Multi-scale prediction method for permeability of heat-proof porous material based on multi-source heterogeneous data fusion

Abstract

The invention relates to the technical field of protection systems, in particular to a multi-source heterogeneous data fusion heat-proof porous material permeability multi-scale prediction method, which comprises the following steps: establishing a heat-proof porous material data set according to a collected three-dimensional structure of a heat-proof porous material; a permeability prediction model is established, the permeability prediction model is used for processing the structure image through a convolution module and a dimension reduction encoder in sequence, processing the structure characteristic parameters through a dimension raising encoder, processing through a cross-modal attention mechanism, and processing through regression prediction to obtain a permeability prediction value; based on the heatproof porous material data set, performing hyper-parameter optimization and training on the permeability prediction model by adopting a TPE sampler and a median pruning device; inputting to-be-evaluated sample data into the trained permeability prediction model to obtain a permeability prediction value; according to the method, the accuracy and efficiency of predicting the macroscopic permeability of the thermal protection material can be improved.

Description

Technical Field

[0001] This invention relates to the field of protection system technology, specifically to a multi-scale prediction method for the permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion. Background Technology

[0002] Due to their extremely high flight speeds, hypersonic vehicles experience deceleration during flight as the hypersonic flow is compressed or viscously resisted by the shock wave. This causes a significant conversion of the gas's kinetic energy into internal energy, resulting in a sharp increase in gas temperature within the shock layer. This high temperature triggers a series of complex physicochemical reactions throughout the shock layer, including energy excitation, dissociation, and ionization of gas molecules. This extreme high-temperature environment can cause severe damage to the vehicle's structure and materials; therefore, thermal protection materials are needed to protect the vehicle's surface structure and internal structure from the effects of high temperatures.

[0003] Pyrolytic carbonization ablation materials are a type of ablation material consisting of a resin-bonded, fiber-reinforced woven matrix, such as epoxy resin, phenolic resin, and silicone resin. During ablation, they often exhibit pyrolysis and carbonization layers, making them commonly used thermal protection materials for spacecraft re-entering under high enthalpy, medium-to-low heat flux, and prolonged thermal environments. During high-speed flight, the pyrolytic carbonization material undergoes complex reactions under the intense influence of the external flow field, resulting in surface ablation. Gases generated by the pyrolysis of the resin matrix flow through the internal porous carbonization layer and are injected to the surface, where they, along with the ablation gases, are injected into the boundary layer, creating a thermal blocking effect that slows heat transfer inward, thus achieving thermal protection.

[0004] After pyrolysis, the material forms a loose and porous carbonized layer. As pyrolysis continues, the carbonized layer thickens, altering the material's transport properties. Furthermore, the presence of a gas pressure difference between the material's surface and interior significantly impacts its permeability, affecting both its thermal conductivity and the entrainment of pyrolysis gases. Therefore, accurate prediction of the transport characteristics of the porous structure in thermal protection materials is crucial.

[0005] Currently, the permeability of porous materials is mainly obtained through experimental measurements or numerical simulations, which requires significant time and computational resources. The permeability of porous materials is directly related to their geometric structural characteristics such as porosity, connectivity, pore shape, and tortuosity. Researchers have established empirical relationships between permeability and geometric structural parameters, but these individual empirical relationships are generally only applicable to a limited number of scenarios. With the development of machine learning, some researchers have constructed permeability regression prediction models using traditional machine learning methods such as support vector machines and random forests. These methods mostly involve first statistically analyzing the structural parameters of porous materials and then establishing the relationship between these parameters and permeability. They lack the ability to directly predict permeability from structural images, limiting their practical application. In recent years, deep learning has developed rapidly. Wang et al. used convolutional neural networks to predict the permeability of two-dimensional porous media structures, and Meng et al. used convolutional neural networks to predict magnetic permeability from porous media images. However, their applications are mainly in soil and gravel, with relatively insufficient research on ultra-high-temperature protective porous materials. Summary of the Invention

[0006] In view of the above problems, the present invention provides a multi-scale prediction method for the permeability of heat-resistant porous materials by fusing multi-source heterogeneous data, which solves the technical problem that the accuracy and efficiency of macroscopic permeability prediction of heat-resistant materials in the prior art are not high enough.

[0007] This invention provides a multi-scale prediction method for the permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion, comprising the following steps:

[0008] Step S1: Obtain multiple sets of sample data based on the collected three-dimensional structure of the heat-resistant porous material, and determine the set of multiple sets of sample data as the heat-resistant porous material dataset; the sample data includes: structural images, structural feature parameters, and permeability;

[0009] Step S2: Establish a penetration rate prediction model. The penetration rate prediction model processes the structural image sequentially through a convolutional module and a dimensionality reduction encoder to obtain dimensionality reduction features; processes the structural feature parameters through a dimensionality increase encoder to obtain dimensionality increase features; processes the dimensionality reduction features and dimensionality increase features through a cross-modal attention mechanism to obtain fused features; and obtains the penetration rate prediction value from the fused features through regression prediction.

[0010] Step S3: Based on the heat-resistant porous material dataset, the permeability prediction model is optimized and trained using a TPE sampler and a median pruner to obtain a trained permeability prediction model.

[0011] Step S4: Input the sample data to be evaluated into the trained penetration rate prediction model to obtain the penetration rate prediction value.

[0012] Preferably, step S1 specifically includes:

[0013] Step S1-1: Obtain the true three-dimensional structure of the heat-resistant porous material using X-ray microtomography; generate an idealized three-dimensional structure based on the traveling cube algorithm, so that the idealized three-dimensional structure is consistent with the shape of the true three-dimensional structure;

[0014] Step S1-2: Obtain the grayscale image of a slice of the idealized three-dimensional structure as the structure image;

[0015] Steps S1-3: Perform Monte Carlo simulation on the idealized three-dimensional structure, obtain the continuous permeability based on the fluid motion parameters obtained from the simulation using Darcy's law, and process the continuous permeability using Klinkenberg's law to obtain the permeability.

[0016] Steps S1-4: The idealized three-dimensional structure is processed using the Ford-Fulkerson algorithm to obtain the maximum flow, and the fractal dimension of the heat-resistant porous material is obtained using the box method; the maximum flow and the fractal dimension are used together as structural feature parameters.

