it difficult to meet the needs of rapid assessment in production environments or large-scale digital twin applications. In recent years, data-driven machine learning methods have been introduced to seek more efficient solutions. By directly inputting defect features into deep learning networks, an end-to-end mapping relationship from structure to performance can be established. However, these methods are essentially "black boxes," lacking physical interpretation in their decision-making process. Their prediction accuracy heavily relies on massive amounts of high-quality labeled data, the cost and time of which are as high as numerical simulations, limiting their application in data-scarce real-world scenarios.
[0004] Therefore, physical information-driven artificial intelligence methods, which can integrate prior physical knowledge, reduce data dependence, and enhance model credibility, have emerged. Especially for the problem of predicting the strength of porous materials, Graph Convolutional Neural Networks (GCNs) have shown unique advantages. GCNs can naturally abstract the disordered and irregularly distributed pore groups within a material into a graph structure, where each pore is a node, and pores are connected by edges through geometric proximity or physical interactions. This structure allows GCNs to accurately capture the topological characteristics between pores that are difficult to quantify using traditional methods, such as pore clustering effects and microscopic interactions. Combining this GCN network, which can capture complex pore characteristics, with the physical laws describing the nature of material failure, to construct a physical information-driven graph neural network provides a promising new approach for solving the problem of accurate, fast, and reliable strength prediction of unique porous components. Summary of the Invention
[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a physical information-driven model, method and device for predicting the strength of porous materials. The purpose is to solve the technical problems of traditional methods relying on a large amount of experimental data, lacking physical consistency of prediction results, and being unable to effectively capture the complex mapping relationship between pore space topology and mechanical properties.
[0006] To achieve the above objectives, this invention provides a porous material strength prediction model based on a physically-informed graph convolutional neural network, comprising a three-layer local feature extraction module and a feature fusion and prediction module, wherein: The three local feature extraction modules each include a GCN convolutional layer, a ReLU activation function, a TopK pooling layer, and a global average pooling layer; the feature fusion and prediction module includes a feature splicing submodule, a fully connected layer, a ReLU activation function and Dropout, and an intensity prediction submodule. In the first-layer local feature extraction module, the GCN convolutional layer is used to extract feature information of nodes in the first-order neighborhood of each pore node in the porous material, extracting the local spatial correlation features between the pore node and its directly adjacent pores; the ReLU activation function is used to introduce nonlinear changes; the TopK pooling layer is used to filter and retain key nodes while reducing the graph size; global average pooling is used to aggregate global information of the node features output by the current layer, generating a fixed-length subset representing the global feature vector extracted by the layer, resulting in a coarsened graph; In the second-layer local feature extraction module, the GCN convolutional layer aggregates the second-order neighborhood feature information of nodes on the coarsened map after the first-layer pooling; the ReLU activation function is used to maintain nonlinear expressive power, and the TopK pooling layer further filters information and retains the core pore community features required for mechanical performance prediction; global average pooling is used to generate a global descriptive subset representing the structural features of the mid-scale. In the third-layer local feature extraction module, the GCN convolutional layer is used to extract the overall topological features of the internal pore network of the component; the ReLU activation function, the TopK pooling layer, and the global average pooling are used to increase the nonlinearity of the model, extract macroscopic features at the highest semantic level, and generate a global descriptive subset representing the overall macroscopic structural features, respectively. In the feature fusion and prediction module, the feature concatenation submodule is used to concatenate the output vectors of the global average pooling layer from the three local feature extraction modules to form a comprehensive feature representation that integrates multi-scale structural information; the fully connected layer is used to perform nonlinear combination and dimensional transformation on the concatenated multi-scale features; the ReLU activation function and Dropout are used to enhance the nonlinearity of the prediction function and to randomly drop some neuron connections during training to prevent model overfitting and improve generalization ability, respectively; the strength prediction submodule is used to output the final predicted values, namely the compressive strength and elastic modulus of the component.
