Method for constructing double-connected three-dimensional microstructure data set with same boundary

Abstract

The invention belongs to the field of material science, and discloses a method for constructing a double-connected three-dimensional microstructure data set with the same boundary, which comprises the following steps of: firstly, determining a boundary type and reconstructing a microstructure by taking the boundary type as a constraint of six surfaces of a cube; then, a related optimization target is selected for each boundary type, and an initial data set is created under corresponding constraint conditions; thirdly, carrying out structure generation by adopting a generative AI to expand an attribute space of the microstructure, and carrying out iterative expansion on a data set by adopting an active learning strategy; and finally, identifying and retaining a structure with a dual-connectivity feature through a connected component marking algorithm, and removing a non-connectivity structure, so as to construct a data set with the same boundary and dual connectivity, and through the LBBM data set constructed by the method, the calculation efficiency of multi-scale assembly is remarkably improved, and the accuracy of the multi-scale assembly is improved. The boundary connectivity between the microstructures and the double connectivity of the whole multi-scale structure are ensured, the material constructed based on the data set has printing and manufacturing friendliness, and the functions of fluid flowing, heat conduction, filtering, gas exchange and the like can be achieved.

Description

Technical Field

[0001] The present invention belongs to the field of material science, and more specifically relates to a three-dimensional microstructure data set with the same boundary and dual connectivity for engineering applications. Background Art

[0002] Natural materials such as cancellous bone, wood, butterfly wings and sponges show highly interconnected pore networks with hierarchical and dual-connected structural characteristics. In this type of dual-connected microstructure, both solid and void phases are continuously distributed, so it has important application value in aerospace, automobile manufacturing, biomedicine and mechanical engineering, especially in complex applications that require high stiffness, large surface area, good air permeability and adjustable permeability. It shows excellent performance. Imitating structures in nature such as starfish and sea urchin spines, the development of functional engineering materials often requires a lot of experiments and repeated adjustments, which is not only costly, but also difficult to achieve structural diversity. Therefore, topology optimization, as a reverse design tool, has become a key means to study and develop such materials with its ability to efficiently explore the design space.

[0003] By combining spinodal structures with topology optimization, biconnected structures with restricted parameter ranges can be generated. However, the related multiscale structural optimization brings huge computational challenges. Triperiodic minimal surfaces (TPMS) structures are widely used in the multiscale design of bone implants, heat exchangers, and energy absorbers due to their excellent mechanical properties. Although TPMS structures have great application potential, insufficient boundary connectivity may also lead to structural failure. Commonly used techniques for enhancing connectivity include optimization, interpolation, and deformation, but these methods also increase the corresponding computational cost. The difficulties in biconnected multiscale design can be decomposed into the following three key issues: (1) a dataset with as wide a range of properties as possible is required; (2) the boundaries of each microstructure are the same; and (3) all microstructures are biconnected. Summary of the invention

[0004] The object of the present invention is to provide a method for constructing a biconnected three-dimensional microstructure data set with the same boundary, so as to solve the problems raised in the above background technology.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for constructing a biconnected three-dimensional microstructure dataset with the same boundary comprises the following steps:

[0007] Step S1: Determine four boundary types through test analysis, and reconstruct the microstructure using the four boundary types as constraints on the six faces of the cube;

[0008] Step S2: for each boundary type, using the LIVE3D framework, using the maximum bulk modulus, the maximum shear modulus, the maximum Young's modulus and the five-mode structure as optimization objectives, and creating an initial data set according to the corresponding constraints;

[0009] Step S3: Generative AI is used for structure generation to expand the attribute space of the microstructure. The generative model adopts a diffusion model, the network structure uses Unet, and the loss function is MSE loss. On this basis, the initial data set in S2 is used to train the Unet network, and an active learning strategy is used to iteratively expand the data set.

[0010] Step S4: Identify and retain structures with biconnectivity characteristics through a connected component labeling algorithm, remove disconnected structures, and construct a data set with the same boundary and biconnectivity under the boundary type described in step S1.

