Formula design method of PVA fiber toughened UHPC material based on hypergraph neural network

Abstract

The invention discloses a hypergraph neural network-based PVA fiber toughened UHPC material formula design method. The method comprises the steps of 1, multi-modal data acquisition and processing, 2, hypergraph structure construction, 3, HGNN model construction, 4, model training, and 5, performance optimization and reverse ratio design. According to the method, the high-order relationship among the multi-modal data such as the raw material, the proportion and the microstructure can be efficiently modeled, the precise prediction of the performance of the PVA fiber toughened UHPC and the optimal design of the proportion are realized, and the method is suitable for the performance prediction and proportion recommendation of various ultra-high performance concrete systems, and has wide engineering application prospects and industrial popularization values.

Description

Technical Field

[0001] The present invention relates to the field of construction engineering technology, and in particular to a method for designing a PVA fiber-reinforced ultra-high performance concrete (UHPC) material formula based on a hypergraph neural network. Background Art

[0002] Ultra-High Performance Concrete (UHPC) has been widely used in engineering fields such as bridges, tunnels, and high-rise buildings due to its excellent compressive strength, ductility, and durability. To further enhance its toughness and crack resistance, polyvinyl alcohol (PVA) fibers are often incorporated into UHPC to achieve fiber reinforcement and toughening. However, the dosage, morphology, spatial distribution, and interfacial interaction of PVA fibers with the matrix produce complex coupling effects with multiple factors such as the water-binder ratio, aggregate gradation, and admixture dosage, significantly affecting the mechanical properties and performance of UHPC materials. The multiple factors reflecting the "molecular structure-material property" structure-activity relationship mentioned above have highly nonlinear, high-order, and multimodal interactions, posing challenges to material design.

[0003] Currently, UHPC material mix optimization and performance prediction still primarily rely on engineers' experience or traditional regression models based on linear assumptions. These methods struggle to accurately capture the deep correlations between raw material parameters, process conditions, microstructure images, and macroscopic properties. In particular, they are significantly deficient in achieving the coordinated optimization of multiple performance objectives, such as strength and toughness.

[0004] Therefore, the present invention proposes a high-order modeling and optimization method for PVA-reinforced UHPC materials, which can effectively integrate multimodal input information, construct a performance prediction model with strong expressiveness and high interpretability, and realize automated ratio optimization design for multiple performance indicators. Summary of the Invention

[0005] Based on the above, the present invention aims to propose a PVA fiber-toughened UHPC material formula design method based on a hypergraph neural network, which can efficiently model high-order relationships between multimodal data such as raw materials, proportions, and microstructures, and realize accurate prediction of PVA fiber-toughened UHPC performance and optimal design of proportions.

[0006] In order to achieve the above technical objectives, the technical solution adopted by the present invention is: a method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network, comprising the following steps: Step 1: Multimodal data acquisition and processing: Collect multimodal material sample data including raw material ratio parameters, PVA fiber performance parameters, microscopic images, and corresponding macroscopic performance indicators; Preprocess the original data and uniformly concatenate and encode all sample features into high-dimensional node feature vectors , forming the initial node feature matrix , as the input of the HGNN model; The macroscopic properties of material samples are used for model output alignment and performance regression prediction; Step 2: Hypergraph structure construction: Defining the hypergraph structure , taking each material sample as a node in the graph structure, construct a node set V ; Construct multiple hyperedge groups based on attribute similarity and feature space neighbor relationships, respectively construct attribute-driven hyperedge sets and feature-driven hyperedge sets, and splice the two to form a hyperedge set E ; Assign a weight to each hyperedge to form a hyperedge weight matrix W , and construct the corresponding correlation matrix H , which is used to characterize the connection relationship between nodes and hyperedges and realize the graph representation of high-order structural information.

[0007] Step 3: HGNN model construction: Based on the constructed hypergraph structure, an HGNN model containing multiple hypergraph convolutional layers is constructed. The model extracts and fuses node features layer by layer through a bidirectional message passing mechanism from node to hyperedge and then from hyperedge back to node, thereby effectively modeling the nonlinear, multimodal, and high-order coupling relationship between material ratio parameters, fiber properties, microstructure characteristics and performance indicators.

[0008] Step 4: Model training: The HGNN model is trained using an end-to-end backpropagation mechanism. The training process includes parameter initialization, forward propagation, loss function construction, gradient backpropagation, and parameter update. Step 5: Performance optimization and reverse ratio design: Based on the trained HGNN model, according to the set target performance vector, the HGNN model is embedded as a prediction function into the performance deviation loss to construct the reverse optimization objective function. Genetic algorithms are used to iteratively search in the input variable space to automatically generate the optimal raw material ratio combination that meets the target performance, and simultaneously output the corresponding macro performance indicators.

[0009] Furthermore, step 1 specifically includes: Step 11: comprehensively collect multi-source heterogeneous characteristic information of the PVA fiber-reinforced ultra-high performance concrete material, wherein the multi-source heterogeneous characteristic information includes raw material ratio parameters, PVA fiber performance parameters, microstructure image information, and corresponding macroscopic performance indicators; The collected raw material ratio parameters, PVA fiber performance parameters, and microstructure image information feature variables are standardized and used as dataset feature vectors to form a data structure suitable for hypergraph neural network input; Step 12: Treat each UHPC material sample as a node in the hypergraph V , the corresponding input feature is the fused multimodal data vector; this feature vector is used as the initial input of the hypergraph neural network and is recorded as ,in i =1, 2, ..., N , is the sample number, d is the feature dimension; Each node The input feature vector is composed of three parts, namely the matching parameter vector , PVA fiber parameter vector and image feature vector ; The concatenated vector is recorded as , which constitutes the single sample input feature of the hypergraph neural network, The table is as follows:

[0010] All samples form nodes to form a feature matrix , as the input of the hypergraph neural network; The table is as follows:

[0011] Step 13: The output of the HGNN model is the predicted value of the macro performance index of the material sample; the macro performance index specifically includes: compressive strength , flexural strength ,tensile strength , flexural strength , expansion and slump , used to guide the reverse optimization of input variables based on target performance and the recommendation of high performance ratio. i samples, whose performance output is defined as :

[0012] in, represents the predicted value of compressive strength; Indicates the predicted value of flexural strength; represents the predicted value of tensile strength; represents the predicted value of flexural strength; represents the predicted value of expansion; Indicates the predicted slump value; Combining the outputs of all samples, we can get the overall prediction output matrix:

[0013] This output matrix is ​​used to compare with the target performance Make comparisons and perform reverse ratio optimization.