[0007] According to another aspect of the present invention, a training method for a porous material strength prediction model based on a physically driven graph convolutional neural network is provided for training the porous material strength prediction model as described above, including data loading, model initialization, forward propagation, loss calculation, backpropagation and optimization, and model verification and testing steps: First, during the data loading phase, all sample data are divided into training set, validation set and test set, and the node features, edge features and adjacency matrix are normalized. Subsequently, during the model initialization phase, the weight matrix of the graph convolutional layer and the parameters of the graph pooling layer are initialized. During the forward propagation process, the data sequentially passes through multiple graph convolutional layers for neighborhood information aggregation and node feature updates. Subsequently, it is refined into a graph-level global feature representation through a TopK-based graph pooling layer. This global feature is finally mapped to the predicted value of the sample's macroscopic intensity via a fully connected layer. ; The loss calculation module then calculates the total loss of the model based on the aforementioned definition. ; During the backpropagation and optimization phase, the gradient descent algorithm is used to calculate the gradient of the total loss with respect to all model parameters, and the parameters are updated accordingly to minimize the total loss function. The model validation and testing phase is used to monitor and evaluate the model's generalization ability; during training, performance metrics are monitored on the validation set to prevent overfitting; after training is completed, the final performance of the model is evaluated on the test set to verify its accuracy and robustness in practical applications.
[0008] Furthermore, this includes methods for generating convolutional network datasets, as shown in the following figure: 1-1 Obtain the internal pore structure parameters of the 3D printed component, including the original structural data, spatial location information of the pores, and equivalent diameter. d ,volume V Surface area S Local porosity P And with a certain pore coordinate as the center, RThe ratio of the total volume of all pores within a spherical region of radius 1 to the total volume of that spherical region. 1-2 Obtain test results for 3D printed components, including sample compressive strength and compressive modulus; 1-3 Construct numerical simulation experiments as a supplement to experimental data. Specifically, based on the power law relationship between the equivalent diameter and the number of pores, establish a discrete element simulation model with equivalent random virtual defects, implement virtual experiments, and record the characteristic parameters of the pore defects and the results of the virtual experiments. 1-4 Constructing a graph neural network to establish edge connections transforms the disordered set of pores into a structured graph; specifically, the spatial location information of the midpoints of the sample pores constitutes the dataset. ,in Representing the i The coordinate vectors of each pore; then, based on the spatial proximity of the pores, n The pores are divided into k Mutually exclusive clusters For each cluster Any two distinct pore node coordinate vectors and Establish an undirected edge between them. m=1~k; 1-5 Define node features and edge features. Specifically, node features include: spatial location information, i.e. X,Y,Z Coordinates, equivalent diameter d ,volume V Surface area S Local porosity P Edge features include: spatial distance D ,inclination Theta Azimuth Phi ; Based on steps 1-4 and 1-5, construct the adjacency matrix A for each sample, and based on steps 1-2 and 1-3, construct the global label vector Y of the graph network to form the graph network dataset to which this scheme belongs.
[0009] Furthermore, the training steps include the following: 2-1 Based on the data information obtained from the Convolutional Graph Neural Network (GCN) and 1-4 and 1-5, a degree matrix is constructed for each sample data. Adjacency matrix Node feature matrix Edge feature matrix ,in It is the identity matrix; For the first layer of a convolutional graph neural network, node features are updated by aggregating the features of their neighboring nodes; that is, the updated feature matrix can be written as:
[0010] in, For the updated feature matrix, For activation function, The weight matrix is a learnable matrix. This is an enhanced node feature matrix that incorporates edge features, i.e. MLP stands for Multilayer Perceptron, which consists of two fully connected layers with a ReLU activation function in between, used to perform nonlinear transformation on the aggregated edge features; For the second and third layers of the convolutional graph neural network, the node feature update formula is:
[0011] in, t Take 1 or 2. These refer to the updated feature matrices of the t-th layer GCN network. For activation function, Let be the learnable weight matrix in the t-th layer of the GCN network.
