A Formulation Design Method for PVA Fiber-Toughened UHPC Materials Based on Hypergraph Neural Networks

Abstract

This invention discloses a formulation design method for PVA fiber-toughened UHPC materials based on a hypergraph neural network, comprising: step 1, multimodal data acquisition and processing; step 2, hypergraph structure construction; step 3, HGNN model construction; step 4, model training; and step 5, performance optimization and reverse mix design. This invention can efficiently model the high-order relationships between multimodal data such as raw materials, mix proportions, and microstructure, achieving accurate prediction of PVA fiber-toughened UHPC performance and optimized mix design. It is applicable to performance prediction and mix recommendation for various ultra-high performance concrete systems, and has broad engineering application prospects and industrial promotion value.

Description

Technical Field

[0001] This invention relates to the field of building engineering technology, and in particular to a material formulation design method for PVA fiber-toughened ultra-high performance concrete (UHPC) based on hypergraph neural networks. Background Technology

[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 improve its toughness and crack resistance, polyvinyl alcohol (PVA) fibers are usually incorporated into UHPC to achieve fiber reinforcement and toughening. However, the dosage, morphology, spatial distribution, and interfacial interaction of PVA fibers with the matrix can generate complex coupling effects with multiple factors such as water-cement ratio, aggregate gradation, and admixture dosage, significantly affecting the mechanical and performance properties of UHPC materials. These factors, reflecting the structure-property relationship between molecular structure and material properties, exhibit highly nonlinear, high-order, and multimodal interactions, posing challenges to material design.

[0003] Currently, the formulation optimization and performance prediction of UHPC materials still mainly rely on engineers' experience or traditional regression models based on linear assumptions. These methods struggle to accurately capture the deep-seated relationships between raw material parameters, process conditions, microstructure, and macroscopic properties, especially in achieving synergistic optimization of multi-objective properties (such as strength and toughness).

[0004] Therefore, this 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 formulation design method for PVA fiber toughened UHPC materials based on hypergraph neural networks, which can efficiently model the high-order relationships between multimodal data such as raw materials, proportions, and microstructure, and realize accurate prediction of the performance of PVA fiber toughened UHPC and optimized design of the proportions.

[0006] To achieve the above-mentioned technical objectives, the technical solution adopted by this invention is: a formulation design method for PVA fiber-toughened UHPC materials based on hypergraph neural networks, comprising the following steps:

[0007] Step 1: Multimodal data acquisition and processing:

[0008] Collect multimodal material sample data including raw material ratio parameters, PVA fiber performance parameters, microscopic images, and corresponding macroscopic performance indicators;

[0009] The raw data is preprocessed, and all sample features are concatenated and encoded into a high-dimensional node feature vector. To form the initial node feature matrix , as input to the HGNN model;

[0010] The macroscopic properties of the material samples are used for model output alignment and performance regression prediction;

[0011] Step 2, Hypergraph Structure Construction:

[0012] Define hypergraph structure Each material sample is used as a node in the graph structure to construct a node set. V ;

[0013] Multiple hyperedge groups are constructed based on attribute similarity and feature space nearest neighbor relationships. Attribute-driven hyperedge sets and feature-driven hyperedge sets are constructed separately, and these two sets are concatenated to form the hyperedge set. E ;

[0014] Assign weights to each hyperedge to form a hyperedge weight matrix. W At the same time, construct the corresponding association matrix. H It is used to characterize the connection relationship between nodes and hyperedges, and realize the graph representation of high-order structural information.

[0015] Step 3: HGNN model construction:

[0016] Based on the constructed hypergraph structure, an HGNN model containing multiple hypergraph convolutional layers is built. The model extracts and fuses node features layer by layer through a bidirectional message passing mechanism from node to hyperedge and back from hyperedge to node, thereby achieving effective modeling of the nonlinear, multimodal, and high-order coupling relationship between material ratio parameters, fiber properties, microstructure features and performance indicators.

[0017] Step 4: Model Training

[0018] 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.

[0019] Step 5, Performance Optimization and Reverse Proportioning Design:

[0020] 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 bias loss to construct the inverse optimization objective function;

[0021] A genetic algorithm is 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 macroscopic performance indicators.

[0022] Furthermore, step 1 specifically includes:

[0023] Step 11: Collect comprehensive information on the multi-source heterogeneous characteristics of PVA fiber-toughened ultra-high performance concrete materials. The multi-source heterogeneous characteristics include raw material proportioning parameters, PVA fiber performance parameters, microstructure image information, and corresponding macroscopic performance indicators.

[0024] 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 input to a hypergraph neural network.

[0025] 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 serves as the initial input to the hypergraph neural network, denoted as... ,in i =1, 2, ..., N , is the sample number. d For feature dimensions;

[0026] Each node The input feature vector is composed of three concatenated parts: the matching parameter vector, etc. PVA fiber parameter vector With image feature vectors The concatenated vector is denoted as The individual sample input features that constitute a hypergraph neural network The format is as follows:

[0027]

[0028] All samples form nodes that together form a feature matrix. , as input to the hypergraph neural network; The format is as follows:

[0029]

[0030] Step 13: The output of the HGNN model is the predicted value of the macroscopic performance index of the material sample; the specific macroscopic performance index includes: compressive strength. Flexural strength ,tensile strength Flexural strength Scalability With slump This is used to guide back-optimization of input variables based on target performance and recommendation of high-performance allocation ratios. For the first... i For each sample, its performance output is defined as :

[0031]

[0032] in, This represents the predicted compressive strength value; This represents the predicted flexural strength. This indicates the predicted tensile strength value; This represents the predicted value of bending strength. This represents the predicted expansion value; This represents the predicted slump value;

[0033] By combining the outputs of all samples, we can obtain the overall predicted output matrix:

[0034]

[0035] This output matrix is ​​used to correlate with the target performance. Compare the results and perform reverse ratio optimization.