[0017] Step S1-5: Return to step S1-1 until a preset number of sample data are collected, and determine the set of multiple sets of sample data as the heat-resistant porous material dataset.

[0018] Preferably, step S1-1, the step of generating the idealized three-dimensional structure, specifically includes:

[0019] Using a straight cylindrical array to represent the porous fiber structure in a real three-dimensional structure, and using fiber radius, fiber length, porosity and spatial azimuth as control parameters, an ideal three-dimensional structure consistent with the real three-dimensional structure is generated based on the traveling cube algorithm.

[0020] Step S1-2 specifically includes: obtaining the grayscale value matrix of the slice image of the ideal porous structure and performing normalization processing, where 0 represents the pore phase and 1 represents the material phase, which serves as the structure image.

[0021] Preferably, in step S2, the processing steps of the convolution module include:

[0022] The structural image is processed sequentially through nine 3D convolutional modules to obtain structural image features; each 3D convolutional module consists of a 3D convolutional layer, a batch normalization layer, a linear correction unit layer with leakage, and a max pooling layer cascaded in sequence.

[0023] The number of convolution kernels in the 3D convolutional layers of the nine 3D convolutional modules increases sequentially.

[0024] The processing steps of the dimensionality reduction encoder include:

[0025] The structural image features are processed sequentially through an average pooling layer, a flattening layer, a fully connected layer, a layer normalization layer, and a linear correction unit layer with leakage to obtain the dimensionality reduction features.

[0026] The processing steps of the up-dimensional encoder include:

[0027] The structural feature parameters are processed sequentially through two dimensionality-upgrading modules to obtain dimensionality-upgrading features; the dimensionality-upgrading module consists of a fully connected layer, a batch normalization layer and a linear correction unit layer with leakage, which are cascaded in sequence.

[0028] Preferably, in step S2, the specific steps for obtaining the fusion features include:

[0029] (1) Upgrade the dimensionality feature H phy and dimensionality reduction features H img Projecting onto the query, key, and value spaces, we can calculate the query vector, key vector, and value vector.

[0030] (2) Calculate the dot product of the query vector and the key vector, and obtain the attention score after scaling. Use the Sigmoid function to activate the attention score and obtain the attention weight.

[0031] (3) The dimensionality-upgrading features are weighted by attention weights and added to the dimensionality-reducing features through residual connections to obtain the fused feature H. fused .

[0032] Preferably, in step S2, the specific steps for obtaining the penetration rate prediction value from the fused features through regression prediction processing include:

[0033] The fused features are sequentially passed through seven fully connected layers and six linear correction unit layers with leakage to obtain the permeability prediction value;

[0034] The number of input features and the number of output features in the seven fully connected layers decrease sequentially.

[0035] Preferably, step S3 specifically includes:

[0036] Step S3-1: Determine the types of hyperparameters in the hyperparameter space and initialize the number of optimization iterations to zero;

[0037] Step S3-2: Determine if the current number of optimizations is less than N1. If it is less than N1, use a random sampler to sample the hyperparameter space to obtain the hyperparameters. If it is not less than N1, start the TPE sampler to obtain the hyperparameters.

[0038] Step S3-3: Use the sampled hyperparameters as model training parameters, calculate the fusion features using sample data in the heat-resistant porous material dataset, and train the permeability prediction model; after training is completed, increment the current optimization order by 1, perform median pruning, obtain the maximum coefficient of determination, and feed the maximum coefficient of determination back to the TPE sampler;

[0039] Step S3-4: Return to step S3-2 until the number of optimizations is greater than N2, and output the optimal combination of hyperparameters;

[0040] Step S3-5: Train the model using the optimal combination of hyperparameters to obtain a well-trained penetration rate prediction model.

[0041] Preferably, in step S3-3, the step of performing median pruning to obtain the maximum coefficient of determination specifically includes:

[0042] (1) Initialize the generation number epoch = 0;

[0043] (2) Calculate and record the determination coefficient based on the sample data; determine whether the current epoch is greater than n1. If the current epoch is not greater than n1, increment the epoch by 1 and return to step (2).

[0044] If the current epoch is greater than n1, then compare the current coefficient of determination with the median of the coefficients of determination at the current epoch in the historical optimization experiments;

[0045] If the current determination coefficient is greater than the median and the current epoch is less than n2, then increment the epoch by 1 and return to step (2);

[0046] If the current coefficient of determination is not greater than the median, then the maximum value of the coefficient of determination across all generations is determined as the maximum coefficient of determination, and the current training is terminated.

[0047] Preferably, the types of hyperparameters in the hyperparameter space include: the learning rate, momentum, and L2 regularization strength of the SGDM optimizer; the values ​​of N1, N2, n1, and n2 are 30, 250, 20, and 50, respectively.

[0048] Compared with the prior art, the present invention has at least the following beneficial effects:

[0049] (1) This invention provides a method for predicting the permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion and convolutional neural networks. By collecting real three-dimensional structural data of heat-resistant porous materials and generating idealized three-dimensional structures, a complete and rich dataset is established by combining structural images, permeability obtained from numerical simulations, and structural feature parameters such as fractal dimension and maximum flow. On this basis, a multi-level deep convolutional neural network and a cross-modal attention fusion mechanism are used to achieve efficient and accurate cross-scale prediction of permeability from microstructure to macrostructure, avoiding complex and time-consuming microscopic simulations or experimental measurements, and providing technical support for the refined design of thermal protection systems.

[0050] (2) This invention provides a method for constructing structural feature parameters, extracting key parameters reflecting the transport properties of materials from an idealized three-dimensional structure. By using the convolutional features of the structural image and these macroscopic structural parameters as heterogeneous feature inputs to the model, the complex microstructure of the material and its impact on macroscopic permeability can be more comprehensively characterized, enabling the model to capture multi-dimensional information across scales. This invention provides structural feature parameters that calculate and characterize the transport properties of materials starting from their microstructure. The microscopic material structure image and macroscopic structural feature parameters can characterize the macroscopic transport properties of materials from multiple perspectives, improving the accuracy and generalization ability of macroscopic transport property prediction.