[0012] Furthermore, the training steps include the following: 2-2 The loss calculation module is constructed in conjunction with physical constraints, specifically including two parts: geometric constraints and mechanical constraints. Assuming local porosity is continuous between two adjacent pores, construct a geometric continuity loss. have:
[0013] in, Representing nodes respectively i , j Local porosity, This is the coordinate vector of the pore node. This represents the summation of the local porosity characteristic gradients over all associated nodes. Let be the number of all edges in the graph neural network; The mechanical constraints consist of two parts: the stress intensity factor constraint at the pore tip and the Griffith fracture criterion constraint. Based on fracture mechanics, the pore can be regarded as a microcrack, and the stress intensity factor corresponding to each pore is... The stress field intensity at the crack tip can be simplified as follows:
[0014] in, Apply stress to the far field, Where is the pore radius, Pi; since failure only occurs when the stress intensity factor reaches the material's fracture strength, based on this physical relationship, and combined with the material's fracture strength... and the intensity predicted by each model The constraint loss based on the material's fracture toughness can be written. expression:
[0015] in, This represents the average value of all pore stress intensity factors; Similarly, based on Griffith's theory, a model can be established based on the geometric characteristics of each hole and the material strength. Relationship:
[0016] in, For the elastic modulus of the material, Let be the pore surface energy; assuming the sample strength is controlled by the most dangerous pores, then the relevant constraint loss is determined by the Griffith criterion. It can be represented as:
[0017] in, This represents the minimum local fracture stress at the pore nodes (i.e., all nodes in the figure), used to assess the overall fracture risk. In summary, the total loss of a graph neural network It can be represented as:
[0018] in, , This represents the mean square error function. Represents the loss due to physical constraints, i.e. This formula introduces an adjustable hyperparameter. Achieving an effective balance between the contributions of each physical information-driven loss, thereby guiding the model to learn representations that conform to physical laws.
[0019] According to another aspect of the present invention, a porous material strength prediction model product based on a physical information-driven graph convolutional neural network is provided, which is obtained by training by the training method described in any of the preceding claims.
[0020] According to another aspect of the present invention, a computer-readable storage medium is provided that stores a porous material strength prediction model product based on a physically driven graph convolutional neural network as described above.
[0021] According to another aspect of the present invention, a method for predicting the strength of porous materials based on a physical information-driven graph convolutional neural network is provided, which uses the porous material strength prediction model product as described above to predict the strength of porous materials.
[0022] According to another aspect of the present invention, a device for predicting the strength of porous materials based on a physically driven graph convolutional neural network is provided, comprising the computer-readable storage medium as described above.
[0023] In summary, the technical solutions conceived in this invention, compared with the prior art, can achieve the following beneficial effects: 1. This invention abstracts the pore structure inside a material into a graph network, with pores as nodes and the relationships between pores as edges. It learns the mapping relationship between the microstructure and macroscopic strength of porous materials through a graph neural network. It innovatively integrates the principles of material mechanics as physical constraints into the network training process, realizing interpretable and high-precision intelligent prediction from microstructure to macroscopic strength. This allows the model to maintain excellent prediction accuracy and physical rationality even with limited data.
[0024] 2. This invention designs a graph structure construction strategy of "pore clustering-centroid connectivity". By determining local connectivity through spatial clustering, the discrete and disordered pore coordinates are transformed into a structured graph containing spatial topological relationships, providing a basis for graph neural network operations that is both in line with physical laws and maintains computational efficiency.
[0025] 3. The method constructs a multi-task learning objective that includes data-driven loss and physical constraint loss. By integrating fracture mechanics criteria into the training process, the model learns both the patterns of observed data and basic physical principles, which significantly improves the generalization ability and physical consistency of prediction results in scenarios with limited data. This provides a complete framework for achieving reliable and interpretable intelligent prediction of "microstructure-macro performance". Attached Figure Description
[0026] Figure 1 A flowchart illustrating the construction and training process of a graph neural network-based porous material strength prediction model according to a preferred embodiment of the present invention.