[0014] Furthermore, in step 11, the collected raw material ratio parameters, PVA fiber performance parameters, and microstructure image information feature variables are standardized and used as data set feature vectors to form a data structure suitable for hypergraph neural network input; specifically, as follows: a) Raw material ratio parameters: Obtain the basic composition ratio of each concrete sample, including: cement (kg / m 3 )、Silica fume(kg / m 3 )、Fly ash(kg / m 3 )、quartz sand(kg / m 3 )、Water(kg / m 3 ), water reducing agent (%), PVA fiber content (%); The above parameters are formed into a matching vector and normalized using the normalization method (min-max) to eliminate the dimension difference and form the input node feature , the expression is as follows:

[0015] in, x c Indicates cement; x sf represents silica fume; x fa represents fly ash; x sand Indicates quartz sand; x water It means water; x ad Indicates water reducing agent; x pva Indicates the PVA fiber content; b) PVA fiber performance parameters: For the PVA fibers used in each test batch, their physical and mechanical properties were collected, including: diameter (μm), length (mm), density (g / cm 3 ), tensile strength (MPa), elongation at break (%), elastic modulus (GPa); The above parameters are combined to form a fiber feature sub-vector, which is normalized using the min-max method to form the input node feature , the expression is as follows:

[0016] in, Indicates diameter; Indicates length; Indicates density; Indicates tensile strength; It represents the elongation at break; Represents the elastic modulus.

[0017] c) Microstructure image information: Scanning electron microscope (SEM) images of individual samples are collected to extract internal microstructure features. Image data is extracted using a pre-trained convolutional neural network (CNN) model and reduced to a fixed-length image feature vector. , the expression is as follows:

[0018] in, I SEM The corresponding scanning electron microscope image of the material sample is shown.

[0019] The pre-trained convolutional neural network (CNN) model used for image feature extraction is a common method in current visual feature processing. The present invention preferably uses the existing mainstream CNN architectures such as ResNet and EfficientNet for image encoding.

[0020] Furthermore, step 2) specifically includes: Step 21: Represent all material samples as nodes in a hypergraph structure, and construct a hypergraph structure for modeling high-order complex relationships. The hypergraph structure is defined as: ,in, is the set of all nodes, corresponding to all material samples, each node in the hypergraph Corresponding to a row of feature vectors ; is a set of hyperedges, each hyperedge connects a set of related nodes; W is the hyperedge weight matrix; the hypergraph structure can be constructed by constructing the association matrix H Implement formal representation; Step 22: To achieve high-order structural expression between material samples in different feature dimensions, the present invention adopts multiple strategies to construct hyperedge sets. E , aggregate related sample nodes into a unified hyperedge; the generation methods of hyperedges include attribute-driven and feature-driven methods, which can be flexibly combined to improve the diversity and expression ability of hypergraph modeling.

[0021] Step 23: Build a hypergraph structure When , a non-negative weight is assigned to each hyperedge to adjust the influence of the hyperedge in the information propagation process. Trainable parameters are set for hyperedge sets from different sources (such as attribute-driven and feature-driven), and the weight matrix is ​​formed by normalizing the hyperedges of attribute-driven and feature-driven hyperedges through the activation function (sigmoid). W， The weights of all hyperedges can be uniformly expressed as a diagonal matrix , and the incidence matrix Participate in the convolution operation of the HGNN model together.

[0022] Furthermore, step 22 specifically includes the following steps: Step 221: Attribute-driven hyperedge generation For discrete or interval-type structured attributes in material samples (such as PVA content, compressive strength grade, etc.), sample nodes with the same attribute value or falling into the same interval are grouped together and a corresponding hyperedge is generated; this hyperedge connects all nodes that meet the attribute conditions together to achieve high-order aggregation modeling in the attribute space; the details are as follows: Let the complete set of attributes be , a certain attribute , the corresponding node set is:

[0023] in, Representation node Attribute value of Indicates that all have the same attribute value a A collection of nodes.

[0024] Therefore, the attribute-driven hyperedge set can be expressed as:

[0025] Attribute-driven hyperedges form an association matrix for:

[0026] in, Drives the number of hyperedges for the attribute.

[0027] Step 222: Feature space driven hyperedge generation Aiming at the similarity relationship of material samples in multidimensional feature space (ratio vector, PVA fiber parameters and image features), a method based on k -nearest neighbors ( k -Nearest Neighbors, KNN) strategy to construct hyperedges; Taking each node sample as the center, select the one with the smallest Euclidean distance from it in the feature space. k Adjacent nodes, together with the central node, form a hyperedge; the details are as follows: For each node , whose eigenvector is , define its k The set of KNN neighbors is:

[0028] in, v ik Representation node v i The kth nearest neighbor node of ; The central node Together with its neighbors, it forms a hyperedge:

[0029] The final feature-driven hyperedge set is expressed as:

[0030] in, N is the number of nodes, indicating that a feature space neighbor hyperedge centered on itself is constructed for each node; Feature-driven hyperedges form an association matrix for:

[0031] in, The number of hyperedges driven by the feature.

[0032] Step 223: Join the hyperedges constructed by attribute drive and feature drive to obtain the total hyperedge set. E , and construct the incidence matrix of the hypergraph accordingly:

[0033] Among them, the total number of super edges Each hyperedge It is a subset of a set of nodes, representing a set of sample nodes that have similarity, coupling or correlation under a certain feature dimension or attribute condition.

[0034] Based on the total hyperedge set E , construct the correlation matrix , , satisfying the following rules:

[0035] in, Representation node Belong to the super edge , Indicates that the node does not belong to the hyperedge.

[0036] What we finally get H As one of the core inputs in the model structure, together with the weight matrix W Participate in the subsequent graph convolution calculation process of the HGNN model.

[0037] Furthermore, in step 3, a hypergraph neural network is used as the learning framework. The constructed hypergraph neural network model mainly consists of the following structure: 3 hypergraph convolutional layers, 2 batch normalization layers, an activation function layer following each convolutional layer, and a fully connected output layer; the activation function layer uses the ReLU function to introduce nonlinear expression capabilities and improve the model's ability to fit complex relationships.