[0036] 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 the dataset feature vector to form a data structure suitable for input to the hypergraph neural network; specifically as follows:

[0037] a) Raw material proportioning parameters: Obtain the basic composition ratio of each concrete sample, including: cement (kg / m³) 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 (%);

[0038] The above parameters are used to construct a ratio vector, which is then standardized using a normalization method (min-max) to eliminate dimensional differences and form the input node features. The expression is as follows:

[0039]

[0040] in, x c It refers to cement; x sf Indicates silica ash; x fa It refers to fly ash;x sand Indicates quartz sand; x water It represents water; x ad Indicates water-reducing agent; x pva Indicates the PVA fiber content;

[0041] b) PVA fiber performance parameters: For each batch of PVA fibers used in the tests, their physical and mechanical properties were collected, including: diameter (μm), length (mm), and density (g / cm³). 3 Tensile strength (MPa), elongation at break (%), and elastic modulus (GPa);

[0042] The above parameters are combined to form fiber feature sub-vectors, which are then standardized using a normalization method (min-max) to form input node features. The expression is as follows:

[0043]

[0044] in, Indicates diameter; Indicates length; Indicates density; Indicates tensile strength; Indicates elongation at break; It represents the elastic modulus.

[0045] c) Microstructural image information: Scanning electron microscope (SEM) images of individual samples are acquired, and their internal microstructural features are extracted; the image data is used for feature extraction through a pre-trained convolutional neural network (CNN) model, and the dimensionality is reduced to a fixed-length image feature vector. The expression is as follows:

[0046]

[0047] in, I SEM This represents the scanning electron microscope image corresponding to the material sample.

[0048] The pre-trained convolutional neural network (CNN) model used for image feature extraction is a common method in current visual feature processing. This invention preferably uses existing mainstream CNN architectures such as ResNet and EfficientNet for image encoding.

[0049] Furthermore, step 2) specifically includes:

[0050] Step 21: Represent all material samples as nodes in a hypergraph structure, construct a hypergraph structure for modeling high-order complex relationships, and define the hypergraph structure as: ,in, For each node in the hypergraph, representing the set of all nodes and corresponding to all material samples, ... Corresponding to a row of feature vectors ; This is a set of hyperedges, where each hyperedge connects a group of related nodes; W This is the hyperedge weight matrix; the hypergraph structure can be constructed by building the incidence matrix. H Implement formal representation;

[0051] Step 22: To achieve higher-order structural representation of material samples across different feature dimensions, this invention employs a multi-strategy approach to construct hyperedge sets. E The system aggregates related sample nodes into a unified hyperedge; the hyperedge generation methods include attribute-driven and feature-driven methods, which can be flexibly combined to enhance the diversity and expressive power of hypergraph modeling.

[0052] Step 23: Constructing the hypergraph structure In this process, a non-negative weight is assigned to each hyperedge to adjust its influence during information propagation. Trainable parameters are set for hyperedge sets from different sources (e.g., attribute-driven and feature-driven), and after normalization using an activation function (sigmoid), these parameters are applied to attribute-driven and feature-driven hyperedges to form a weight matrix. W， The weights of all hyperedges can be uniformly represented as a diagonal matrix. , and the correlation matrix They participate in the convolution operation of the HGNN model together.

[0053] Furthermore, step 22 specifically includes the following steps:

[0054] Step 221: Attribute-driven hyperedge generation

[0055] For material samples with discrete or interval-based structured properties (such as PVA content, compressive strength grade, etc.), sample nodes with the same property value or falling into the same interval are grouped into a set, and a corresponding hyperedge is generated. This hyperedge connects all nodes that satisfy the property condition, realizing high-order aggregation modeling in the property space; specifically as follows:

[0056] Let the set of attributes be A certain attribute The corresponding set of nodes is:

[0057]

[0058] in, Represents a node The attribute value; This indicates all attributes with the same value. a The set of nodes.

[0059] Therefore, the attribute-driven hyperedge set can be represented as:

[0060]

[0061] Attribute-driven hyperedges form an association matrix for:

[0062]

[0063] in, The number of hyperedges is driven by attributes.

[0064] Step 222: Feature Space-Driven Hyperedge Generation

[0065] To address the similarity relationships of material samples in a multidimensional feature space (ratio vector, PVA fiber parameters, and image features), a method based on... k - Neighbors ( k -Nearest Neighbors (KNN) strategy to construct superedges;

[0066] Centered on each node sample, select the node with the smallest Euclidean distance in the feature space. k Each pair of adjacent nodes, together with the central node, forms a hyperedge; as detailed below:

[0067] For each node Its eigenvector is Define its first k The set of KNN neighbors is:

[0068]

[0069] in, v ik Represents a node v i The k-th nearest neighbor node;

[0070] Then from the central node Together with its nearest neighbor, they form a superedge:

[0071]

[0072] The final feature-driven hyperedge set is represented as:

[0073]

[0074] in, N The value represents the number of nodes, indicating that for each node, a feature space nearest neighbor superedge centered on itself is constructed;

[0075] Feature-driven hyperedges form the correlation matrix for:

[0076]

[0077] in, The number of feature-driven hyperedges.

[0078] Step 223: Concatenate the hyperedges constructed by attribute-driven and feature-driven approaches to obtain the total hyperedge set. E And based on this, construct the hypergraph's association matrix:

[0079]

[0080] Among them, the total number of hyperedges Each super edge A subset of nodes represents a set of sample nodes that are similar, coupled, or related under a certain feature dimension or attribute condition.

[0081] Based on the total hyperedge set E Construct an association matrix , It meets the following rules:

[0082]

[0083] in, Represents a node Belongs to superedge , This indicates that the node does not belong to the superedge.

[0084] The final result H As one of the core inputs in the model structure, it is related to the weight matrix. W They will also participate in the graph convolution calculation process of the subsequent HGNN model.

[0085] 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:

[0086] The system consists of three hypergraph convolutional layers, two 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 non-linear expressive power and improve the model's ability to fit complex relationships.

[0087] Furthermore, step 3 specifically includes:

[0088] 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; simultaneously, it utilizes a pre-constructed correlation matrix. and hyperedge weight matrix Model the higher-order connections between nodes to achieve structured feature aggregation across nodes and attributes;

[0089] Step 32: Adopt a hypergraph convolution module based on spatial domain propagation mechanism. Each hypergraph convolution operation is divided into two stages: the first stage realizes information aggregation from nodes to hyperedges, and the second stage realizes feature reverse update from hyperedges to nodes, thus forming a complete information interaction closed loop.