[0051] (3) This invention provides a cross-modal attention mechanism fusion strategy that can dynamically learn and mine the deep correlation between structural image convolutional features and structural feature parameters. Through query, key, and value attention weight calculation and residual fusion, the relationship between image convolutional features and structural feature parameter features can be dynamically captured, revealing the influence of the interaction between structural images and structural feature parameters on the macroscopic transport properties of materials. Attached Figure Description

[0052] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0053] Figure 1 The flowchart shows the multi-scale prediction method for the permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion provided by this invention.

[0054] Figure 2 A flowchart illustrating the specific steps of feature fusion using the cross-modal attention mechanism provided by this invention.

[0055] Figure 3 The flowchart of the TPE sampler provided by the present invention is shown.

[0056] Figure 4 The flowchart of the median pruning process provided by this invention.

[0057] Figure 5This is a schematic diagram of the actual reconstructed structure of the carbon fiber material provided by the present invention.

[0058] Figure 6 A schematic diagram of the idealized structure of the carbon fiber material provided by the present invention.

[0059] Figure 7 The grayscale image of a material slice of carbon fiber provided for this invention.

[0060] Figure 8 The scatter plot of maximum flow and permeability of the material provided for this invention.

[0061] Figure 9 The scatter plot of fractal dimension and permeability provided by this invention.

[0062] Figure 10 The diagram shows the relationship between predicted and true values ​​of the optimal model provided by this invention on the training set.

[0063] Figure 11 The diagram shows the relationship between predicted and actual values ​​of the optimal model provided by this invention on the prediction set.

[0064] Figure 12 The optimal model provided by this invention has a 15% error band plot on the prediction set. Detailed Implementation

[0065] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0066] like Figure 1As shown, this invention discloses a multi-scale prediction method for the permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion. First, a high-fidelity idealized microstructure model corresponding to different structural parameters is established. The macroscopic transport characteristics of the internal flow of the microstructure are obtained using a direct Monte Carlo simulation of particle classes, and the structural feature parameters of the microstructure model are calculated. A dataset containing microstructure images of porous materials, structural feature parameters, and transport permeability is constructed. Then, a convolutional module is used to extract material structure image features. A dimensionality reduction encoder is used to reduce the dimensionality of the extracted structure image features, and a dimensionality increase encoder is used to increase the dimensionality of the structural feature parameters. A cross-modal attention mechanism is used to fuse the extracted multi-source heterogeneous data features. Finally, the fused features are input into a multilayer perceptron, and an automatic hyperparameter optimization algorithm is used to optimize the model's hyperparameters to predict the permeability of the heat-resistant porous material. Through the above technical solution, this invention can perform high-accuracy and high-efficiency cross-scale prediction of permeability, as described in detail below.

[0067] Step S1: Obtain multiple sets of sample data based on the collected three-dimensional structure of the heat-resistant porous material, and determine the set of multiple sets of sample data as the heat-resistant porous material dataset; the sample data includes: structural images, structural feature parameters and permeability.

[0068] This invention first establishes a dataset based on the three-dimensional structure of real heat-resistant porous materials for subsequent feature extraction and training. The specific steps for establishing the heat-resistant porous material dataset are as follows:

[0069] (1) Establish high-fidelity idealized microscopic three-dimensional structures and structural images from real materials.

[0070] This invention first obtains the internal structural information of real carbon fiber materials with micron-scale resolution using X-ray microtomography, extracts triangular gray-scale isopleths using gray-scale thresholding, and reconstructs representative units of the real carbon fiber materials using the moving cube algorithm to obtain the real three-dimensional structure of the heat-resistant porous material.

[0071] Then, based on the idealized structure generation algorithm, a randomly generated array of straight cylinders is used to represent the porous fiber structure. Structural feature parameters such as fiber radius, fiber length, porosity, and spatial azimuth are used as control parameters. Based on the traveling cube algorithm, an idealized porous structure described by a triangular unstructured surface mesh is generated as the idealized three-dimensional structure for subsequent permeability calculation.

[0072] Obtaining the grayscale image of the slice of the idealized three-dimensional structure specifically includes: converting the slice image of the idealized porous structure in MATLAB to obtain its grayscale value matrix and performing normalization processing. In the matrix, 0 represents the pore phase and 1 represents the material phase, which can be used as a material structure image input into the prediction model.

[0073] (2) The permeability is obtained by performing Monte Carlo simulation on the idealized three-dimensional structure.

[0074] In this step, the present invention uses the Monte Carlo simulation particle class method to obtain the permeability of the flow inside the microstructure.

[0075] For the permeability of porous materials, when the fluid is considered to be a continuous medium, Darcy's law can be used for calculation as follows:

[0076]

[0077] Where K0 is Darcy permeability (continuous permeability), and μ is the viscosity coefficient of the fluid. It is the pressure gradient in the material, and U is the apparent velocity of the fluid motion.

[0078] When heat-resistant porous materials are used in actual missions in aircraft, the internal flow exhibits a discontinuous slip effect. In this case, the permeability calculation formula expressed by Klinkenberg's law is required:

[0079] K = K0(1 + b / P) (2.2)

[0080] Where K is the permeability and b is an additional parameter. This formula requires the additional parameter b to obtain the permeability K. This parameter represents the effect of slippage on the permeability. To determine b, consider one-dimensional isothermal laminar flow at both ends of the porous material. Combining the above equation with the mass conservation of flow, the ideal gas equation, the geometry of the material, and Darcy's law, we can obtain the following relationship:

[0081]

[0082] Where F is a parameter related to permeability. Here, T is the mass flow rate, L is the length of the material sample along the flow direction, A is the sample cross-sectional area, M is the gas molar mass, and ΔP represents the pressure difference between the upstream and downstream sides of the material sample. av This is the internal average pressure. As you can see, F and P... av The relationship is linear. For the same material structure, F can be obtained by calculating the flow under different pressure conditions, and then K0 and b can be obtained by fitting. Then, the permeability K under the specific pressure can be calculated by Klinkenberg's law, i.e., formula (2.2).