[0011] As a further solution of the present invention: in the objective function of the optimization target in step S2, ρ is the density of the structure, C(ρ) is the flexibility when the structure density is ρ, and the objective function of the optimization target is as follows:

[0012] The objective function for maximizing the bulk modulus is: C 1111 With C 1122 are the two components in the elastic tensor matrix C;

[0013] The objective function for maximizing the shear modulus is: f(C(ρ)) = C 1212 , where C 1212 is a component of the elastic tensor matrix C;

[0014] The purpose function to maximize Young's modulus is:

[0015] The objective function of the five-module structure is: The bulk modulus K is given by the formula Definition: Shear modulus G is given by the formula G = C 1212 Definition: K0 and G0 are the initial values ​​of bulk modulus and shear modulus obtained by random initial calculation, respectively.

[0016] As a further solution of the present invention: the constraint condition in step S2 specifically refers to:

[0017] Equilibrium equation constraint: K(ρ)u=f, where K(ρ) is the stiffness matrix, u is the displacement vector, and f is the applied external force;

[0018] Volume fraction constraint: Where M is the total number of discrete elements of the material, v e and ρ eare the volume fraction and density of the material at the eth position, respectively, and |Ω| represents the volume of the microstructure design domain. This constraint ensures that the total volume of the material does not exceed V during the optimization process;

[0019] Boundary condition constraints: During the optimization process, ensure that the boundary b1 is as close to the boundary b2 as possible, and ε is the allowable convergence error;

[0020] Isotropic constraint:

[0021] Poisson's ratio constraint: Where v0 is the specified initial Poisson's ratio;

[0022] Density variable constraints: M is the total number of discrete units of the material, that is, among the total discrete units, any unit ρ e The material density is between [0,1].

[0023] As a further solution of the present invention: the diffusion model in step S3 includes a forward denoising process and a reverse denoising process, and the forward denoising process is performed by equation Step by step to x t Add noise to the real data x0, where ε t-1 Sampling from a standard Gaussian distribution with parameter α t To control the noise level, the reverse denoising process is to obtain the data x close to pure noise. t First, use a neural network to predict the noise and indirectly recover x t-1 , until the real data x0 is restored.

[0024] As a further solution of the present invention: the loss function of the diffusion model in step S3 is trained according to the following relationship: It is used to guide the neural network to learn to denoise the noisy data. In the relationship, t represents the time step in the diffusion process, t~[1,T] represents the time step t is uniformly sampled from the time interval [1,T], x0 represents a real data in the training data, q(x0) represents the probability distribution of the real data, x0~q(x0) represents randomly sampling a data point x0 from q(x0), that is, selecting a sample from the training data as the input of the diffusion model, ε~N(0,I) represents the noise sampled from the standard normal distribution, with a mean of 0, and the covariance matrix is ​​the unit matrix I, x t is the noisy data of the diffusion process at time t. The noisy data is generated by adding noise to the real data x0. θ (x t ,t) represents the predicted value of the neural network model with parameter θ.

[0025] As a further solution of the present invention: in the network training in step S3, voxels are used to represent all microstructures, that is, each structure is represented as a three-dimensional binary matrix of n×n×n. Since the structure has cubic symmetry, only the upper left corner 1 / 8 of the structure needs to be considered as input during training. At the same time, due to the symmetry, symmetrical noise is also used in the forward and reverse diffusion processes.

[0026] As a further solution of the present invention: the step S3 adopts a self-condition strategy to improve the generation quality, that is, the content previously generated by the network is used as the condition for the next generation.

[0027] As a further solution of the present invention: in terms of the network structure in step S3, the U-Net encoder and decoder both include 5 stages, and each stage is composed of a Resblock with an attention mechanism.

[0028] As a further solution of the present invention: in order to meet the demand of constructing a large-scale microstructure data set, step S3 adopts an active learning strategy for iterative training.

[0029] As a further solution of the present invention: the connection component marking algorithm in step S4 specifically includes:

[0030] First scan: For each pixel point p at the coordinate (i, j), output the image label L(i, j). The calculation process is as follows:

[0031]

[0032] Where N(p) represents the neighboring pixels of p. If there are multiple labels in N(p), select the smallest label and record these labels as equivalent relations;

[0033] Second scan: traverse each pixel point p in the image again, update the label to ensure that all equivalent labels are unified into one label: L(i,j)=find(L(i,j)), where the find function finds the minimum label equivalent to L(i,j) to achieve label unification.