[0090] Furthermore, each hypergraph convolution operation in step 32 is divided into two stages: the first stage realizes information aggregation from nodes to hyperedges, and the second stage realizes feature back-update from hyperedges to nodes, thus forming a complete information interaction closed loop; as detailed below:

[0091] Step 321: Node-to-hyperedge feature aggregation. For each hyperedge, aggregate the features of its associated nodes to generate a hyperedge feature set. :

[0092]

[0093] in, W This is the hyperedge weight matrix; D e It is the hypermarginality matrix; H For the hypergraph incidence matrix, ; This is the transpose of the incidence matrix, used to control the nodes connected by each hyperedge. ; For the first t The node features of the layer input.

[0094] Step 322: Backpropagate the features from the hyperedges to the nodes, passing the information of each hyperedge back to its adjacent nodes, and update the feature nodes, as shown below:

[0095]

[0096] in, The output features are represented by σ(·), which is the ReLU activation function. D v This is the node degree matrix; For the first t The learnable parameter matrix of the layer;

[0097] Combining the two equations from steps 321 and 322, we obtain the hypergraph convolution expression:

[0098] .

[0099] Furthermore, step 4 specifically includes:

[0100] Step 41, Parameter Initialization and Hyperparameter Setting: Randomly initialize the parameter weights of all HGNN layers. The initial learning rate was set to 0.0001 and the weight coefficients of the loss function were set accordingly. λ j ;

[0101] Step 42, Forward Propagation: Input the node feature matrix The HGNN model is input, and features are extracted and propagated through multiple HGNNConv convolutional layers, batch normalization layers, and activation function layers. The output is a prediction matrix. ,in K To determine the number of output performance dimensions;

[0102] Step 43, Loss Function Construction and Backpropagation: The training objective is to minimize the error between the predicted value and the true target value, using the multi-objective weighted mean square error (MSE) loss function. :

[0103]

[0104] in, λ j For the first j The weight of each objective; For the first i The first sample j Target values ​​for each indicator; For the first i The first sample j Predicted values ​​for each indicator;

[0105] The backpropagation algorithm 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, thereby gradually minimizing the prediction error during training.

[0106] Step 44, Training Control and Convergence Judgment: Divide all training samples into training set and validation set in an 8:2 ratio, with 80% of the samples used for model parameter learning and 20% of the samples used as validation set.

[0107] The predictive performance is evaluated in real time for each epoch. When the loss function on the validation set stops decreasing or begins to rise after several consecutive epochs, the model is considered to have reached its optimal state, and training is terminated early to prevent overfitting.

[0108] Furthermore, step 5 specifically includes:

[0109] Step 51: Task Modeling and Problem Definition

[0110] The target performance vector is set as follows:

[0111]

[0112] in, The target performance vector is defined by the user. Target compressive strength; Target flexural strength; Target tensile strength; Target bending strength; For target scalability; Target slump;

[0113] Step 52: Model the reverse mix design problem as an optimization problem based on performance objectives: within the feasible region of the set material input variables. In the process, the optimization module automatically generates candidate input combinations x, and the performance prediction model is then used to predict the results using the trained HGNN. Calculate its corresponding performance prediction value ;

[0114] The optimization objective is to minimize the difference between the prediction performance and the user-defined target performance. The deviation between them is used to search for the optimal input combination x. * ,satisfy:

[0115]

[0116] in, This is the performance deviation loss function; Input feasible ranges for the defined material design (such as upper and lower limits of doping, proportioning constraints, etc.); x includes proportioning parameters. Fiber parameters Image feature vectors ; For the first j Predicted values ​​for each performance indicator; λ j For the first j The weight of each objective.

[0117] The optimization module is in The system continuously generates candidate input combinations and predicts their performance through the model. The predicted values ​​are then compared with the target performance to gradually optimize the input variable x in order to approach the minimum loss.

[0118] Step 53: After completing the reverse mix design optimization, output one or more material design schemes; each scheme includes recommended material mix proportions (cement, silica fume, fly ash, quartz sand, water, water-reducing agent, PVA fiber content and its performance parameters) and corresponding predicted performance indicators (compressive strength, flexural strength, tensile strength, bending strength, spread, slump).

[0119] By adopting the above technical solution, the present invention has the following beneficial effects compared with the prior art:

[0120] This invention introduces a Hypergraph Neural Network (HGNN) model, which can effectively model multi-attribute, multi-dimensional, and high-order complex relationships between material samples. Through a hyperedge construction mechanism combining attribute-driven and feature space-driven approaches, it overcomes the limitation of traditional graph structures that can only express binary relationships, thus improving the ability to express the laws governing the "preparation parameters-mechanical behavior" of materials. Simultaneously, this invention 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 such as compressive strength, flexural strength, tensile strength, bending toughness, and scalability.

[0121] Furthermore, this invention employs a performance-target-driven reverse optimization mechanism that automatically searches for the optimal combination of mix proportions under set performance requirements. This eliminates the inefficient process of repeated trial mixing and experimental verification, significantly improving the intelligence and efficiency of material design. The method possesses good generalization and scalability, making it suitable for performance prediction and mix proportion recommendation of various ultra-high performance concrete systems, and has broad engineering application prospects and industrial promotion value. Attached Figure Description

[0122] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0123] Figure 1 A schematic diagram illustrating the formulation design method for PVA fiber-toughened UHPC materials based on hypergraph neural networks provided by this invention;

[0124] Figure 2 A simplified flowchart of the formulation design method for PVA fiber-toughened UHPC materials based on hypergraph neural networks provided by this invention;

[0125] Figure 3 This is a schematic diagram of the hypergraph structure provided by the present invention;

[0126] Figure 4 This is a schematic diagram of the attribute-driven and feature-driven hyperedge construction process provided by the present invention;

[0127] Figure 5 The flowchart for performance optimization and reverse proportioning design provided for this invention. Detailed Implementation

[0128] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be particularly noted that the following embodiments are for illustrative purposes only and do not limit the scope of the invention. Similarly, the following embodiments are only some, not all, embodiments of the present invention, and all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0129] See attached document Figure 1-2 As shown, this embodiment provides a method for designing formulations of PVA fiber-toughened UHPC materials based on hypergraph neural networks, specifically including the following steps:

[0130] Step 1) Multimodal data acquisition and processing:

[0131] Multimodal material sample data was collected, 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 was performed separately, and all sample features were uniformly concatenated and encoded into a high-dimensional node feature vector. To form the initial node feature matrix This serves as input to the hypergraph neural network model. The macroscopic properties of the material samples are used for model output alignment and performance regression prediction tasks. Specifically, this includes:

[0132] Step 11: Comprehensively collect multi-source heterogeneous characteristic information of PVA fiber toughened ultra-high performance concrete material. The multi-source heterogeneous characteristic information includes raw material proportioning parameters, PVA fiber performance parameters, microstructure image information and corresponding macroscopic performance indicators.