[0083] This invention provides the characteristics of fluid in microstructures, such as effective flow rate, flow volume, and local velocity distribution, through Monte Carlo simulation particle method. Based on these results, the permeability under continuous medium is obtained through Darcy's law, and the actual permeability is obtained by combining flow data under multiple pressure conditions with Klinkenberg's law.

[0084] (3) The maximum flow and fractal dimension are obtained by calculation based on the idealized three-dimensional structure.

[0085] In order to characterize the transport properties of heat-resistant porous materials in a comprehensive way, this invention adopts structural characteristic parameters calculated from the material structure: maximum flow and fractal dimension.

[0086] (3.1) Calculate the maximum flow

[0087] The maximum flow problem is typically defined in a directed graph, which includes source, sink, and intermediate nodes. Each edge has a capacity limit, representing the maximum allowed flow rate. The goal is to find the maximum flow rate from the source to the sink. For thermally insulating porous materials, the voxel blocks corresponding to the pores are treated as nodes in the graph. If there is no corresponding material voxel block in the line connecting two voxel blocks corresponding to two pores, the two nodes are connected, becoming an edge in the graph. Due to the equivalence of gas flow, each edge has the same weight set to 1. Given the direction of external fluid flow and the source and sink points, the 3D voxel blocks of the idealized 3D structure can thus be viewed as a directed graph.

[0088] Specifically, when constructing a directed graph from 3D voxel blocks of materials, the number of nodes in the graph is large, and directly representing the directed graph through the adjacency matrix will consume a lot of memory. Therefore, this invention adopts the method of folding networks, which only retains the nodes and the indices of the adjacent nodes, thereby reducing memory consumption. When calculating the maximum flow of the directed graph, this invention adopts the Ford-Fulkerson algorithm.

[0089] Maximum flow represents the degree of obstruction to flow in each flow path. A large maximum flow indicates that the sample is mainly composed of wide flow paths, and vice versa. Determining the maximum flow is approximately equivalent to determining the porosity of the porous medium involved in fluid transport.

[0090] (3.2) Calculate the fractal dimension

[0091] The pore structure distributed within porous media constitutes a complex nonlinear system. Based on the unique fractal characteristics of porous material microstructures, this study explores the transport properties of porous materials. A key feature of fractal media is their fractal dimension. The fractal dimension of porous materials is closely related to the characteristics of their internal pore structure, revealing the cross-scale non-uniformity of pore distribution and reflecting the space-filling capacity and self-similarity of the pore structure. A larger fractal dimension indicates a more irregular and complex pore distribution, while a smaller fractal dimension indicates a pore structure closer to a simple geometric shape.

[0092] This invention uses the box counting method to calculate the fractal dimension D of porous materials. boxBy using grid-covered images at different scales, the required number of grids for covering pores is statistically analyzed, and the fractal dimension is calculated using scaling relationships. The specific steps are as follows:

[0093] (1) Perform mesh generation, cover the material block with a cube mesh with a side length of ε, and count the number of meshes containing pores N(ε).

[0094] (2) Gradually reduce the size of the grid (ε1>ε2>…>ε) n ), where n is the total number of all grid sizes, and N(ε) is counted repeatedly. i ), N(ε i ) represents the i-th dimension ε i The number of meshes containing pores.

[0095] (3) According to the fractal scaling law N(ε)∝ε -D Where ∝ represents proportionality, and D represents the fractal dimension to be calculated by regression. The slope of the linear regression on lnN(ε) and ln(1 / ε) is the fractal dimension D. box The calculation formula is as follows:

[0096]

[0097] Among them, D box ε is the fractal dimension, N(ε) is the side length of the cube mesh, N(ε) represents the number of meshes including pores, and ln(·) represents the calculation of the natural logarithm.

[0098] Through the above steps, this invention obtains the structural image, structural feature parameters, and permeability corresponding to a single sample of the heat-resistant porous material. To establish a dataset, sample data from multiple samples are repeatedly acquired, and the collection of multiple sets of sample data is determined as the heat-resistant porous material dataset.

[0099] In some embodiments, the thermally insulating porous material dataset can be divided, for example, into a training set, a validation set, and a prediction set, for subsequent training.

[0100] Step S2: Establish a penetration rate prediction model. The penetration rate prediction model processes the structural image sequentially through a convolutional module and a dimensionality reduction encoder to obtain dimensionality reduction features; processes the structural feature parameters through an up-dimensional encoder to obtain up-dimensional features; processes the dimensionality reduction features and up-dimensional features through a cross-modal attention mechanism to obtain fused features; and obtains the penetration rate prediction value by performing regression prediction processing on the fused features.

[0101] The penetration rate prediction model of the present invention includes processing the structural image and structural feature parameters separately, and then performing feature fusion on the results of the two.

[0102] Multi-source data fusion refers to the integration of information from multiple different data sources, absorbing the characteristics of different data to obtain more comprehensive and accurate information. Based on the degree of data fusion, fusion strategies can be divided into three levels: data-level fusion, feature-level fusion, and decision-level fusion. Based on whether the data types are the same, it can be divided into multi-source homogeneous data fusion and multi-source heterogeneous data fusion.

[0103] Specifically, this invention uses data from two different sources—material structure image features and material structure feature parameters—for feature layer fusion. Feature layer-based multi-source data fusion first extracts features from data from different sources, and then fuses these extracted features. The key is determining the methods for feature extraction from different source data and the methods for fusing these features.

[0104] The specific steps for feature extraction and fusion of multi-source heterogeneous data are as follows:

[0105] (1) Constructing a convolutional module to extract structural image features

[0106] This invention extracts structural image features from the microscopic structural images of materials using nine 3D convolutional modules. Each 3D convolutional module consists of a 3D convolutional layer, a batch normalization layer, a linear correction unit layer with leakage (leakage coefficient of 0.1), and a max pooling layer.

[0107] Local features are extracted from the input structural blocks through 3D convolutional layers, internal covariate bias is reduced through batch normalization layers, nonlinear factors are introduced through linear unit layers with leakage correction, and feature maps are downsampled through max pooling layers to reduce data size while retaining important feature information.

[0108] The specific values ​​of the nine 3D convolutional modules are shown in Table 1.