[0038] Furthermore, step 3 specifically includes: Step 31: During the model training phase, the hypergraph neural network uses the node feature matrix As input, the sample features are extracted and transformed layer by layer through a multi-layer hypergraph convolution structure; at the same time, the model uses the pre-built association matrix and the hyperedge weight matrix Model high-order connection relationships between nodes to achieve cross-node and cross-attribute structured feature aggregation; Step 32: Using a hypergraph convolution module based on the spatial domain propagation mechanism, each layer of hypergraph convolution operation is divided into two stages: the first stage realizes information aggregation from nodes to hyperedges, and the second stage realizes the reverse update of features from hyperedges to nodes, thereby forming a complete information interaction closed loop.

[0039] Furthermore, the convolution operation of each layer of the hypergraph in step 32 is divided into two stages: the first stage realizes information aggregation from nodes to hyperedges, and the second stage realizes the reverse update of features from hyperedges to nodes, thereby forming a complete information interaction closed loop; the details are as follows: Step 321: Node to hyperedge feature aggregation. Each hyperedge aggregates its associated node features to generate a hyperedge feature set. :

[0040] in, W is the hyperedge weight matrix; D e is the hyperedge degree matrix; H is the hypergraph incidence matrix, ; is the transposed incidence matrix, which is used to control the nodes connected by each hyperedge. ; For the t Node features of the layer input.

[0041] Step 322: Back propagation of hyperedge-to-node features. The information of each hyperedge is transmitted back to its adjacent nodes. The feature nodes are updated. The expression is as follows:

[0042] in, is the output feature; σ(·) is the activation function ReLU; D v is the node degree matrix; For the t The learnable parameter matrix of the layer; Combining the two formulas in step 321 and step 322, we can get the hypergraph convolution expression: .

[0043] Furthermore, step 4 specifically includes: Step 41: Parameter initialization and hyperparameter setting: Randomly initialize the parameter weights of all HGNN layers , and set the initial learning rate to 0.0001 and the loss function weight coefficient λ j ; Step 42, forward propagation: input the node feature matrix Input the HGNN model, perform feature extraction and propagation through multiple layers of HGNNConv convolutional layers, batch normalization layers, and activation function layers, and output the prediction result matrix ,in K is the number of output performance dimensions; Step 43, loss function construction and back propagation: The training goal is to minimize the error between the predicted value and the true target value, using a multi-objective weighted mean square error (MSE) loss function :

[0044] in, λ j For the j The weight of each goal; For the i Sample No. j The target value of each indicator; For the i Sample No. j The predicted value of an indicator; Backpropagation is used to calculate the gradient of the loss function with respect to the parameters of each layer, and the Adam optimizer is used to update the model parameters, gradually minimizing the prediction error during training; Step 44: Training control and convergence judgment: All training samples are divided into a training set and a validation set in a ratio of 8:2, where 80% of the samples are used for learning model parameters and 20% of the samples are used as a validation set. The prediction performance of each epoch is evaluated in real time. When the validation set loss function stops decreasing or starts to increase over several consecutive epochs, the model is considered to have reached its optimal state, and training is terminated early to prevent overfitting.

[0045] Furthermore, step 5 specifically includes: Step 51: Task modeling and problem definition Set the target performance vector as:

[0046] in, is the target performance vector, set by the user; is the target compressive strength; is the target flexural strength; is the target tensile strength; is the target flexural strength; is the target expansion; is the target slump; Step 52: Model the reverse mix design problem as an optimization problem based on performance objectives: In the process, the optimization module is used to automatically generate candidate input combinations x, and the trained HGNN performance prediction model is used to predict the Calculate its corresponding performance prediction value ; The optimization goal is to minimize the difference between the predicted performance and the target performance set by the user. The deviation between them, searching for the optimal input combination x * ,satisfy:

[0047] in, is the performance deviation loss function; Input feasible range for the defined material design (such as upper and lower limits of dosage, ratio constraints, etc.); x includes ratio parameters , fiber parameters , image feature vector ; For the j The predicted value of a performance indicator; λ jFor the j The weight of a target.

[0048] Optimization module in Candidate input combinations are continuously generated, and their performance is predicted by the model. The predicted value is then compared with the target performance, and the input variable x is gradually optimized to approach the minimum loss. Step 53: After the reverse mix optimization is completed, one or more material design schemes are output; each scheme includes a recommended material mix (cement, silica fume, fly ash, quartz sand, water, water reducer, PVA fiber dosage and performance parameters) and corresponding predicted performance indicators (compressive strength, flexural strength, tensile strength, bending strength, expansion, and slump).

[0049] By adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art: By introducing a hypergraph neural network (HGNN) model, this paper effectively models multi-attribute, multi-dimensional, and high-order complex relationships between material samples. Through a hyperedge construction mechanism that combines attribute-driven and feature-space-driven approaches, this approach overcomes the limitations of traditional graph structures, which can only express binary relationships, and enhances the ability to express the relationship between material preparation parameters and mechanical behavior. Furthermore, this paper supports the unified encoding of multimodal information such as raw material ratio parameters, PVA fiber performance parameters, and microscopic image features as node inputs, enabling multi-objective predictive modeling of multiple macroscopic performance indicators, including compressive strength, flexural strength, tensile strength, flexural toughness, and elongation.

[0050] Furthermore, this invention incorporates a performance-driven reverse optimization mechanism that automatically searches for the optimal mix parameter combination under specified performance requirements. This eliminates the inefficient traditional process of repeated trial mixes and experimental verification, significantly improving the intelligence and efficiency of material design. This method possesses excellent generalization and scalability, making it suitable for performance prediction and mix ratio recommendations for a wide range of ultra-high performance concrete systems, and holds broad potential for engineering applications and industrial promotion. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0052] Figure 1 Schematic diagram of the method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network provided by the present invention; Figure 2A simplified flow chart of the method for designing a PVA fiber-toughened UHPC material formula based on a hypergraph neural network provided by the present invention; Figure 3 A schematic diagram of the hypergraph structure provided by the present invention; Figure 4 Schematic diagram of the attribute-driven and feature-driven hyperedge construction process provided by the present invention; Figure 5 This is a flow chart of the performance optimization and reverse ratio design provided by the present invention. DETAILED DESCRIPTION

[0053] The present invention will be described in further detail below with reference to the accompanying drawings and examples. It is particularly noted that the following examples are intended only to illustrate the present invention and are not intended to limit the scope of the present invention. Similarly, the following examples are only some embodiments of the present invention and are not intended to be exhaustive. All other embodiments obtained by those of ordinary skill in the art without creative effort are intended to fall within the scope of protection of the present invention.