[0133] The collected raw material ratio parameters, PVA fiber performance parameters, and microstructure image information feature variables are standardized and used as feature vectors for the dataset, forming a data structure suitable for input to a hypergraph neural network; specifically as follows:

[0134] a) Raw material proportioning parameters: Obtain the basic composition ratio of each concrete sample, including: cement (kg / m³) 3 ), silica fume (kg / m 3 ), fly ash (kg / m 3 ), Quartz sand (kg / m 3 ), water (kg / m3 ), water-reducing agent (%), PVA fiber content (%).

[0135] The above parameters are used to construct a ratio vector, which is then standardized using a normalization method (min-max) to eliminate dimensional differences and form the input node features. The expression is as follows:

[0136]

[0137] in, x c It refers to cement; x sf Indicates silica ash; x fa It refers to fly ash; x sand Indicates quartz sand; x water It represents water; x ad Indicates water-reducing agent; x pva This indicates the amount of PVA fiber.

[0138] b) PVA fiber performance parameters: For each batch of PVA fibers used in the tests, their physical and mechanical properties were collected, including: diameter (μm), length (mm), and density (g / cm³). 3 ), tensile strength (MPa), elongation at break (%), and elastic modulus (GPa).

[0139] The above parameters are combined to form fiber feature sub-vectors, which are then standardized using a normalization method (min-max) to form input node features. The expression is as follows:

[0140]

[0141] in, Indicates diameter; Indicates length; Indicates density; Indicates tensile strength; Indicates elongation at break; It represents the elastic modulus.

[0142] c) Microstructural Image Information: Scanning electron microscopy (SEM) images of individual samples are acquired, and their internal microstructural features are extracted. Image data is processed using a pre-trained convolutional neural network (CNN) model for feature extraction, reducing the dimensionality to a fixed-length image feature vector. The expression is as follows:

[0143]

[0144] in, I SEM This represents the scanning electron microscope image corresponding to the material sample.

[0145] 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 serves as the initial input to the hypergraph neural network, denoted as... ,in i =1,2, ..., N , is the sample number. d For feature dimensions.

[0146] Each node The input feature vector is composed of three concatenated parts: the matching parameter vector, etc. PVA fiber parameter vector With image feature vectors The concatenated vector is denoted as These constitute the individual sample input features of the hypergraph neural network; The format is as follows:

[0147]

[0148] All samples form nodes that together form a feature matrix. , as input to the hypergraph neural network; The format is as follows:

[0149]

[0150] Step 13: The output of the HGNN model is the predicted value of the macroscopic performance index of the material sample; the specific macroscopic performance index includes: compressive strength. Flexural strength ,tensile strength Flexural strength Scalability With slump This is used to guide back-optimization of input variables based on target performance and recommendation of high-performance allocation ratios. For the first... i For each sample, its performance output is defined as :

[0151]

[0152] in, This represents the predicted compressive strength value; This represents the predicted flexural strength. This indicates the predicted tensile strength value; This represents the predicted value of bending strength; This represents the predicted expansion value; This represents the predicted slump value;

[0153] By combining the outputs of all samples, we can obtain the overall predicted output matrix:

[0154]

[0155] This output matrix is ​​used to correlate with the target performance. Compare the results and perform reverse ratio optimization.

[0156] Step 2) Hypergraph structure construction:

[0157] See attached document Figure 3 As shown, a hypergraph structure is defined. ; Construct a node set using each material sample as a node in the graph structure. V Multiple hyperedge groups are constructed based on attribute similarity (such as PVA fiber doping range and target strength level) and feature space nearest neighbor relationship (such as similarity between ratio features and image features). Attribute-driven hyperedge sets and feature-driven hyperedge sets are constructed separately, and the two are concatenated to form a hyperedge set. E Assign weights to each hyperedge to form a hyperedge weight matrix. W Simultaneously construct the corresponding association matrix. H This is used to characterize the connection relationships between nodes and hyperedges, enabling graph representation of higher-order structural information. Specifically, it includes:

[0158] Step 21) After completing the multimodal feature extraction, represent all material samples as nodes in a hypergraph structure, construct a hypergraph structure for modeling high-order complex relationships, and define the hypergraph structure as: ,in, For each node in the hypergraph, representing the set of all nodes and corresponding to all material samples, ... Corresponding to a row of feature vectors ; This is a set of hyperedges, where each hyperedge connects a group of related nodes; W This is the hyperedge weight matrix. Hypergraph structures can be constructed by building an incidence matrix. H Implement formal representation.

[0159] Step 22) Constructing Hyperedges

[0160] See attached document Figure 4 As shown, to achieve high-order structural representation of material samples across different feature dimensions, this embodiment employs a multi-strategy approach to construct hyperedge sets. EThis process aggregates related sample nodes into a unified hyperedge. Hyperedge generation can be achieved through attribute-driven and feature-driven methods, which can be flexibly combined to enhance the diversity and expressive power of hypergraph modeling. Specifically, the process includes the following steps:

[0161] Step 221) Attribute-driven hyperedge generation

[0162] For material samples with discrete or interval-based structured properties (such as PVA content, compressive strength grade, etc.), sample nodes with the same attribute value or falling within the same interval can be grouped into a set, and a corresponding hyperedge can be generated. This hyperedge connects all nodes that satisfy the attribute condition, realizing high-order aggregation modeling in the attribute space (e.g., grouping samples with PVA content in the range of 1.5%–2.0% into the same hyperedge); as detailed below:

[0163] Let the set of attributes be A certain attribute The corresponding set of nodes is:

[0164]

[0165] in, Represents a node The attribute value; This indicates all attributes with the same value. a A set of nodes.