[0109] Table 1

[0110]

[0111] (2) Dimensionality reduction of extracted structural image features

[0112] The dimension of the structural image features extracted by the convolution module is significantly reduced compared to the original structural image dimension, but the dimension is still relatively large, so dimensionality reduction is required for the structural image features extracted by the convolution module.

[0113] The dimensionality reduction encoder consists of an average pooling layer, a flattening layer, a fully connected layer, a layer normalization layer, and a linear correction unit layer with leakage (leakage coefficient of 0.1). The average pooling layer compresses the feature map in spatial dimension, the flattening layer converts the feature data into vectors, the fully connected layer and the normalization layer reduce the dimensionality of the aforementioned vectors, and the linear correction unit layer with leakage introduces nonlinear factors.

[0114] The structural image features are processed by a dimensionality reduction encoder to obtain the final dimensionality reduction features.

[0115] (3) Dimensional increase of structural feature parameters

[0116] Since the structural feature parameters have a small dimension, in order to prevent them from being marginalized during fusion due to their small dimension, thus losing the original purpose of feature fusion to some extent, a dimension-up encoder is used to increase the dimension of the structural feature parameters.

[0117] The dimension-up encoder consists of two dimension-up modules, each comprising a fully connected layer, a batch normalization layer, and a linear correction unit layer with leakage (leakage coefficient of 0.1). The fully connected layer and the normalization layer increase the dimension of the feature vector, while the linear correction unit layer with leakage introduces a nonlinear factor.

[0118] The structural feature parameters are processed by the up-dimensional encoder to obtain the up-dimensional features.

[0119] (4) Use cross-modal attention mechanism for feature fusion

[0120] For the dimensionality-reduced features H extracted by the convolutional module and the dimensionality-reducing encoder img Compared with the up-dimensional features H obtained by the up-dimensional encoder phy The fused feature H is obtained by using a cross-modal attention mechanism to perform feature fusion. fused Its core idea is to dynamically capture the relationship between different features, thereby achieving more scientific information complementarity and making full use of different features and the relationship between features. Figure 2 This is a flowchart of feature fusion using a cross-modal attention mechanism.

[0121] The specific steps for feature fusion using cross-modal attention mechanisms are as follows:

[0122] (4-1) H phy H img Projecting onto the Query, Key, and Value spaces, the expression is:

[0123] Q = H img W Q K = H phy W K V = Hphy W V (2.5)

[0124] Where Q, K, and V represent the query vector, key vector, and value vector, respectively, and W... Q W K W V These are the learnable parameters for the query vector, key vector, and value vector, respectively.

[0125] (4-2) Calculate the dot product of Q and K, scale it to obtain the attention score, activate the attention score using the Sigmoid function, and obtain the attention weight, expressed as:

[0126]

[0127] α=σ(AttentionScores) (2.7)

[0128] Where Attention Scores represent attention scores, K T d is the transpose of K. k Let σ be the dimension of the key vector, σ(·) be the Sigmoid function, and α be the attention weight.

[0129] (4-3) The obtained attention weights are used to weight the structural features, and then added to the image features through residual connections to obtain the final fused feature vector, expressed as:

[0130] V weighted =α·V (2.8)

[0131] H fused =H img +V weighted (2.9)

[0132] Among them, V weighted This is the weighted value vector.

[0133] (5) The penetration rate prediction value is obtained by regression prediction processing based on the fusion features.

[0134] Based on the features fused using a cross-modal attention mechanism, a regression module is used to predict the permeability of the heat-resistant porous material. The regression module consists of seven fully connected layers and six linear correction unit layers with leakage (leakage coefficient of 0.1).

[0135] Seven linear layers are connected sequentially, progressively mapping high-dimensional input features to low-dimensional outputs, continuously extracting and transforming features to fit the target value. By adding a leaky linear correction unit layer after each linear layer, the network can learn more complex nonlinear functions, enhancing the model's expressive power. The specific structural parameters of the regression module are shown in Table 2.

[0136] Table 2

[0137]

[0138] The fused features are processed by the regression module to obtain the penetration rate prediction value.

[0139] Step S3: Based on the heat-resistant porous material dataset, the permeability prediction model is optimized and trained using a TPE sampler and a median pruner to obtain a trained permeability prediction model.

[0140] This invention uses TPE sampling to obtain hyperparameters and performs pruning based on the median of historical optimization targets to complete the hyperparameter optimization and training of the penetration rate prediction model.

[0141] For the training process, this invention uses a stochastic gradient descent with momentum (SGDM) optimizer based on the constructed model structure. To suppress overfitting, this invention introduces an L2 regularization term during model training. Among these, the hyperparameters learning rate, momentum in the optimizer, and the strength of L2 regularization have a significant impact on model performance. The learning rate controls the step size of the model parameter updates; an excessively large step size can cause the loss function to oscillate around the optimum or even diverge, while an excessively small step size can lead to slow convergence. L2 regularization suppresses model complexity by adding a squared penalty term to the weight parameters in the loss function. A stronger regularization strength results in stronger weight decay, reducing the risk of overfitting; a weak regularization strength may lead to overfitting. The momentum in stochastic gradient descent accelerates convergence by accumulating historical gradient directions. The "inertia" of momentum accumulation may help the model escape local minima, but excessive momentum may cause it to miss the optimal point.

[0142] To obtain suitable hyperparameters, this invention employs a hyperparameter optimization algorithm that combines a TPE (Tree-structured Parzen Estimator) sampler with a median pruner.

[0143] Figure 3 This is a flowchart of the TPE sampler, where N1 represents the sampling performed using a random sampler in N1 attempts to provide basic data reference for the TPE sampler, and N2 represents the total number of attempts performed in one hyperparameter optimization process. Figure 4 This is a flowchart using the median pruning tool, where n1 represents the first n1 epochs in a single trial without pruning, n2 represents the total number of epochs in a single trial, and median(R) 2(epoch) represents the objective function R of the historical attempts at the current epoch. 2 The median. The objective function is the coefficient of determination. The processing procedures of the TPE sampler and the median pruner are described in detail below.