[0054] Refer to the attached Figure 1-2 As shown, this embodiment provides a method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network, which specifically includes the following steps: Step 1), multimodal data acquisition and processing: Collect multimodal material sample data including raw material ratio parameters, PVA fiber performance parameters, microscopic images (such as SEM / X-CT), and corresponding macroscopic performance indicators. For different types of raw data, standardization, encoding or feature extraction processing are performed respectively, and all sample features are uniformly spliced ​​and encoded into high-dimensional node feature vectors. , forming the initial node feature matrix , as the input of the hypergraph neural network model. The macroscopic properties of the material sample are used for model output alignment and performance regression prediction tasks. Specifically, it includes: Step 11: Comprehensively collect multi-source heterogeneous characteristic information of PVA fiber-reinforced ultra-high performance concrete materials, wherein the multi-source heterogeneous characteristic information includes raw material ratio parameters, PVA fiber performance parameters, microstructure image information, and corresponding macroscopic performance indicators.

[0055] The collected raw material ratio parameters, PVA fiber performance parameters, and microstructure image information feature variables are standardized and used as dataset feature vectors to form a data structure suitable for hypergraph neural network input; the details are as follows: a) Raw material ratio parameters: Obtain the basic composition ratio of each concrete sample, including: cement (kg / m 3 )、Silica fume(kg / m 3 )、Fly ash(kg / m 3)、quartz sand(kg / m 3 )、Water(kg / m 3 ), water reducing agent (%), PVA fiber content (%).

[0056] The above parameters are formed into a matching vector and normalized using the normalization method (min-max) to eliminate the dimension difference and form the input node feature , the expression is as follows:

[0057] in, x c Indicates cement; x sf represents silica fume; x fa represents fly ash; x sand Indicates quartz sand; x water It means water; x ad Indicates water reducing agent; x pva Indicates the PVA fiber content.

[0058] b) PVA fiber performance parameters: For the PVA fibers used in each test batch, their physical and mechanical properties were collected, including: diameter (μm), length (mm), density (g / cm 3 ), tensile strength (MPa), elongation at break (%), and elastic modulus (GPa).

[0059] The above parameters are combined to form a fiber feature sub-vector, which is normalized using the min-max method to form the input node feature , the expression is as follows:

[0060] in, Indicates diameter; Indicates length; Indicates density; Indicates tensile strength; It represents the elongation at break; Represents the elastic modulus.

[0061] c) Microstructure image information: Scanning electron microscope (SEM) images of individual samples are collected to extract internal microstructure features. Image data is extracted using a pre-trained convolutional neural network (CNN) model and reduced to a fixed-length image feature vector. , the expression is as follows:

[0062] in, I SEM The corresponding scanning electron microscope image of the material sample is shown.

[0063] Step 12: Treat each UHPC material sample as a node in the hypergraph V , the corresponding input feature is the fused multimodal data vector; this feature vector is used as the initial input of the hypergraph neural network and is recorded as ,in i =1, 2, ..., N , is the sample number, d is the feature dimension.

[0064] Each node The input feature vector is composed of three parts, namely the matching parameter vector , PVA fiber parameter vector and image feature vector ; The concatenated vector is recorded as , constituting a single sample input feature of the hypergraph neural network; The table is as follows:

[0065] All samples form nodes to form a feature matrix , as the input of the hypergraph neural network; The table is as follows:

[0066] Step 13: The output of the HGNN model is the predicted value of the macro performance index of the material sample; the macro performance index specifically includes: compressive strength , flexural strength ,tensile strength , flexural strength , expansion and slump , used to guide the reverse optimization of input variables based on target performance and the recommendation of high performance ratio. i samples, whose performance output is defined as :

[0067] in, represents the predicted value of compressive strength; Indicates the predicted value of flexural strength; represents the predicted value of tensile strength; represents the predicted value of flexural strength; represents the predicted value of expansion; Indicates the predicted slump value; Combining the outputs of all samples, we can get the overall prediction output matrix:

[0068] This output matrix is ​​used to compare with the target performance Make comparisons and perform reverse ratio optimization.

[0069] Step 2), hypergraph structure construction: Refer to the attached Figure 3 As shown, define the hypergraph structure ; Take each material sample as a node in the graph structure and build a node set V ; According to the attribute similarity (such as PVA fiber content range and target strength level) and the feature space neighbor relationship (such as the similarity of ratio features and image features), multiple hyperedge groups are constructed, and attribute-driven hyperedge sets and feature-driven hyperedge sets are constructed respectively. The two are spliced ​​to form a hyperedge set E ; Assign weights to each hyperedge to form a hyperedge weight matrix W ; At the same time, construct the corresponding correlation matrix H , used to represent the connection relationship between nodes and hyperedges, and realize the graph representation of high-order structural information. Specifically including: Step 21) After completing the multimodal feature extraction, all material samples are represented as nodes in a hypergraph structure, and a hypergraph structure for modeling high-order complex relationships is constructed. The hypergraph structure is defined as: ,in, is the set of all nodes, corresponding to all material samples, each node in the hypergraph Corresponding to a row of feature vectors ; is a set of hyperedges, each hyperedge connects a set of related nodes; W is the hyperedge weight matrix. The hypergraph structure can be constructed by constructing the association matrix H Implement formal representation.

[0070] Step 22) Build a hyperedge Refer to the attached Figure 4 As shown, in order to achieve high-order structural expression between material samples in different feature dimensions, this embodiment adopts multiple strategies to construct hyperedge sets E , aggregating related sample nodes into a unified hyperedge. Hyperedge generation methods include attribute-driven and feature-driven methods, which can be flexibly combined to enhance the diversity and expressiveness of hypergraph modeling. The specific steps include the following: Step 221), attribute-driven hyperedge generation For discrete or interval-type structured attributes in material samples (such as PVA content, compressive strength grade, etc.), sample nodes with the same attribute value or falling into the same interval can be grouped together and a corresponding hyperedge is generated. This hyperedge connects all nodes that meet the attribute conditions together, realizing high-order aggregation modeling in the attribute space (for example, samples with PVA content in the range of 1.5%–2.0% are grouped together into a single hyperedge); the details are as follows: Let the complete set of attributes be , a certain attribute , the corresponding node set is:

[0071] in, Representation node Attribute value of Indicates that all have the same attribute value a A collection of nodes.