[0166] Therefore, the attribute-driven hyperedge set can be represented as:

[0167]

[0168] Attribute-driven hyperedges form an association matrix for:

[0169]

[0170] in, The number of hyperedges is driven by attributes.

[0171] For example: when the attribute is "PVA doping 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 range a i A hyperedge can be constructed. e i All node samples that meet the conditions are assigned to this hyperedge. For the interval a1: [1.0%, 1.5%], the corresponding set of nodes can be defined as:

[0172]

[0173] Thus, the super-edge e 1 represents the higher-order structural unit formed by connecting all sample nodes whose PVA doping levels fall within this interval. Similarly, attribute-driven hyperedge sets can be constructed based on multiple attributes or attribute sub-intervals.

[0174] .

[0175] Step 222): Feature Space-Driven Hyperedge Generation

[0176] To address the similarity relationships of material samples in a multidimensional feature space (ratio vector, PVA fiber parameters, and image features), this embodiment employs a method based on... k - Neighbors ( k The Nearest Neighbors (KNN) strategy is used to construct hyperedges. Specifically, for each node sample, the hyperedge with the smallest Euclidean distance in the feature space is selected. k Each adjacent node, together with the central node, forms a hyperedge. This strategy can systematically capture higher-order relationships between groups of samples with "similar features" and achieve enhanced propagation of information from similar structures during hypergraph convolution. Specifically:

[0177] For each node Its eigenvector is Define its first k The KNN neighbor set is as follows:

[0178]

[0179] in, v ik Represents a node v i The k-th nearest neighbor node;

[0180] Then from the central node Together with its nearest neighbor, they form a superedge:

[0181]

[0182] The final feature-driven hyperedge set is represented as:

[0183]

[0184] in, NThe value represents the number of nodes, indicating that for each node, a feature space nearest neighbor hyperedge is constructed centered on itself.

[0185] Feature-driven hyperedges form the correlation matrix for:

[0186]

[0187] in, The number of feature-driven hyperedges.

[0188] For example: Suppose a certain node The corresponding feature vector is the vector obtained by concatenating the image features with the matching parameters. After calculating the Euclidean distance between it and other samples in the standardized feature space, the nearest one is selected. k =3 nodes are respectively , , .

[0189] Then the center node of the sample The corresponding feature space-driven hyperedge is:

[0190]

[0191] This hyperedge will be used in the hypergraph for information propagation and feature enhancement learning of similar samples.

[0192] Step 223) Concatenate the hyperedges constructed by attribute-driven and feature-driven approaches to obtain the total hyperedge set. E And based on this, construct the hypergraph's association matrix:

[0193]

[0194] Among them, the total number of hyperedges Each super edge A subset of nodes represents a set of sample nodes that are similar, coupled, or related under a certain feature dimension or attribute condition.

[0195] Based on the total hyperedge set E Construct an association matrix , It meets the following rules:

[0196]

[0197] in, Represents a node Belongs to superedge , This indicates that the node does not belong to the superedge.

[0198] The final result H It will serve as one of the core inputs in the model structure, along with the weight matrix. W They will also participate in the graph convolution calculation process of the subsequent HGNN model.

[0199] Step 23) Constructing the hypergraph structure At that time, a non-negative weight is assigned to each hyperedge to adjust the degree of influence of the hyperedge in the information propagation process.

[0200] This embodiment introduces an adaptive hyperedge weighting mechanism, which sets trainable parameters for hyperedge sets from different sources (such as attribute-driven and feature-driven hyperedges), normalizes them using an activation function (sigmoid), and then applies them to attribute-driven and feature-driven hyperedges to form a weight matrix. W The weights can be automatically updated during model training, thus enabling dynamic adjustment of the contribution of different structural information. All hyperedge weights can be uniformly represented as a diagonal matrix. , and the correlation matrix They participate in the convolution operation of the HGNN model together.

[0201] For example: the total set of hyperedges is E Classified as P A set of hyperedges from different sources Each set E P Corresponding to a trainable weight parameter The weights are then applied to all hyperedges within the group after transformation using the sigmoid function, ultimately constructing the hyperedge weight matrix:

[0202]

[0203] in, , w j Indicates the first j The weight of each superedge.

[0204] Step 3) Hypergraph Neural Network Model Construction:

[0205] After completing node feature extraction and hypergraph structure construction, a hypergraph neural network model containing multiple hypergraph convolutional layers (HGNNConv) is constructed based on the 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, thereby effectively modeling the nonlinear, multimodal, and high-order coupling relationships between material proportioning parameters, fiber properties, microstructure features, and performance indicators.

[0206] In this embodiment, a Hypergraph Neural Network (HGNN) is used as the learning framework. The constructed HGNN model mainly consists of the following structure: three hypergraph convolutional layers (HGNNConv), two batch normalization layers, an activation function layer following each convolutional layer, and a fully connected output layer. The activation function layer uses the ReLU (Rectified Linear Unit) function to introduce non-linear expressive power and improve the model's ability to fit complex relationships.

[0207] In this embodiment, step 3 specifically includes the following steps:

[0208] 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. Simultaneously, the model utilizes a pre-constructed correlation matrix. and hyperedge weight matrix Model the higher-order connections between nodes to achieve structured feature aggregation across nodes and attributes.

[0209] Step 32) To improve computational efficiency and enhance the model's high-order expressive power, a hypergraph convolution module based on spatial domain propagation (HGNNConv) is adopted. This structure achieves efficient information propagation and a trainable representation update mechanism by explicitly defining the message passing function between nodes and hyperedges. Each hypergraph convolution operation consists of two stages: the first stage realizes information aggregation from nodes to hyperedges, and the second stage realizes feature back-update from hyperedges to nodes, thus forming a complete information interaction closed loop. Specifically:

[0210] Step 321): Node-to-hyperedge feature aggregation. For each hyperedge, aggregate the features of its associated nodes to generate a hyperedge feature set. The expression is as follows:

[0211]

[0212] in, W This is the hyperedge weight matrix; D e It is the hypermarginality matrix; H For the hypergraph incidence matrix, ; This is the transpose of the incidence matrix, used to control the nodes connected by each hyperedge. ; For the first t The node features of the layer input.