[0144] (1) TPE sampler

[0145] TPE is a Bayesian optimization-based algorithm. Its core idea is to model historical observations to guide subsequent sampling directions, thereby maximizing the probability of finding the optimal solution. The algorithm consists of three main steps: first, the existing observations are divided into good and bad samples according to the objective function value; second, the probability density of the good and bad samples is modeled separately using kernel density estimation; and finally, the next sampling point is selected by maximizing the expected value, and then the good and bad samples are re-divided according to the objective function value.

[0146] Specifically, the goal is to find the hyperparameter x through continuous iteration and optimization. * To maximize the objective function f(x). Assume we have existing observation data D = {(x...} 1 y 1 ), ..., (x n′ y n′ )}, where x 1 y 1 Let n' and n' represent the first hyperparameter vector and the first objective function value, respectively. Let n' represent the total number of observed hyperparameter vectors, and D be the set of observed data.

[0147] First, set a quantile threshold γ to divide the data into two groups, with good sample D. l The difference sample D corresponds to the observation data of the first γ×n′ largest objective function values. g For the remaining observation data, y * It is the current optimal objective function value.

[0148] Then, a probability density model is constructed for the good and bad samples using a kernel function, where l(x) corresponds to the density estimation function for the good samples, g(x) corresponds to the density estimation function for the bad samples, and K(·,·) is the kernel function, usually a Gaussian kernel function. Then:

[0149]

[0150] Where |·| represents the calculation of the magnitude of the vector, x i Let represent the i-th hyperparameter vector.

[0151] The goal of TPE is to maximize the expected improvement function EI(x), that is, when the hyperparameter vector takes the value x, the objective function value y exceeds the preset objective function value y. * Therefore:

[0152]

[0153] Where EI(x) is the expected boost function for hyperparameter vector x, E[·] represents the mathematical expectation, f(x) represents the objective function value when the hyperparameter vector takes the value x, and p(y|x) represents the conditional probability of the objective function value when the hyperparameter vector x is x.

[0154] From Bayes' theorem and the definitions of l(x) and g(x), we can obtain:

[0155]

[0156] Here, ∝ indicates a direct proportion. Maximizing EI(x) is equivalent to sampling in a region with high density of good samples and low density of bad samples. In implementation, a set of candidate points is generated based on l(x), and then selected. The largest candidate point is evaluated, and then D is redefined. l With D g Perform iterations.

[0157] In some embodiments, the hyperparameters of the present invention may include: the learning rate and momentum of the SGDM optimizer, and the L2 regularization strength, etc.

[0158] The TPE sampling process is as follows:

[0159] If the number of optimizations performed is less than N1, a random sampler is used to sample the hyperparameter space to obtain the hyperparameters; if the number of optimizations performed is not less than N1, the TPE sampler is started to obtain the hyperparameters.

[0160] The sampled hyperparameter combinations are used as model training parameters to calculate fusion features and train the penetration rate prediction model. Each sampling corresponds to one training and validation.

[0161] After training, median pruning is performed on the validation set to obtain the maximum R. 2 The results are returned to the TPE sampler until the upper limit of the number of optimizations N2 is reached, at which point the optimal combination of hyperparameters is output for training the final penetration rate prediction model.

[0162] (2) Median pruning tool

[0163] The core idea of ​​median pruning in this invention is to determine whether to terminate an unsuccessful experiment early by comparing the intermediate result of the current experiment with the median of historical experiments at the same stage. The main steps are: first, conduct the first N experiments without pruning to ensure sufficient data for median calculation in the initial stage; then, in subsequent experiments, compare the intermediate result of the current experiment with the historical median, and determine whether to perform pruning based on the results.

[0164] The process for calculating median pruning on the validation set is as follows:

[0165] Initialize the number of generations (epoch) to 0; for the current number of training generations (epoch), if it is the first n1 epochs, no pruning is performed, and the data is accumulated for subsequent pruning decisions.

[0166] When the epoch is greater than n1, compare R on the current validation set. 2 Compared with historical trials in the current epoch R 2 median.

[0167] If the current R 2 If the current test is lower than the historical median and has not yet reached the maximum epoch (n2), then the current test is terminated early; otherwise, training continues.

[0168] The maximum R is retained for each epoch. 2 The score, when training ends, outputs the maximum R. 2 Fraction.

[0169] To avoid getting trapped in local optima, this invention selects the top 10% of experiments with the largest objective function and takes the average of their hyperparameters as the parameters of the final model.

[0170] Using the final hyperparameters obtained to train the model, it is possible to achieve highly accurate and efficient cross-scale prediction of the macroscopic permeability of thermal protection materials.

[0171] Step S4: Input the sample data to be evaluated into the trained penetration rate prediction model to obtain the penetration rate prediction value.

[0172] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution is provided through a specific embodiment. The specific implementation steps are as follows:

[0173] Example 1

[0174] The following uses a three-dimensional carbon fiber needled preform used in carbon fiber reinforced ablation heat protection materials as an example to illustrate the specific steps for predicting its permeability.

[0175] (1) Create a dataset

[0176] Taking a three-dimensional carbon fiber needled preform used in carbon fiber reinforced ablation heat protection materials as the research object, we first obtained the internal structural information of the real carbon fiber material at the micron scale using X-ray microtomography. Then, we extracted triangular gray-level isopleths using gray-level thresholding, and reconstructed representative units of the real carbon fiber material using a moving cube algorithm to obtain its three-dimensional structural model. Figure 5 As shown.

[0177] Then, based on an idealized structure generation algorithm, a randomly generated array of straight cylindrical bodies represents the porous fiber structure. Structural characteristic parameters such as fiber radius, fiber length, porosity, and spatial azimuth are used as control parameters. An idealized porous structure described by a triangular unstructured surface mesh is generated based on a traveling cube algorithm, such as... Figure 6 As shown, this serves as a representative unit for permeability calculation.

[0178] In MATLAB, the image is transformed to obtain its grayscale matrix and then normalized. In the matrix, 0 represents the porous phase and 1 represents the material phase, which can be used as a material structure image to be input into the prediction model. Figure 7 This is the exported grayscale image.

[0179] This example generates 312 structural samples, which are divided into training, validation, and prediction sets in an 8:1:1 ratio. The idealized structure has a representative unit size of 100*100*100μm. 3 The specific structural parameter values ​​are shown in Table 3.