[0072] Therefore, the attribute-driven hyperedge set can be expressed as:

[0073] Attribute-driven hyperedges form an association matrix for:

[0074] in, Drives the number of hyperedges for the attribute.

[0075] For example, when the attribute is "PVA dosage range", it is divided into: Attribute 1 ( a 1): [1.0%, 1.5%]; Attribute 2( a 2): (1.5%, 2.0%]; Attribute 1 ( a 3): (2.0%, 2.5%). For each attribute interval a i , a hyperedge can be constructed e i , all node samples that meet the conditions are included in this hyperedge. a 1: [1.0%, 1.5%], the corresponding node set can be defined as:

[0076] Thus, the super edge e 1 is a high-order structural unit consisting of connecting all sample nodes that satisfy the PVA dosage within this interval. Similarly, attribute-driven hyperedge sets can be constructed based on multiple attributes or attribute sub-intervals: .

[0077] Step 222), feature space driven hyperedge generation In view of the similarity relationship of material samples in the multidimensional feature space (ratio vector, PVA fiber parameters and image features), this embodiment adopts k -nearest neighbors ( k -Nearest Neighbors (KNN) strategy is used to construct hyperedges. Specifically, with each node sample as the center, the node with the smallest Euclidean distance to it is selected in the feature space. k Adjacent nodes, together with the central node, form a hyperedge. This strategy can systematically capture high-order relationships between groups of samples with "similar features" and achieve enhanced information propagation of similar structures during the hypergraph convolution process. The details are as follows: For each node , whose eigenvector is , define its k The set of KNN neighbors is:

[0078] in, v ik Representation node v i The kth nearest neighbor node of ; The central node Together with its neighbors, it forms a hyperedge:

[0079] The final feature-driven hyperedge set is expressed as:

[0080] in, N is the number of nodes, which means that a feature space neighbor hyperedge centered on itself is constructed for each node.

[0081] Feature-driven hyperedges form an association matrix for:

[0082] in, The number of hyperedges driven by the feature.

[0083] For example: suppose a node The corresponding feature vector is the vector of the image features after its matching parameters are spliced ​​together , after calculating the Euclidean distance between it and other samples in the standardized feature space, the nearest k =3 nodes are , , .

[0084] Then the central node of the sample The corresponding feature space driven hyperedge is:

[0085] This hyperedge will be used in the hypergraph for information propagation and feature enhancement learning of similar samples.

[0086] Step 223) Join the hyperedges constructed by attribute drive and feature drive to obtain the total hyperedge set E , and construct the incidence matrix of the hypergraph accordingly:

[0087] Among them, the total number of super edges Each hyperedge It is a subset of a set of nodes, representing a set of sample nodes that have similarity, coupling or correlation under a certain feature dimension or attribute condition.

[0088] Based on the total hyperedge set E , construct the correlation matrix , , satisfying the following rules:

[0089] in, Representation node Belong to the super edge , Indicates that the node does not belong to the hyperedge.

[0090] What we finally get H It will be used as one of the core inputs in the model structure, together with the weight matrix W Participate in the subsequent graph convolution calculation process of the HGNN model.

[0091] Step 23) When building the hypergraph structure When , a non-negative weight is assigned to each hyperedge to adjust the influence of the hyperedge in the information propagation process.

[0092] This embodiment introduces an adaptive hyperedge weight mechanism, which sets trainable parameters for hyperedge sets from different sources (such as attribute-driven and feature-driven), and applies them to attribute-driven and feature-driven hyperedges after normalization through an activation function (sigmoid) to form a weight matrix. W , which can be automatically updated during model training, thereby achieving dynamic regulation of the contribution of different structural information. The weights of all hyperedges can be uniformly represented as a diagonal matrix , and the incidence matrix Participate in the convolution operation of the HGNN model together.

[0093] For example: the total set of hyperedges is E Divided into P Hyperedge sets from different sources , each set E P Corresponding to a trainable weight parameter , and after being transformed by the normalization function sigmoid, it is assigned to all hyperedges in the group, and finally the hyperedge weight matrix is ​​constructed:

[0094] in, , w j Indicates the j The weight of the hyperedge.

[0095] Step 3) Hypergraph neural network model construction: After node feature extraction and hypergraph structure construction, a hypergraph neural network model consisting of multiple hypergraph convolutional layers (HGNNConv) was constructed based on this hypergraph structure. This model extracts and fuses node features layer by layer through a bidirectional message passing mechanism from nodes to hyperedges and back from hyperedges to nodes, effectively modeling the nonlinear, multimodal, and high-order coupling relationships between material ratio parameters, fiber properties, microstructural characteristics, and performance indicators.

[0096] In this example, a hypergraph neural network (HGNN) is used as the learning framework. The constructed hypergraph neural network model mainly consists of the following structure: three hypergraph convolutional layers (HGNNConv), two batch normalization layers (BatchNormalization), an activation function layer following each convolutional layer, and a fully connected output layer (Fully ConnectedLayer). The activation function layer uses the ReLU (Rectified Linear Unit) function to introduce nonlinear expression capabilities and improve the model's ability to fit complex relationships.

[0097] In this embodiment, step 3 specifically includes the following steps: Step 31) During the model training phase, the hypergraph neural network uses the node feature matrix As input, the model extracts and transforms sample features layer by layer through a multi-layer hypergraph convolutional structure. At the same time, the model uses the pre-built correlation matrix and the hyperedge weight matrix Model the high-order connection relationships between nodes to achieve structured feature aggregation across nodes and attributes.