[0027] Figure 2 A diagram illustrating the establishment of a GCN network dataset based on physical information in a preferred embodiment of the present invention.
[0028] Figure 3 The preferred embodiment of the present invention establishes a GCN network structure based on physical information. Detailed Implementation
[0029] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.
[0030] Please see Figure 1 and Figure 2 As shown in the figure, this implementation case provides a method for generating graph convolutional network datasets. The specific steps are as follows: 1-1 Obtaining the internal pore structure parameters of the 3D printed component. Specifically, the original data of the constructed structure is obtained using computed tomography (CT) technology. Pore reconstruction is then performed using the AVIZO software platform, which employs representative volume element extraction, threshold segmentation, and label analysis steps to obtain the spatial location information of the pores. X,Y,Z Coordinates), equivalent diameter ( d ),volume( V ), surface area ( S ), local porosity ( P Centered on a certain pore coordinate, R (The ratio of the total volume of all pores within a spherical region of radius 1 to the total volume of the spherical region).
[0031] 1-2 Obtain test results of 3D printed components. Specifically, obtain the uniaxial compression force-displacement curve of the scanned printed component through unconfined uniaxial compression test, and calculate the compressive strength and compressive modulus of the sample.
[0032] 1-3 Construct numerical simulation experiments as a supplement to experimental data. Specifically, based on the power law relationship between the equivalent diameter and the number of pores, establish a discrete element simulation model with equivalent random virtual defects, implement virtual experiments, and record the characteristic parameters of the pore defects and the results of the virtual experiments as described in steps 2 and 3.
[0033] 1-4 Constructing a graph neural network to connect the edges transforms the disordered set of pores into a structured graph. Specifically, this involves using the spatial location information of the midpoints of the sample pores summarized in steps 1-1 and 1-3. , constitute the dataset ,in Representing the i The coordinate vectors of each pore are then used. This pore coordinate data is then input into a K-Means clustering algorithm, which groups pores based on their spatial proximity. n The pores are divided into k Mutually exclusive clusters For each cluster Connect all the porous nodes contained within it pairwise, that is, for a cluster Any two distinct pore node coordinate vectors and Establish an undirected edge between them. To establish global connectivity, calculate the centroid coordinates of each cluster. For each cluster, find the other cluster whose centroid is closest to it, and select the pore node in each of these two clusters that is closest to the centroid of the other cluster. Add an undirected connectivity edge between the two selected nodes.
[0034] 1-5 Define node features and edge features. Specifically, node features include: spatial location information ( X,Y,Z Coordinates), equivalent diameter ( d ),volume( V ), surface area ( S ), local porosity ( P Edge features include: spatial distance ( r ),inclination( Theta ), azimuth ( Phi ).
[0035] 1-6 Based on the graph neural network edge connection relationships and node / edge feature definitions in steps 1-4 and 1-5, construct the adjacency matrix for each sample. Degree matrix and node feature matrix Edge feature matrix Based on steps 1-2 and 1-3, the global label vector Y of the graph network is constructed to form the graph network dataset to which this scheme belongs.