[0213] Step 322) Backpropagation of superedge features to nodes: Information of each superedge is transmitted back to its adjacent nodes, and feature nodes are updated.

[0214]

[0215] in, The output features are represented by σ(·), which is the ReLU activation function. D v This is the node degree matrix; For the first t The learnable parameter matrix of the layer;

[0216] Combining the two equations in steps 321) and 322), we obtain the hypergraph convolution expression:

[0217]

[0218] Step 4) Model training:

[0219] This embodiment employs 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 including:

[0220] Step 41) Parameter initialization and hyperparameter setting: Randomly initialize the parameter weights of all HGNN layers. The initial learning rate was set to 0.0001 and the weight coefficients of the loss function were set accordingly. λ j In this example, the performance indicators are as follows: compressive strength f c Flexural strength f b ,tensile strength f t Flexural strength F flex Scalability d slump s Loss function weight coefficients λ j The values ​​are 1.0, 0.8, 0.5, 1.2, 0.7, and 0.7 respectively.

[0221] Step 42) Forward Propagation: Input the node feature matrix The HGNN model is input, and features are extracted and propagated through multiple HGNNConv convolutional layers, batch normalization layers, and activation function layers. The output is a prediction matrix. ,in K To determine the number of performance dimensions in the output, this example... K = 6.

[0222] The final output of this model is a vector of predicted macroscopic performance indicators for each sample. For the _____, ... i For each sample, its output vector is represented as:

[0223]

[0224] in, This is the predicted compressive strength value; This is the predicted value for flexural strength; This is the predicted value for tensile strength; This is the predicted value for flexural strength; This is the predicted value for scalability; This is the predicted slump value.

[0225] The set of outputs from all samples constitutes the prediction matrix. :

[0226]

[0227] Step 43) Loss Function Construction and Backpropagation: The training objective is to minimize the error between the predicted value and the true target value, using the multi-objective weighted mean square error (MSE) loss function. :

[0228]

[0229] in, λ j For the first j The weight of each objective; For the first i The first sample j Target values ​​for each indicator; For the first i The first sample j The predicted values ​​of each indicator.

[0230] The backpropagation algorithm 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.

[0231] Step 44) Training Control and Convergence Judgment: To ensure the stability of the HGNN model training process and the generalization ability of the final result, all training samples are specifically divided into training and validation sets in an 8:2 ratio. 80% of the samples are used for model parameter learning, and 20% serve as the validation set, used only for performance evaluation and not for parameter updates. The prediction performance is evaluated in real time for each epoch. When the validation set loss function no longer decreases or begins to rise after several consecutive epochs, the model is considered to have reached its optimal state, and training is terminated early to prevent overfitting. After training, the model can be used to predict and evaluate the performance of material samples with arbitrary input ratio parameters.

[0232] Step 5) Performance optimization and reverse proportioning design:

[0233] See attached document Figure 5 As shown, based on the trained HGNN model, according to the user-defined target performance vector, the HGNN model is embedded as a prediction function into the performance bias loss to construct the inverse optimization objective function. A genetic algorithm is 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 outputs the corresponding macroscopic performance indicators; specifically including:

[0234] Step 51) Task Modeling and Problem Definition

[0235] The target performance vector is set as follows:

[0236]

[0237] in, The target performance vector is defined by the user. Target compressive strength; Target flexural strength; Target tensile strength; Target bending strength; For target scalability; The target collapse degree.

[0238] Step 52) In this embodiment, the reverse mix design problem is modeled as an optimization problem based on a performance objective: within the feasible region of the set material input variables... In the process, the optimization module automatically generates candidate input combinations x, and the performance prediction model is then used to predict the results using the trained HGNN. Calculate its corresponding performance prediction value The optimization objective is to minimize the difference between the prediction performance and the user-defined target performance. The deviation between them is used to search for the optimal input combination x. * ,satisfy:

[0239]

[0240] in, This is the performance deviation loss function; Input feasible ranges for the defined material design (such as upper and lower limits of doping, proportioning constraints, etc.); x includes proportioning parameters. Fiber parameters Image feature vectors ; For the first j Predicted values ​​for each performance indicator; λ j For the firstj The weight of each objective.

[0241] The optimization module is in The system continuously generates candidate input combinations and predicts their performance using the model. The predicted values ​​are then compared with the target performance to gradually optimize the input variable x in order to approximate the minimum loss.

[0242] The above scheme can automatically search for the optimal combination of raw material ratio parameters that meet the performance requirements based on the performance goals set by the user, thereby realizing intelligent material design under specific process constraints.

[0243] Step 53) After completing the reverse mix design optimization, output one or more material design schemes. Each scheme includes the recommended material mix ratio (cement, silica fume, fly ash, quartz sand, water, water-reducing agent, PVA fiber content and its performance parameters) and the corresponding predicted performance indicators (compressive strength, flexural strength, tensile strength, bending strength, spread, slump).

[0244] In summary, this invention proposes an AI design method for PVA fiber-toughened UHPC material formulation that combines multimodal feature input, hypergraph structure modeling, and hypergraph neural network-based formulation. By introducing attribute-driven and feature-driven hyperedge construction mechanisms, a hypergraph representation of high-order structure association is constructed, which can effectively capture the complex nonlinear coupling relationship between raw material parameters, fiber properties, and microstructure in material design.