[0034] Compared with the prior art, the beneficial effects of the present invention are: multi-scale structure design is carried out using a constructed three-dimensional microstructure dataset with the same boundary and dual connectivity, the elastic modulus of each unit is determined by optimizing the macrostructure, and then the corresponding microstructure is selected from the dataset. Since the dataset constructed by the present invention has a unified boundary and guarantees dual connectivity, the natural connectivity between the microstructures in the multi-scale assembly process is ensured. The LBBM dataset constructed by the present invention significantly improves the computational efficiency of the multi-scale assembly, ensures the boundary connectivity between the microstructures and the dual connectivity of the overall multi-scale structure, and the materials constructed based on the dataset are printing-friendly and can realize functions such as fluid flow, heat conduction, filtration and gas exchange. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Schematic diagram of four boundary condition structures obtained by testing and analysis of the present invention;

[0036] Figure 2 Attribute relationship diagram of the optimized data set under four boundary conditions of the present invention;

[0037] Figure 3 This is a schematic diagram of the active learning network framework in the present invention;

[0038] Figure 4 Attribute relationship diagram of a large-scale, boundary-consistent and bicontinuous microstructure (LBBM) data set under the four boundary conditions of the present invention. DETAILED DESCRIPTION

[0039] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] The method for constructing a doubly connected three-dimensional microstructure data set with the same boundary in the embodiment of the present invention, for the mechanical properties of the material, in the homogenization process, the complex microstructure is simplified to an equivalent uniform material, making the macroscopic analysis more direct. The method in the embodiment of the present invention uses a representative volume element (RVE) of the microstructure to capture microscale changes to predict the overall mechanical behavior. All RVEs considered in this method exhibit cubic symmetry, which means that these microstructures remain unchanged under the symmetry operation of the cubic crystal system. This symmetry indicates that the material has the same physical properties on three mutually perpendicular axes. For a cubically symmetric material, the elastic tensor matrix C is expressed as follows:

[0041]

[0042] Among them C 1111 ,C 1122 ,C 1212 is the elastic constant of the material.

[0043] The bulk modulus K and shear modulus G of a cubically symmetric material can be obtained from the elastic constant C 1111 ,C 1122 ,C 1212 The calculation formula is as follows:

[0044] The calculation formulas for Young's modulus E and Poisson's ratio v are as follows:

[0045]

[0046] The parameter Zener ratio A that describes the anisotropy of the material is calculated as follows:

[0047]

[0048] A Zener ratio A closer to 1 indicates greater isotropy, and a deviation from 1 indicates greater anisotropy.

[0049] The method for constructing a biconnected three-dimensional microstructure data set with the same boundary in the embodiment of the present invention, the four boundary conditions in the method are as follows: Figure 1 As shown in the figure, four data sets are constructed with these four boundary conditions as constraints. Taking the first boundary mask1 as an example, the specific steps of constructing a data set with mask1 as the boundary are as follows:

[0050] In order to design a biconnected microstructure with a wide range of properties and with mask1 as the boundary, 10 optimization models are designed in the embodiment of the present invention, including 5 isotropic models and 5 anisotropic models. The relevant parameters in the 10 optimization models are explained as follows: ρ represents the design variable vector, that is, the density of the material; f(C(ρ)) is the objective function, which is the negative value of the minimized bulk modulus here; u is the displacement field in the microstructure design domain; f is the applied external force; K(ρ) is the global stiffness matrix; overall, K(ρ)u=f represents the equilibrium equation constraint; M is the number of discrete elements in the design domain; ρ e is the density of the e-th unit of the material; v e is the volume of the e-th unit, and represents the volume of the material; |Ω| represents the volume of the microstructure design domain; V represents the specified volume fraction; here the volume fraction constraint is that the ratio of the total volume of the material to the volume of the design domain does not exceed V; b1 is the boundary of the material, b2 is the specified boundary, ε is the allowable convergence error, and the boundary constraint condition Ensure that the material boundary b1 is as close as possible to the specified boundary b2; (A-1) 2 <ε is an isotropic constraint, which requires the Zener ratio A to be as close to 1 as possible within the allowable error range; is the density variable constraint, 0 means the material is empty, and 1 means the material is real.