[0036] See Figure 1 and Figure 3 The physically-driven graph network architecture in this scheme includes a three-layer local feature extraction module and a feature fusion and prediction module, wherein: The three local feature extraction modules each include a GCN convolutional layer, a ReLU activation function, a TopK pooling layer, and a global average pooling layer; the feature fusion and prediction module includes a feature splicing submodule, a fully connected layer, a ReLU activation function and Dropout, and an intensity prediction submodule. The first-layer local feature extraction module consists of a GCN convolutional layer, a ReLU activation function, a TopK pooling layer, and a global average pooling layer. The GCN convolutional layer extracts feature information from nodes within the first-order neighborhood of each pore node, extracting the local spatial correlation features between the node and its directly adjacent pores. The ReLU activation function introduces non-linear changes, increasing the model's ability to fit complex pore structures. The TopK pooling layer filters and retains key nodes based on their importance scores, while reducing the graph size, focusing on the most important structural features in the first layer and improving computational efficiency. The global average pooling layer aggregates global information from the node features output by the current layer, generating a fixed-length subset representing the global feature vector extracted by that layer. The second-layer local feature extraction module consists of a GCN convolutional layer, a ReLU activation function, a TopK pooling layer, and a global average pooling layer. The GCN convolutional layer aggregates second-order neighborhood features of nodes on the coarsened map after the first pooling layer, capturing a wider range of interaction patterns within the pore structure. The ReLU activation function maintains nonlinear expressive power, while the TopK pooling layer further filters information, retaining core pore community features crucial for predicting mechanical properties. Global average pooling generates a global descriptive subset representing mid-scale structural features. The third-layer local feature extraction module consists of a GCN convolutional layer, a ReLU activation function, a TopK pooling layer, and a global average pooling layer. Here, the GCN convolutional layer is used to extract the overall topological features of the internal pore network of the component. The ReLU activation function, TopK pooling layer, and global average pooling layer are used to increase the model's nonlinearity, extract macroscopic features at the highest semantic level, and generate a global descriptive subset representing the overall macroscopic structural features, respectively.
[0037] The feature fusion and prediction module's feature concatenation submodule concatenates global average pooling output vectors from three different levels (local, meso-level, and macro-level) to form a comprehensive feature representation that integrates multi-scale structural information. Fully connected layers perform nonlinear combination and dimensionality transformation on the concatenated multi-scale features. The ReLU activation function and Dropout are used to enhance the nonlinearity of the prediction function and randomly discard some neuron connections during training to prevent overfitting and improve generalization ability, respectively. The strength prediction submodule outputs the final predicted values, namely the compressive strength and elastic modulus of the component.
[0038] The creation and training of the physically-driven graph network architecture in this solution includes the following steps: 2-1 Based on the principle of Convolutional Graph Neural Network (GCN) and the edge connection relationships and predefined node and edge feature information obtained in 1-4 and 1-5 respectively, the adjacency matrix can be obtained from the edge and node connection relationships in 1-4. Sum-degree matrix The node features and edge features in 1-5 are used to construct the node feature matrix. Edge feature matrix .
[0039] The graph neural network designed in this technical solution adopts a three-layer serial architecture, in which each layer shares the same graph topology, that is, the set of nodes and the edge connection relationship remain unchanged in each level of the network.
[0040] For the first layer of a convolutional graph neural network, node features are updated by aggregating the features of their neighboring nodes; that is, the updated feature matrix can be written as:
[0041] in, For the updated feature matrix, For activation function, The weight matrix is a learnable matrix. This is an enhanced node feature matrix that incorporates edge features, i.e. MLP stands for Multilayer Perceptron, which consists of two fully connected layers with a ReLU activation function in between, used to perform nonlinear transformation on the aggregated edge features.
[0042] For the second and third layers of the convolutional graph neural network, the node feature update formula is:
[0043] in, t Take 1 or 2. These refer to the updated feature matrices of the t-th layer GCN network. For activation function, Let be the learnable weight matrix in the t-th layer of the GCN network.
[0044] 2-2 The loss calculation module is constructed in conjunction with physical constraints, specifically including two parts: geometric constraints and mechanical constraints. Assuming local porosity is continuous between two adjacent pores, construct a geometric continuity loss. have:
[0045] in, Representing nodes respectively i , j Local porosity, This is the coordinate vector of the pore node. This represents the summation of the local porosity characteristic gradients over all associated nodes. Let be the number of edges in the graph neural network.
[0046] The mechanical constraints consist of two parts: the stress intensity factor constraint at the pore tip and the Griffith fracture criterion constraint. Based on fracture mechanics, the pore can be regarded as a microcrack, and the stress intensity factor corresponding to each pore (node i) is... The stress field intensity at the crack tip can be simplified as follows:
[0047] in, Apply stress to the far field, Where is the pore radius, Pi is the mathematical constant. Since failure only occurs when the stress intensity factor reaches the material's fracture strength, based on this physical relationship, and considering the material's fracture strength... and the intensity predicted by each model The constraint loss based on the material's fracture toughness can be written. expression:
[0048] in, This represents the average stress intensity factor of all pores (i.e., all nodes in the graph neural network).