[0180] Table 3

[0181]

[0182] For each material structure sample, the macroscopic permeability of the flow within the microstructure was obtained using a direct Monte Carlo simulation of particle classes. The maximum flow and fractal dimension of the material structure were then calculated using the Ford-Fulkerson algorithm and the box-counting method, respectively, resulting in a dataset containing the material's microstructure, structural characteristic parameters, and permeability. Scatter plots of the calculated maximum flow and permeability, fractal dimension and permeability are shown below. Figure 8 and Figure 9 As shown.

[0183] (2) Model building and hyperparameter optimization

[0184] The convolutional module is used to extract features from the structural image data. The extracted convolutional features are then reduced in dimensionality using a dimensionality reduction encoder. The structural feature parameters are then increased in dimensionality using a dimensionality increase encoder. Finally, a cross-modal attention mechanism is used to complete feature-level data fusion.

[0185] Based on the different structural feature parameters added, three prediction models were established in this example. Specifically, Model 1 is a multi-source data fusion of fractal dimension and structural image, Model 2 is a multi-source data fusion of maximum flow and structural image, and Model 3 is a multi-source data fusion of fractal dimension, maximum flow, and structural image.

[0186] The fused features are input into the regression module, and a hyperparameter optimization algorithm is used to optimize the hyperparameters to obtain the final model hyperparameters. Specifically, the optimization objective is to improve the model's R-value on the validation set. 2 The range of hyperparameter values ​​to be optimized is shown in Table 4. The parameter settings of the TPE sampler and median pruner are shown in Table 5. During training, the Batch_size is set to 32 and the Epoch is set to 150.

[0187] Table 4

[0188]

[0189] Table 5

[0190]

[0191] (3) Analysis of prediction results of different structural characteristic parameters

[0192] To evaluate the model performance, this paper mainly selects R... 2 The three indicators are (coefficient of determination), RMSE (root mean square error), and MAPE (mean absolute percentage error). Among them, R... 2 To evaluate the goodness of fit of the model, RMSE reflects the degree of deviation between the predicted and actual values, while MAPE reflects the relative error of the model's predictions. 2 The closer the values ​​are to 1, the closer the RMSE and MAPE are to 0, and the better the model's performance.

[0193] For models 1 to 3, hyperparameter optimization was performed based on the set range of hyperparameter values ​​and the relevant parameters in the hyperparameter optimization algorithm to obtain the final parameters. The final parameters were used to train the model, and the evaluation index of the final model on the training set and prediction set were calculated respectively. The results are shown in Tables 6 and 7.

[0194] Table 6

[0195]

[0196] Table 7

[0197]

[0198]

[0199] From the perspective of model fitting performance: Model 1 > Model 2 > Model 3. From the perspective of model error on the prediction set: Model 3 > Model 2 > Model 1. This indicates that the model obtained by fusing fractal dimension and structural image through multi-source heterogeneous data fusion has the best performance.

[0200] Specifically Figure 10 , Figure 11 and Figure 12The diagram shows the relationship between the predicted and actual values ​​of the optimal model (Model 1) on the prediction set and the training set, along with the error distribution histogram and a 15% error band plot on the prediction set. Analysis of its prediction bias on the prediction set shows that 60% of the prediction set samples have a bias within 5%, 87% have a bias within 10%, and the overall bias is within 16%, indicating relatively stable prediction results.

[0201] To illustrate the prediction accuracy and advantages of this method, other models were established in this example: Model 4 is a support vector machine regression model based on structural feature parameters, Model 5 is a convolutional neural network model based on material structure images, Model 6 is a decision-level fusion model based on least squares, Model 7 is a model based on the direct concatenation of fractal dimension and structural image features, and Model 8 is a model based on the direct concatenation of maximum flow and structural image features.

[0202] Specifically, Model 6 uses the least squares method for linear fitting based on the prediction results of Models 4 and 5 to obtain the final prediction result. Models 7 and 8 directly concatenate the convolutional features and structural feature parameters extracted by the convolution module and input them into the regression module for prediction. Hyperparameter optimization algorithms were used to optimize Models 4 to 8, and the evaluation metrics of the final models on the training and prediction sets were calculated respectively. The results are shown in Tables 8 and 9.

[0203] Table 8

[0204]

[0205] Table 9

[0206]

[0207]

[0208] Comparing the performance of models 1, 4 through 8 on the prediction set, from the perspective of fit: Model 1 > Model 8 > Model 7 > Model 6 > Model 5 > Model 4; from the perspective of error: Model 4 > Model 6 > Model 5 > Model 7 > Model 8 > Model 1. Therefore, Model 1 has the best fit and accuracy. From the perspective of overfitting, Model 5 and Model 6 perform best on the training set, with R0... 2 The result is close to 1, but it is not as good as Model 1 on the prediction set, indicating that Model 5 and Model 6 have a serious overfitting problem. The method of this invention can suppress the overfitting phenomenon to a certain extent.

[0209] In summary, in this example, R on the prediction set... 2The value is 0.95, and the MAPE is 5.29%. The method of this invention can efficiently and accurately predict the macroscopic permeability of thermal protection materials based on the material's microstructure.

[0210] While the specific embodiments of the present invention depict actions or steps in a particular order, this should be understood as requiring such actions or steps to be performed in the shown specific order or sequential order, or requiring all illustrated actions or steps to be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, although several specific implementation details are included in the above discussion, these should not be construed as limiting the scope of this disclosure. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations. The above descriptions are merely preferred embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention.

[0211] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-scale prediction method for the permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion, characterized in that, Includes the following steps: Step S1: Obtain multiple sets of sample data based on the collected three-dimensional structure of the heat-resistant porous material, and determine the set of multiple sets of sample data as the heat-resistant porous material dataset; the sample data includes: structural images, structural feature parameters, and permeability; Step S2: Establish a penetration rate prediction model. The penetration rate prediction model processes the structural image sequentially through a convolutional module and a dimensionality reduction encoder to obtain dimensionality reduction features; processes the structural feature parameters through a dimensionality increase encoder to obtain dimensionality increase features; processes the dimensionality reduction features and dimensionality increase features through a cross-modal attention mechanism to obtain fused features; and obtains the penetration rate prediction value from the fused features through regression prediction. Step S3: Based on the heat-resistant porous material dataset, the permeability prediction model is optimized and trained using a TPE sampler and a median pruner to obtain a trained permeability prediction model. Step S4: Input the sample data to be evaluated into the trained penetration rate prediction model to obtain the penetration rate prediction value.