[0098] Step 32) To improve computational efficiency and enhance the model's high-level expressiveness, a hypergraph convolution module (HGNNConv) based on a spatial domain propagation mechanism is employed. This structure explicitly defines the message passing function between nodes and hyperedges, enabling efficient information propagation and a trainable representation update mechanism. Each layer of hypergraph convolution is divided into two phases: the first phase aggregates information from nodes to hyperedges, and the second phase reversely updates features from hyperedges to nodes, thus forming a complete closed loop of information interaction. The details are as follows: Step 321), node to hyperedge feature aggregation, each hyperedge aggregates its associated node features to generate a hyperedge feature set , the expression is as follows:

[0099] in, W is the hyperedge weight matrix; D e is the hyperedge degree matrix; H is the hypergraph incidence matrix, ; is the transposed incidence matrix, which is used to control the nodes connected by each hyperedge. ; For the t Node features of the layer input.

[0100] Step 322 ) Back propagation of hyperedge-to-node features, transmitting the information of each hyperedge back to its adjacent node, and updating the feature node.

[0101]

[0102] in, is the output feature; σ(·) is the activation function ReLU; D v is the node degree matrix; For the t The learnable parameter matrix of the layer; Combining the two formulas in step 321) and step 322) yields the hypergraph convolution expression:

[0103] Step 4) Model training: This embodiment uses an end-to-end backpropagation mechanism to train the hypergraph neural network model. The training process includes steps such as parameter initialization, forward propagation, loss function construction, gradient backpropagation, and parameter update. Specifically, it includes: Step 41), parameter initialization and hyperparameter setting: Randomly initialize the parameter weights of all HGNN layers , and set the initial learning rate to 0.0001 and the loss function weight coefficient λ j , each performance index in this example: compressive strength f c , flexural strength f b ,tensile strength f t , flexural strength F flex , expansion d , slump s The loss function weight coefficient λ j Take 1.0, 0.8, 0.5, 1.2, 0.7, and 0.7 respectively.

[0104] Step 42), forward propagation: input the node feature matrix Input the HGNN model, perform feature extraction and propagation through multiple layers of HGNNConv convolutional layers, batch normalization layers, and activation function layers, and output the prediction result matrix ,in K is the number of output performance dimensions. In this example, K = 6.

[0105] The final output of this model is the macro performance index prediction value vector for each sample. i samples, and its output vector is expressed as:

[0106] in, is the predicted value of compressive strength; is the predicted value of flexural strength; is the predicted value of tensile strength; is the predicted value of flexural strength; is the predicted value of expansion; is the predicted slump value.

[0107] The output set of all samples constitutes the prediction matrix :

[0108] Step 43), loss function construction and back propagation: The training goal is to minimize the error between the predicted value and the true target value, using a multi-objective weighted mean square error (MSE) loss function :

[0109] in, λ j For the j The weight of each goal; For thei Sample No. j The target value of each indicator; For the i Sample No. j The predicted value of an indicator.

[0110] The back-propagation algorithm is used to calculate the gradient of the loss function with respect to the parameters of each layer, and the optimizer Adam is used to update the model parameters, gradually minimizing the prediction error during training.

[0111] Step 44) Training Control and Convergence Assessment: To ensure the stability of the HGNN model training process and the generalizability of the final results, all training samples are divided into a training set and a validation set in an 8:2 ratio. 80% of the samples are used for learning model parameters, and 20% of the samples are used as a validation set, which is used only for performance evaluation and does not participate in parameter updates. The prediction performance of each epoch is evaluated in real time. When the validation set loss function stops decreasing or begins to increase after several consecutive epochs, the model is considered to have reached optimality, and training is terminated early to prevent overfitting. After training is complete, the model can be used to predict the performance of material samples with any input ratio parameters.

[0112] Step 5) Performance optimization and reverse ratio design: Refer to the attached Figure 5 As shown in the figure, based on the trained HGNN model, the HGNN model is embedded as a prediction function in the performance deviation loss according to the user-defined target performance vector to construct an inverse optimization objective function. A genetic algorithm is used to iteratively search in the input variable space, automatically generating the optimal raw material ratio combination that meets the target performance and simultaneously outputting the corresponding macro-performance indicators; specifically, Step 51), Task modeling and problem definition Set the target performance vector as:

[0113] in, is the target performance vector, set by the user; is the target compressive strength; is the target flexural strength; is the target tensile strength; is the target flexural strength; is the target expansion; is the target slump.

[0114] Step 52), this embodiment models the reverse ratio design problem as an optimization problem based on performance objectives: in the feasible domain of the set material input variables In the process, the optimization module is used to automatically generate candidate input combinations x, and the trained HGNN performance prediction model is used to predict the Calculate its corresponding performance prediction value The optimization goal is to minimize the difference between the prediction performance and the target performance set by the user. The deviation between them, searching for the optimal input combination x * ,satisfy:

[0115] in, is the performance deviation loss function; Input feasible range for the defined material design (such as upper and lower limits of dosage, ratio constraints, etc.); x includes ratio parameters , fiber parameters , image feature vector ; For the j The predicted value of a performance indicator; λ j For the j The weight of a target.

[0116] Optimization module in Candidate input combinations are continuously generated, and their performance is predicted by the model. The predicted value is then compared with the target performance, and the input variable x is gradually optimized to approach the minimum loss.

[0117] The above solution can automatically search for the optimal raw material ratio parameter combination that meets the performance requirements based on the performance goals set by the user, thereby realizing intelligent material design under specific process constraints.

[0118] Step 53) After the reverse mix optimization is complete, one or more material design solutions are output. Each solution includes a recommended material mix (cement, silica fume, fly ash, quartz sand, water, water reducer, PVA fiber dosage and performance parameters) and corresponding predicted performance indicators (compressive strength, flexural strength, tensile strength, bending strength, expansion, and slump).

[0119] In summary, the present invention proposes an AI design method for PVA fiber-reinforced UHPC material formula that combines multimodal feature input, hypergraph structure modeling and hypergraph neural network-based design. By introducing attribute-driven and feature-driven hyperedge construction mechanisms, a hypergraph representation of high-order structural associations is constructed, which can effectively capture the complex nonlinear coupling relationship between raw material parameters, fiber properties and microstructure in material design.