[0245] The above description is only a part of the embodiments of the present invention and does not limit the scope of protection of the present invention. Any equivalent device or equivalent process transformation made based on the content of the present invention specification and drawings, or direct or indirect application in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for designing formulations of PVA fiber-toughened UHPC materials based on hypergraph neural networks, characterized in that, 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, and corresponding macroscopic performance indicators; The raw data is preprocessed, and all sample features are concatenated and encoded into a high-dimensional node feature vector. To form the initial node feature matrix , as input to the HGNN model; Macroscopic performance indicators of material samples are used for HGNN model output alignment and performance regression prediction; Step 2, Hypergraph Structure Construction: Define hypergraph structure Each material sample is used as a node in the hypergraph structure to construct a node set. V ; Multiple hyperedge groups are constructed based on attribute similarity and feature space nearest neighbor relationships. Attribute-driven hyperedge sets and feature-driven hyperedge sets are constructed separately, and these two sets are concatenated to form the hyperedge set. E ; Assign weights to each hyperedge to form a hyperedge weight matrix. W At the same time, construct the corresponding association matrix. H , used to characterize the connection relationship between nodes and hyperedges; Step 3: HGNN model construction: Based on the constructed hypergraph structure, an HGNN model containing multiple hypergraph convolutional layers is constructed. The HGNN 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. 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 Proportioning Design: Based on the set target performance vector, the HGNN model is embedded as a prediction function into the performance deviation loss to construct the inverse optimization objective function; A genetic algorithm is used to iteratively search in the input variable space to automatically generate the optimal raw material ratio combination that satisfies the target performance vector, and simultaneously output the corresponding macroscopic performance indicators.

2. The method for formulating PVA fiber-toughened UHPC materials based on hypergraph neural networks according to claim 1, characterized in that, Step 1 specifically includes: Step 11: Collect comprehensive information on the multi-source heterogeneous characteristics of PVA fiber-toughened ultra-high performance concrete materials. The multi-source heterogeneous characteristics include raw material proportioning 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 input to a hypergraph neural network. Step 12: Treat each material sample as a node in the hypergraph. V The corresponding input features are the fused multimodal data vectors; this dataset feature vector serves as the initial input to the hypergraph neural network, denoted as... ,in i =1, 2, ..., N , is the sample number. d For feature dimensions; Each node The input feature vector is composed of three concatenated parts: the matching parameter vector, etc. PVA fiber parameter vector With image feature vectors The concatenated vector is denoted as The individual sample input features that constitute a hypergraph neural network The expression is as follows: All samples form nodes that together form a feature matrix. , as input to the hypergraph neural network; The format is as follows: Step 13: The output of the HGNN model is the predicted value of the macroscopic performance index of the material sample; the specific macroscopic performance index includes: compressive strength. Flexural strength ,tensile strength Flexural strength Scalability With slump For the first i For each sample, the predicted value of its macroscopic performance index is defined as follows: : in, This represents the predicted compressive strength value; This represents the predicted flexural strength. This indicates the predicted tensile strength value; This represents the predicted value of bending strength. This represents the predicted expansion value; This represents the predicted slump value; By combining the outputs of all samples, we can obtain the overall predicted output matrix: The overall prediction output matrix is ​​used in conjunction with the target performance vector. Compare the results and perform reverse ratio optimization.

3. The method for formulating PVA fiber-toughened UHPC materials based on hypergraph neural networks 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 the dataset feature vector to form a data structure suitable for input to the hypergraph neural network; specifically as follows: a) Raw material proportioning parameters: Obtain the basic composition ratio of each concrete sample, including: cement, silica fume, fly ash, quartz sand, water, water-reducing agent, and PVA fiber content; The above parameters are used to construct a ratio vector, which is then standardized using a normalization method to eliminate dimensional differences and form the input node features. The expression is as follows: in, x c It refers to cement; x sf Indicates silica ash; x fa It refers to fly ash; x sand Indicates quartz sand; x water It represents water; x ad Indicates water-reducing agent; x pva Indicates the PVA fiber content; b) PVA fiber performance parameters: For each batch of PVA fibers used in the test, 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 fiber feature sub-vectors, which are then standardized using a normalization method to form input node features. The expression is as follows: in, Indicates diameter; Indicates length; Indicates density; Indicates tensile strength; Indicates elongation at break; Indicates the elastic modulus; c) Microstructural Image Information: Scanning electron microscopy images of individual samples are acquired, and their internal microstructural features are extracted. The image data is then processed using a pre-trained convolutional neural network (CNN) model for feature extraction, reducing the dimensionality to a fixed-length image feature vector. The expression is as follows: in, I SEM This represents the scanning electron microscope image corresponding to the material sample.

4. The formulation design method for PVA fiber-toughened UHPC materials based on hypergraph neural networks according to claim 1, characterized in that, Step 2 specifically includes: Step 21: Represent all material samples as nodes in a hypergraph structure, construct a hypergraph structure for modeling high-order complex relationships, and define the hypergraph structure as: ,in, For each node in the hypergraph, representing the set of all nodes and corresponding to all material samples, ... Corresponding to a row of feature vectors ; This is a set of hyperedges, where each hyperedge connects a group of related nodes; W The hyperedge weight matrix; the hypergraph structure is constructed by building the correlation matrix. H Implement formal representation; Step 22: Construct a set of superedges using multiple strategies. E The process involves aggregating related sample nodes into a unified hyperedge; the hyperedge can be generated using either attribute-driven or feature-driven methods. Step 23: Constructing the hypergraph structure At that time, a non-negative weight is assigned to each hyperedge, and trainable parameters are set for hyperedge sets from different sources. After normalization by activation functions, these parameters are applied to attribute-driven and feature-driven hyperedges to form a weight matrix. W The weights of all hyperedges are uniformly represented as a diagonal matrix. , and the correlation matrix They participate in the convolution operation of the HGNN model together.