[0049] Similarly, based on Griffith theory, a model can be established based on the geometric characteristics and material strength of each hole (node i). Relationship:
[0050] in, For the elastic modulus of the material, Let be the pore surface energy. Assuming the sample strength is controlled by the most dangerous pores, then the relevant constraint loss is determined by the Griffith criterion. It can be represented as:
[0051] in, This represents the minimum local fracture stress at the pore nodes (i.e., all nodes in the figure), used to assess the overall fracture risk.
[0052] In summary, the total loss of a graph neural network It can be represented as:
[0053] in, , The Mean Square Error function measures the difference between the model's predicted intensity `strength_pred` and the true intensity label `Y`. Represents the loss due to physical constraints, i.e. This formula introduces an adjustable hyperparameter. Achieving an effective balance between the contributions of each physical information-driven loss, thereby guiding the model to learn representations that conform to physical laws.
[0054] 2-3 Based on the key architecture of the graph neural network established in 2-1 and 2-2, this scheme constructs a complete model training process (such as...). Figure 1 (As shown). This process specifically includes a series of steps such as dataset preparation, model initialization, forward propagation loss calculation, backpropagation and optimization, and model validation and testing. First, in the dataset preparation stage, the graph dataset constructed in step 1 is divided into a training set, a validation set, and a test set, and the node features, edge features, and adjacency matrix are normalized.
[0055] Subsequently, during the model initialization phase, the weight matrix in the three-layer graph neural network is initialized. and each Top Node weights in the K-pooling layer. During the forward propagation, the function sequentially passes through three layers of local feature extraction modules (each layer contains GCN convolution, ReLU activation, and Top...). K-pooling and global average pooling are used, and the final intensity prediction value is output through feature concatenation and a fully connected layer. .
[0056] The loss calculation module then calculates the total loss of the model based on the aforementioned definition (2-2). .
[0057] During the backpropagation and optimization phase, the gradient descent algorithm is used to calculate the gradient of the total loss with respect to all model parameters, and the total loss function is minimized accordingly to optimize and update the parameters.
[0058] The model validation and testing phase aims to evaluate the generalization ability and practical effectiveness of the trained model. First, the model performance during training is monitored using a reserved validation set; second, the final performance of the model is evaluated using a test set, and the error index between the predicted strength and the true strength is calculated to verify its generalization ability.
[0059] After the model passes validation and testing, it can be deployed for practical prediction. For a new 3D printed component, the corresponding graph structure data is first constructed based on its CT scan data, following the methods described in steps 1-1 to 1-6. Subsequently, this data is input into the pre-optimized graph neural network model, which directly outputs the predicted uniaxial compressive strength of the new component.