[0120] The above descriptions are only some embodiments of the present invention and do not limit the scope of protection of the present invention. Any equivalent device or equivalent process transformation made by using the contents of the description and drawings of the present invention, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network, characterized in that: The steps include: Step 1: Multimodal data acquisition and processing: Collect multimodal material sample data including raw material ratio parameters, PVA fiber performance parameters, microscopic images, and corresponding macroscopic performance indicators; Preprocess the original data and uniformly concatenate and encode all sample features into high-dimensional node feature vectors , forming the initial node feature matrix , as the input of the HGNN model; The macroscopic properties of material samples are used for model output alignment and performance regression prediction; Step 2: Hypergraph structure construction: Defining the hypergraph structure , taking each material sample as a node in the graph structure, construct a node set V ; Construct multiple hyperedge groups based on attribute similarity and feature space neighbor relationships, respectively construct attribute-driven hyperedge sets and feature-driven hyperedge sets, and splice the two to form a hyperedge set E ; Assign a weight to each hyperedge to form a hyperedge weight matrix W , and construct the corresponding correlation matrix H , used to represent the connection relationship between nodes and hyperedges; Step 3: HGNN model construction: Based on the constructed hypergraph structure, an HGNN model consisting of multiple hypergraph convolutional layers is constructed. The model extracts and fuses node features layer by layer through a bidirectional message passing mechanism from nodes to hyperedges and then from hyperedges back to nodes. Step 4: Model training: The HGNN model is trained using an end-to-end backpropagation mechanism. The training process includes parameter initialization, forward propagation, loss function construction, gradient backpropagation, and parameter update. Step 5: Performance optimization and reverse ratio design: According to the set target performance vector, the HGNN model is embedded into the performance deviation loss as a prediction function to construct the reverse optimization objective function; Genetic algorithms are used to iteratively search in the input variable space to automatically generate the optimal raw material ratio combination that meets the target performance, and simultaneously output the corresponding macro performance indicators.

2. The method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network according to claim 1, characterized in that: Step 1 specifically includes: Step 11: comprehensively collect multi-source heterogeneous characteristic information of the PVA fiber-reinforced ultra-high performance concrete material, wherein the multi-source heterogeneous characteristic information includes raw material ratio parameters, PVA fiber performance parameters, microstructure image information, and corresponding macroscopic performance indicators; The collected raw material ratio parameters, PVA fiber performance parameters, and microstructure image information feature variables are standardized and used as dataset feature vectors to form a data structure suitable for hypergraph neural network input; Step 12: Treat each UHPC material sample as a node in the hypergraph V , the corresponding input feature is the fused multimodal data vector; this feature vector is used as the initial input of the hypergraph neural network and is recorded as ,in i =1,2, ..., N , is the sample number, d is the feature dimension; Each node The input feature vector is composed of three parts, namely the matching parameter vector , PVA fiber parameter vector and image feature vector ; The concatenated vector is recorded as , which constitutes the single sample input feature of the hypergraph neural network, The table is as follows: All samples form nodes to form a feature matrix , as the input of the hypergraph neural network; The table is as follows: Step 13: The output of the HGNN model is the predicted value of the macro performance index of the material sample; the macro performance index specifically includes: compressive strength , flexural strength ,tensile strength , flexural strength , expansion and slump , for the i samples, whose performance output is defined as : in, represents the predicted value of compressive strength; Indicates the predicted value of flexural strength; represents the predicted value of tensile strength; represents the predicted value of flexural strength; represents the predicted value of expansion; Indicates the predicted slump value; Combining the outputs of all samples, we can get the overall prediction output matrix: This output matrix is ​​used to compare with the target performance Make comparisons and perform reverse ratio optimization.

3. The method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network according to claim 2, characterized in that: In step 11, the collected raw material ratio parameters, PVA fiber performance parameters, and microstructure image information feature variables are standardized and used as data set feature vectors to form a data structure suitable for hypergraph neural network input; the details are as follows: a) Raw material ratio parameters: obtain the basic composition ratio of each concrete sample, including: cement, silica fume, fly ash, quartz sand, water, water reducer, and PVA fiber content; The above parameters are formed into a matching vector and normalized using the normalization method to eliminate the dimension difference and form the input node feature , the expression is as follows: in, x c Indicates cement; x sf represents silica fume; x fa represents fly ash; x sand Indicates quartz sand; x water It means water; x ad Indicates water reducing agent; x pva Indicates the PVA fiber content; b) PVA fiber performance parameters: For the PVA fibers used in each test batch, their physical and mechanical properties were collected, including: diameter, length, density, tensile strength, elongation at break, and elastic modulus; The above parameters are combined to form a fiber feature sub-vector, which is normalized using the normalization method to form the input node feature , the expression is as follows: in, Indicates diameter; Indicates length; Indicates density; Indicates tensile strength; It represents the elongation at break; represents the elastic modulus; c) Microstructure image information: Scanning electron microscope images of a single sample are collected to extract its internal microstructure features; the image data is extracted through a pre-trained convolutional neural network (CNN) model and reduced to a fixed-length image feature vector. , the expression is as follows: in, I SEM The corresponding scanning electron microscope image of the material sample is shown.

4. The method for designing a PVA fiber-toughened UHPC material formula based on a hypergraph neural network according to claim 1, wherein: Step 2) specifically includes: Step 21: Represent all material samples as nodes in a hypergraph structure, and construct a hypergraph structure for modeling high-order complex relationships. The hypergraph structure is defined as: ,in, is the set of all nodes, corresponding to all material samples, each node in the hypergraph Corresponding to a row of feature vectors ; is a set of hyperedges, each hyperedge connects a set of related nodes; W is the hyperedge weight matrix; the hypergraph structure can be constructed by constructing the association matrix H Implement formal representation; Step 22: Use multiple strategies to build a hyperedge set E , aggregate the associated sample nodes into a unified hyperedge; the generation methods of hyperedge include attribute-driven method and feature-driven method; Step 23: Build a hypergraph structure When , a non-negative weight is assigned to each hyperedge, and trainable parameters are set for hyperedge sets from different sources. After normalization by the activation function, it acts on the attribute-driven and feature-driven hyperedges to form a weight matrix W , the weights of all hyperedges can be uniformly expressed as a diagonal matrix , and the incidence matrix Participate in the convolution operation of the HGNN model together.