5. The formulation design method for PVA fiber-toughened UHPC materials based on hypergraph neural networks according to claim 4, characterized in that, Step 22 specifically includes the following steps: Step 221: Attribute-driven hyperedge generation For material samples with discrete or interval-based structured properties, sample nodes with the same property value or falling into the same interval are grouped into a set, and a corresponding hyperedge is generated. This hyperedge connects all nodes that satisfy the property conditions, realizing high-order aggregation modeling in the property space; specifically as follows: Let the set of attributes be A certain attribute The corresponding set of nodes is: in, Represents a node The attribute value; This indicates all attributes with the same value. a The set of nodes; Therefore, the attribute-driven hyperedge set is represented as: Attribute-driven hyperedges form an association matrix for: in, The number of hyperedges is driven by attributes; Step 222: Feature Space-Driven Hyperedge Generation To address the similarity relationships of material samples in a multidimensional feature space, a method based on... k - The nearest neighbor strategy is used to construct superedges; Centered on each node sample, select the node with the smallest Euclidean distance in the feature space. k Each pair of adjacent nodes, together with the central node, forms a hyperedge; as detailed below: For each node Its eigenvector is Define its first k The set of KNN neighbors is: in, v ik Represents a node v i The k-th nearest neighbor node; Then from the central node Together with its nearest neighbor, they form a superedge: The final feature-driven hyperedge set is represented as: in, N The value represents the number of nodes, indicating that for each node, a feature space nearest neighbor superedge centered on itself is constructed; Feature-driven hyperedges form the correlation matrix for: in, The number of hyperedges is driven by features; Step 223: Concatenate the hyperedges constructed by attribute-driven and feature-driven approaches to obtain the total hyperedge set. E And based on this, construct the hypergraph's association matrix: Among them, the total number of hyperedges Each super edge A subset of nodes represents a set of sample nodes that are similar, coupled, or related under a certain feature dimension or attribute condition; Based on the total hyperedge set E Construct an association matrix , It meets the following rules: in, Represents a node Belongs to superedge , This indicates that the node does not belong to the superedge.

6. The method for formulating PVA fiber-toughened UHPC materials based on hypergraph neural networks according to claim 1, characterized in that, Step 3 uses a hypergraph neural network as the learning framework. The constructed hypergraph neural network model mainly consists of the following structure: The system consists of three hypergraph convolutional layers, two 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 non-linear expressive power and improve the HGNN model's ability to fit complex relationships.

7. The method for formulating PVA fiber-toughened UHPC materials based on hypergraph neural networks 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 model extracts and transforms sample features layer by layer through a multi-layer hypergraph convolutional structure; simultaneously, it utilizes a pre-constructed correlation matrix. and hyperedge weight matrix Model the higher-order connections between nodes to achieve structured feature aggregation across nodes and attributes; Step 32: Adopt a hypergraph convolution module based on spatial domain propagation mechanism. Each hypergraph convolution operation is divided into two stages: the first stage realizes information aggregation from nodes to hyperedges, and the second stage realizes feature reverse update from hyperedges to nodes, thus forming a complete information interaction closed loop.

8. The method for formulating PVA fiber-toughened UHPC materials based on hypergraph neural networks according to claim 7, characterized in that, In step 32, each hypergraph convolution operation is divided into two stages: the first stage realizes information aggregation from nodes to hyperedges, and the second stage realizes feature back-update from hyperedges to nodes, thus forming a complete information interaction closed loop; as detailed below: Step 321: Node-to-hyperedge feature aggregation. For each hyperedge, aggregate the features of its associated nodes to generate a hyperedge feature set. : in, W This is the hyperedge weight matrix; D e It is the hypermarginality matrix; H For the hypergraph incidence matrix, ; This is the transpose of the incidence matrix, used to control the nodes connected by each hyperedge. ; For the first t Node features of the layer input; Step 322: Backpropagate the hyperedge features to the node features, passing the information of each hyperedge back to its adjacent nodes, and update the feature nodes, as shown below: in, The output features are represented by σ(·), which is the ReLU activation function. D v This is the node degree matrix; For the first t The learnable parameter matrix of the layer; Combining the two equations from steps 321 and 322, we obtain the hypergraph convolution expression: 。 9. The method for formulating PVA fiber-toughened UHPC materials based on hypergraph neural networks according to claim 1, characterized in that, Step 4 specifically includes: Step 41, Parameter Initialization and Hyperparameter Setting: Randomly initialize the parameter weights of all HGNN layers. The initial learning rate was set to 0.0001 and the weight coefficients of the loss function were set accordingly. λ j ; Step 42, Forward Propagation: Input the node feature matrix The HGNN model is input, and features are extracted and propagated through multiple HGNNConv convolutional layers, batch normalization layers, and activation function layers. The output is a prediction matrix. ,in K To determine the number of output performance dimensions; Step 43, Loss Function Construction and Backpropagation: The training objective is to minimize the error between the predicted value and the true target value. A multi-objective weighted mean square error loss function is used. : in, λ j For the first j The weight of each objective; For the first i The first sample j Target values ​​for each indicator; For the first i The first sample j Predicted values ​​for each indicator; The backpropagation algorithm 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, thereby gradually minimizing the prediction error during training. Step 44, Training Control and Convergence Judgment: Divide all training samples into training set and validation set in an 8:2 ratio, with 80% of the samples used for model parameter learning and 20% of the samples used as validation set. The prediction performance is evaluated in real time for each round; when the loss function on the validation set no longer decreases or begins to rise after several consecutive rounds, the model is considered to have reached its optimal state, and training is terminated early.

10. The method for formulating PVA fiber-toughened UHPC materials based on hypergraph neural networks according to claim 1, characterized in that, Step 5 specifically includes: Step 51: Task Modeling and Problem Definition The target performance vector is set as follows: in, The target performance vector is defined by the user. Target compressive strength; Target flexural strength; Target tensile strength; Target bending strength; For target scalability; Target slump; Step 52: Model the reverse mix design problem as an optimization problem based on performance objectives: within the feasible region of the set material input variables. In the process, the optimization module automatically generates candidate input combinations x, and the performance prediction model is then used to predict the results using the trained HGNN. Calculate its corresponding performance prediction value ; The optimization objective is to minimize the vector between the prediction performance and the user-defined target performance. The deviation between them is used to search for the optimal input combination x. * ,satisfy: in, This is the performance deviation loss function; Input the feasible range for the defined material design; x includes proportioning parameters. Fiber parameters Image feature vectors ; For the first j Predicted values ​​of several macro performance indicators; λ j For the first j The weight of each objective; The optimization module is in The model continuously generates candidate input combinations and predicts their performance. The predicted values ​​are then compared with the target performance vector to gradually optimize the input variable x in order to approximate the minimum loss. Step 53: After completing the reverse proportioning optimization, output one or more material design schemes; each scheme includes the recommended material proportions and the corresponding predicted macroscopic performance indicators.

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