[0060] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A strength prediction model for porous materials based on physically-informed graph convolutional neural networks, characterized in that, It includes a three-layer local feature extraction module and a feature fusion and prediction module, wherein: The three local feature extraction modules each include a GCN convolutional layer, a ReLU activation function, a TopK pooling layer, and a global average pooling layer; the feature fusion and prediction module includes a feature splicing submodule, a fully connected layer, a ReLU activation function and Dropout, and an intensity prediction submodule. In the first-layer local feature extraction module, the GCN convolutional layer is used to extract the feature information of nodes in the first-order neighborhood of each pore node in the porous material, and to extract the local spatial correlation features between the pore node and its directly adjacent pores; the ReLU activation function is used to introduce nonlinear changes; the TopK pooling layer is used to filter and retain key nodes, while reducing the graph size; global average pooling is used to aggregate the global information of the node features output by the current layer, and generate a fixed-length subset representing the global feature vector extracted by the layer, thus obtaining the coarsened graph; In the second-layer local feature extraction module, the GCN convolutional layer aggregates the second-order neighborhood feature information of nodes on the coarsened map after the first-layer pooling; the ReLU activation function is used to maintain nonlinear expressive power, and the TopK pooling layer further filters information and retains the core pore community features required for mechanical performance prediction; global average pooling is used to generate a global descriptive subset representing the structural features of the mid-scale. In the third-layer local feature extraction module, the GCN convolutional layer is used to extract the overall topological features of the internal pore network of the component; the ReLU activation function, the TopK pooling layer, and the global average pooling are used to increase the nonlinearity of the model, extract macroscopic features at the highest semantic level, and generate a global descriptive subset representing the overall macroscopic structural features, respectively. In the feature fusion and prediction module, the feature concatenation submodule is used to concatenate the output vectors of the global average pooling layer from the three local feature extraction modules to form a comprehensive feature representation that integrates multi-scale structural information; the fully connected layer is used to perform nonlinear combination and dimensional transformation on the concatenated multi-scale features; the ReLU activation function and Dropout are used to enhance the nonlinearity of the prediction function and to randomly drop some neuron connections during training to prevent model overfitting and improve generalization ability, respectively; the strength prediction submodule is used to output the final predicted values, namely the compressive strength and elastic modulus of the component.
2. A training method for a porous material strength prediction model based on a physically-informed graph convolutional neural network, used to train the porous material strength prediction model of claim 1, characterized in that, This includes the following steps: data loading, model initialization, forward propagation, loss calculation, back propagation and optimization, and model validation and testing. First, during the data loading phase, all sample data are divided into training set, validation set and test set, and the node features, edge features and adjacency matrix are normalized. Subsequently, during the model initialization phase, the weight matrix of the graph convolutional layer and the parameters of the graph pooling layer are initialized. During the forward propagation process, the data sequentially passes through multiple graph convolutional layers for neighborhood information aggregation and node feature updates. Subsequently, it is refined into a graph-level global feature representation through a TopK-based graph pooling layer. This global feature is finally mapped to the predicted value of the sample's macroscopic intensity via a fully connected layer. ; The loss calculation module then calculates the total loss of the model based on the aforementioned definition. ; During the backpropagation and optimization phase, the gradient descent algorithm is used to calculate the gradient of the total loss with respect to all model parameters, and the parameters are updated accordingly to minimize the total loss function. The model validation and testing phase is used to monitor and evaluate the model's generalization ability; during training, overfitting is prevented by monitoring performance metrics on the validation set. After training, the final performance of the model is evaluated on the test set to verify its accuracy and robustness in practical applications.
3. The training method for a porous material strength prediction model based on a physically driven graph convolutional neural network according to claim 2, characterized in that, This includes methods for generating convolutional network datasets, as shown in the image below: 1-1 Obtain the internal pore structure parameters of the 3D printed component, including the original structural data, spatial location information of the pores, and equivalent diameter. d ,volume V Surface area S Local porosity P And with a certain pore coordinate as the center, R The ratio of the total volume of all pores within a spherical region of radius 1 to the total volume of that spherical region. 1-2 Obtain test results for 3D printed components, including sample compressive strength and compressive modulus; 1-3 Construct numerical simulation experiments as a supplement to experimental data. Specifically, based on the power law relationship between the equivalent diameter and the number of pores, establish a discrete element simulation model with equivalent random virtual defects, implement virtual experiments, and record the characteristic parameters of the pore defects and the results of the virtual experiments. 1-4 Constructing a graph neural network to establish edge connections transforms the disordered set of pores into a structured graph; specifically, the spatial location information of the midpoints of the sample pores constitutes the dataset. ,in Representing the i The coordinate vectors of each pore; then, based on the spatial proximity of the pores, n The pores are divided into k Mutually exclusive clusters For each cluster Any two distinct pore node coordinate vectors and Establish an undirected edge between them. m=1~k; 1-5 Define node features and edge features. Specifically, node features include: spatial location information, i.e. X,Y,Z Coordinates, equivalent diameter d ,volume V Surface area S Local porosity P Edge features include: spatial distance D ,inclination Theta Azimuth Phi ; Based on steps 1-4 and 1-5, construct the adjacency matrix A for each sample, and based on steps 1-2 and 1-3, construct the global label vector Y of the graph network to form the graph network dataset to which this scheme belongs.