5. The method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network according to claim 4, characterized in that: Step 22 specifically includes the following steps: Step 221: Attribute-driven hyperedge generation For discrete or interval-type structured attributes in material samples, sample nodes with the same attribute value or falling into the same interval are grouped together and a corresponding hyperedge is generated. This hyperedge connects all nodes that meet the attribute conditions together to achieve high-order aggregation modeling in the attribute space. The details are as follows: Let the complete set of attributes be , a certain attribute , the corresponding node set is: in, Representation node Attribute value of Indicates that all have the same attribute value a The node set of Therefore, the attribute-driven hyperedge set can be expressed as: Attribute-driven hyperedges form an association matrix for: in, Drive the number of hyperedges for the attribute; Step 222: Feature space driven hyperedge generation Aiming at the similarity relationship of material samples in multidimensional feature space, a k -Nearest neighbor strategy to construct hyperedges; Taking each node sample as the center, select the one with the smallest Euclidean distance from it in the feature space. k Adjacent nodes, together with the central node, form a hyperedge; the details are as follows: For each node , whose eigenvector is , define its k The set of KNN neighbors is: in, v ik Representation node v i The kth nearest neighbor node of ; The central node Together with its neighbors, it forms a hyperedge: The final feature-driven hyperedge set is expressed as: in, N is the number of nodes, indicating that a feature space neighbor hyperedge centered on itself is constructed for each node; Feature-driven hyperedges form an association matrix for: in, The number of hyperedges driven by features; Step 223: Join the hyperedges constructed by attribute drive and feature drive to obtain the total hyperedge set. E , and construct the incidence matrix of the hypergraph accordingly: Among them, the total number of super edges Each hyperedge It is a subset of a set of nodes, representing a set of sample nodes that have similarity, coupling or correlation under a certain feature dimension or attribute condition; Based on the total hyperedge set E , construct the correlation matrix , , satisfying the following rules: in, Representation node Belong to the super edge , Indicates that the node does not belong to the hyperedge.

6. The method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network according to claim 1, characterized in that: In step 3, a hypergraph neural network is used as the learning framework. The constructed hypergraph neural network model mainly consists of the following structure: 3 hypergraph convolutional layers, 2 batch normalization layers, an activation function layer following each convolutional layer, and a fully connected output layer; the activation function layer uses the ReLU function to introduce nonlinear expression capabilities and improve the model's ability to fit complex relationships.

7. The method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network according to claim 6, characterized in that: Step 3 specifically includes: Step 31: During the model training phase, the hypergraph neural network uses the node feature matrix As input, the sample features are extracted and transformed layer by layer through a multi-layer hypergraph convolution structure; at the same time, the model uses the pre-built association matrix and the hyperedge weight matrix Model high-order connection relationships between nodes to achieve cross-node and cross-attribute structured feature aggregation; Step 32: Using a hypergraph convolution module based on the spatial domain propagation mechanism, each layer of hypergraph convolution operation is divided into two stages: the first stage realizes information aggregation from nodes to hyperedges, and the second stage realizes the reverse update of features from hyperedges to nodes, thereby forming a complete information interaction closed loop.

8. The method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network according to claim 7, characterized in that: The convolution operation of each layer of the hypergraph in step 32 is divided into two stages: the first stage realizes the information aggregation from the node to the hyperedge, and the second stage realizes the reverse update of the features from the hyperedge to the node, thereby forming a complete information interaction closed loop; the details are as follows: Step 321: Node to hyperedge feature aggregation. Each hyperedge aggregates its associated node features to generate a hyperedge feature set. : in, W is the hyperedge weight matrix; D e is the hyperedge degree matrix; H is the hypergraph incidence matrix, ; is the transposed incidence matrix, which is used to control the nodes connected by each hyperedge. ; For the t Node features of layer input; Step 322: Back propagation of hyperedge-to-node features. The information of each hyperedge is transmitted back to its adjacent nodes. The feature nodes are updated. The expression is as follows: in, is the output feature; σ(·) is the activation function ReLU; D v is the node degree matrix; For the t The learnable parameter matrix of the layer; Combining the two formulas in step 321 and step 322, we can get the hypergraph convolution expression: 。 9. The method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network according to claim 1, wherein: Step 4 specifically includes: Step 41: Parameter initialization and hyperparameter setting: Randomly initialize the parameter weights of all HGNN layers , and set the initial learning rate to 0.0001 and the loss function weight coefficient λ j ; Step 42, forward propagation: input the node feature matrix Input the HGNN model, perform feature extraction and propagation through multiple layers of HGNNConv convolutional layers, batch normalization layers, and activation function layers, and output the prediction result matrix ,in K is the number of output performance dimensions; Step 43, loss function construction and back propagation: The training goal is to minimize the error between the predicted value and the true target value, using a multi-objective weighted mean square error loss function : in, λ j For the j The weight of each goal; For the i Sample No. j The target value of each indicator; For the i Sample No. j The predicted value of an indicator; The back-propagation algorithm is used to calculate the gradient of the loss function with respect to the parameters of each layer, and the optimizer Adam is used to update the model parameters, gradually minimizing the prediction error during training; Step 44: Training control and convergence judgment: All training samples are divided into a training set and a validation set in a ratio of 8:2, where 80% of the samples are used for learning model parameters and 20% of the samples are used as a validation set. The prediction performance of each round is evaluated in real time. When the validation set loss function stops decreasing or starts to rise over several consecutive rounds, the model is considered to have reached the optimal state and training is terminated early.

10. The method for designing a PVA fiber-reinforced UHPC material formula based on a hypergraph neural network according to claim 1, wherein: Step 5 specifically includes: Step 51: Task modeling and problem definition Set the target performance vector as: in, is the target performance vector, set by the user; is the target compressive strength; is the target flexural strength; is the target tensile strength; is the target flexural strength; is the target expansion; is the target slump; Step 52: Model the reverse mix design problem as an optimization problem based on performance objectives: In the process, the optimization module is used to automatically generate candidate input combinations x, and the trained HGNN performance prediction model is used to predict the Calculate its corresponding performance prediction value ; The optimization goal is to minimize the difference between the predicted performance and the target performance set by the user. The deviation between them, searching for the optimal input combination x * ,satisfy: in, is the performance deviation loss function; Input feasible range for the defined material design; x includes the ratio parameters , fiber parameters , image feature vector ; For the j The predicted value of a performance indicator; λ j For the j The weight of each goal; Optimization module in Candidate input combinations are continuously generated, and their performance is predicted by the model. The predicted value is then compared with the target performance, and the input variable x is gradually optimized to approach the minimum loss. Step 53: After the reverse ratio optimization is completed, one or more sets of material design solutions are output; each set of solutions includes a recommended material ratio and corresponding predicted performance indicators.

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