2. The method for multi-scale prediction of permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion according to claim 1, characterized in that, Step S1 specifically includes: Step S1-1: Obtain the true three-dimensional structure of the heat-resistant porous material using X-ray microtomography; generate an idealized three-dimensional structure based on the traveling cube algorithm, so that the idealized three-dimensional structure is consistent with the shape of the true three-dimensional structure; Step S1-2: Obtain the grayscale image of a slice of the idealized three-dimensional structure as the structure image; Steps S1-3: Perform Monte Carlo simulation on the idealized three-dimensional structure, obtain the continuous permeability based on the fluid motion parameters obtained from the simulation using Darcy's law, and process the continuous permeability using Klinkenberg's law to obtain the permeability. Steps S1-4: The idealized three-dimensional structure is processed using the Ford-Fulkerson algorithm to obtain the maximum flow, and the fractal dimension of the heat-resistant porous material is obtained using the box method; the maximum flow and the fractal dimension are used together as structural feature parameters. Step S1-5: Return to step S1-1 until a preset number of sample data are collected, and determine the set of multiple sets of sample data as the heat-resistant porous material dataset.

3. The method for multi-scale prediction of permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion according to claim 2, characterized in that, In step S1-1, the steps for generating the idealized three-dimensional structure specifically include: Using a straight cylindrical array to represent the porous fiber structure in a real three-dimensional structure, and using fiber radius, fiber length, porosity and spatial azimuth as control parameters, an ideal three-dimensional structure consistent with the real three-dimensional structure is generated based on the traveling cube algorithm. Step S1-2 specifically includes: obtaining the grayscale value matrix of the slice image of the ideal porous structure and performing normalization processing, where 0 represents the pore phase and 1 represents the material phase, which serves as the structure image.

4. The method for multi-scale prediction of permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion according to claim 3, characterized in that, In step S2, the processing steps of the convolution module include: The structural image is processed sequentially through nine 3D convolutional modules to obtain structural image features; each 3D convolutional module consists of a 3D convolutional layer, a batch normalization layer, a linear correction unit layer with leakage, and a max pooling layer cascaded in sequence. The number of convolution kernels in the 3D convolutional layers of the nine 3D convolutional modules increases sequentially. The processing steps of the dimensionality reduction encoder include: The structural image features are processed sequentially through an average pooling layer, a flattening layer, a fully connected layer, a layer normalization layer, and a linear correction unit layer with leakage to obtain the dimensionality reduction features. The processing steps of the up-dimensional encoder include: The structural feature parameters are processed sequentially through two dimensionality-upgrading modules to obtain dimensionality-upgrading features; the dimensionality-upgrading module consists of a fully connected layer, a batch normalization layer and a linear correction unit layer with leakage, which are cascaded in sequence.

5. The method for multi-scale prediction of permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion according to claim 4, characterized in that, In step S2, the specific steps for obtaining the fusion features include: (1) Upgrade the dimensionality feature H phy and dimensionality reduction features H img Projecting onto the query, key, and value spaces, we can calculate the query vector, key vector, and value vector. (2) Calculate the dot product of the query vector and the key vector, and obtain the attention score after scaling. Use the Sigmoid function to activate the attention score and obtain the attention weight. (3) The dimensionality-upgrading features are weighted by attention weights and added to the dimensionality-reducing features through residual connections to obtain the fused feature H. fused .

6. The method for multi-scale prediction of permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion according to claim 5, characterized in that, In step S2, the specific steps for obtaining the penetration rate prediction value from the fused features through regression prediction processing include: The fused features are sequentially passed through seven fully connected layers and six linear correction unit layers with leakage to obtain the permeability prediction value; The number of input features and the number of output features in the seven fully connected layers decrease sequentially.

7. The method for multi-scale prediction of permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion according to claim 6, characterized in that, Step S3 specifically includes: Step S3-1: Determine the types of hyperparameters in the hyperparameter space and initialize the number of optimization iterations to zero; Step S3-2: Determine if the current number of optimizations is less than N1. If it is less than N1, use a random sampler to sample the hyperparameter space to obtain the hyperparameters. If it is not less than N1, start the TPE sampler to obtain the hyperparameters. Step S3-3: Use the sampled hyperparameters as model training parameters, calculate the fusion features using sample data in the heat-resistant porous material dataset, and train the permeability prediction model; after training is completed, increment the current optimization order by 1, perform median pruning, obtain the maximum coefficient of determination, and feed the maximum coefficient of determination back to the TPE sampler; Step S3-4: Return to step S3-2 until the number of optimizations is greater than N2, and output the optimal combination of hyperparameters; Step S3-5: Train the model using the optimal combination of hyperparameters to obtain a well-trained penetration rate prediction model.

8. The method for multi-scale prediction of permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion according to claim 7, characterized in that, In step S3-3, the step of performing median pruning to obtain the maximum coefficient of determination specifically includes: (1) Initialize the generation number epoch = 0; (2) Calculate and record the determination coefficient based on the sample data; determine whether the current epoch is greater than n1. If the current epoch is not greater than n1, increment the epoch by 1 and return to step (2). If the current epoch is greater than n1, then compare the current coefficient of determination with the median of the coefficients of determination at the current epoch in the historical optimization experiments; If the current determination coefficient is greater than the median and the current epoch is less than n2, then increment the epoch by 1 and return to step (2); If the current coefficient of determination is not greater than the median, then the maximum value of the coefficient of determination across all generations is determined as the maximum coefficient of determination, and the current training is terminated.

9. The method for multi-scale prediction of permeability of heat-resistant porous materials based on multi-source heterogeneous data fusion according to claim 8, characterized in that: The types of hyperparameters in the hyperparameter space include: the learning rate, momentum, and L2 regularization strength of the SGDM optimizer; the values ​​of N1, N2, n1, and n2 are 30, 250, 20, and 50, respectively.

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