4. The training method for a porous material strength prediction model based on a physically driven graph convolutional neural network according to claim 3, characterized in that, The training steps include the following: 2-1 Based on the data information obtained from the Convolutional Graph Neural Network (GCN) and 1-4 and 1-5, a degree matrix is constructed for each sample data. Adjacency matrix Node feature matrix Edge feature matrix ,in It is the identity matrix; For the first layer of a convolutional graph neural network, node features are updated by aggregating the features of their neighboring nodes; that is, the updated feature matrix can be written as: in, For the updated feature matrix, For activation function, The weight matrix is a learnable matrix. This is an enhanced node feature matrix that incorporates edge features, i.e. MLP stands for Multilayer Perceptron, which consists of two fully connected layers with a ReLU activation function in between, used to perform nonlinear transformation on the aggregated edge features; For the second and third layers of the convolutional graph neural network, the node feature update formula is: in, t Take 1 or 2. These refer to the updated feature matrices of the t-th layer GCN network. For activation function, Let be the learnable weight matrix in the t-th layer of the GCN network.
5. The training method for a porous material strength prediction model based on a physically-informed graph convolutional neural network according to claim 4, characterized in that, The training steps include the following: 2-2 The loss calculation module is constructed in conjunction with physical constraints, specifically including two parts: geometric constraints and mechanical constraints. Assuming local porosity is continuous between two adjacent pores, construct a geometric continuity loss. have: in, Representing nodes respectively i , j Local porosity, This is the coordinate vector of the pore node. This represents the summation of the local porosity characteristic gradients over all associated nodes. Let be the number of all edges in the graph neural network; The mechanical constraints consist of two parts: the stress intensity factor constraint at the pore tip and the Griffith fracture criterion constraint. Based on fracture mechanics, the pore can be regarded as a microcrack, and the stress intensity factor corresponding to each pore is... The stress field intensity at the crack tip can be simplified as follows: in, Apply stress to the far field, Where is the pore radius, Pi; since failure only occurs when the stress intensity factor reaches the material's fracture strength, based on this physical relationship, and combined with the material's fracture strength... and the intensity predicted by each model The constraint loss based on the material's fracture toughness can be written. expression: in, This represents the average value of all pore stress intensity factors; Similarly, based on Griffith's theory, a model can be established based on the geometric characteristics of each hole and the material strength. Relationship: in, For the elastic modulus of the material, Let be the pore surface energy; assuming the sample strength is controlled by the most dangerous pores, then the relevant constraint loss is determined by the Griffith criterion. It can be represented as: in, This represents the minimum local fracture stress at the pore nodes (i.e., all nodes in the figure), used to assess the overall fracture risk. In summary, the total loss of a graph neural network It can be represented as: in, , This represents the mean square error function. Represents the physical constraint loss, i.e. This formula introduces an adjustable hyperparameter. Achieving an effective balance between the contributions of each physical information-driven loss, thereby guiding the model to learn representations that conform to physical laws.
6. A product for predicting the strength of porous materials based on a physically-informed graph convolutional neural network, characterized in that, It is obtained by training using the training method described in any one of claims 2 to 5.
7. A computer-readable storage medium, characterized in that, The product containing the porous material strength prediction model based on a physically driven graph convolutional neural network as described in claim 6 is stored.
8. A method for predicting the strength of porous materials based on physically-informed graph convolutional neural networks, characterized in that, The strength prediction model product for porous materials described in claim 6 is used to predict the strength of porous materials.
9. A device for predicting the strength of porous materials based on a physically-informed graph convolutional neural network, characterized in that, Includes the computer-readable storage medium as described in claim 7.