[0051] (I) Five isotropic optimization models

[0052] The Solid Isotropic Material with Penalty (SIMP) model is used, which is a commonly used material interpolation method in topology optimization. By introducing a penalty factor, the SIMP model guides the material distribution to a 0-1 distribution.

[0053] (1) Optimization model for maximizing bulk modulus

[0054] Considering isotropy and boundary constraints, the optimization formula for maximizing the bulk modulus is as follows:

[0055]

[0056] stK(ρ)u=f

[0057]

[0058]

[0059] (A-1) 2 <ε

[0060]

[0061] (2) Maximizing shear modulus optimization model

[0062] In order to expand the data set, the embodiment of the present invention also designs a fixed boundary maximum shear modulus optimization model:

[0063]

[0064] stK(ρ)u=f

[0065]

[0066]

[0067] (A-1) 2 <ε

[0068]

[0069] (3) Optimization model for maximizing Young's modulus

[0070] Similarly, by modifying the objective function, the optimization model for maximizing Young's modulus with a fixed boundary is obtained:

[0071]

[0072] stK(ρ)u=f

[0073]

[0074]

[0075] (A-1) 2 <ε

[0076]

[0077] (4) Five-mode structural optimization model with Poisson's ratio close to 0.5

[0078] For an isotropic microstructure, the upper limit of the Poisson's ratio is 0.5. In order to generate a five-mode structure with a Poisson's ratio close to 0.5, the following optimization model is designed in the embodiment of the present invention:

[0079]

[0080] stK(ρ)u=f

[0081]

[0082] (A-1) 2 <ε

[0083]

[0084] Among them, the bulk modulus K and shear modulus G are respectively given by the formula With G = C 1212 Definition, in order to prevent singularities in the denominator, a correction of 0.05 is added to the denominator.

[0085] (5) Negative Poisson's ratio structural optimization model

[0086] After using these four optimization models, the embodiment of the present invention designs a microstructure with a Poisson's ratio of about 0.2 and close to 0.5. In order to design a microstructure with a wider range of properties, reducing the Poisson's ratio of the material is a key factor. The embodiment of the present invention introduces a specific Poisson's ratio as a constraint condition into the optimization process and designs a structure with a negative Poisson's ratio and a fixed boundary. The specific optimization model is as follows:

[0087]

[0088] stK(ρ)u=f

[0089]

[0090] (A-1) 2 <ε

[0091]

[0092]

[0093] in, is the constraint that specifies the Poisson's ratio to be v0.

[0094] (II) Five anisotropic optimization models

[0095] Anisotropic microstructures have unique physical properties such as negative refractive index, negative Poisson's ratio, and ultra-high elastic modulus, which are crucial in science and engineering. In order to enhance the data set of the present invention, a batch of anisotropic material data was optimized. (6) Maximizing bulk modulus optimization model:

[0096]

[0097] stK(ρ)u=f

[0098]

[0099]

[0100]

[0101] (7) Maximizing shear modulus optimization model:

[0102]

[0103] stK(ρ)u=f

[0104]

[0105] (8) Optimization model for maximizing Young's modulus:

[0106]

[0107] stK(ρ)u=f

[0108]

[0109] (9) Five-mode structural optimization model with Poisson's ratio close to 0.5:

[0110]

[0111] stK(ρ)u=f

[0112]

[0113] (10) Negative Poisson’s ratio structural optimization model:

[0114] The optimization model for specifying Poisson's ratio is as follows:

[0115]

[0116] stK(ρ)u=f

[0117]

[0118]

[0119] Through the above 10 fixed boundary optimization models, the embodiment of the present invention optimizes the microstructure with mask1 boundary, and finally obtains 21620 high-quality microstructures (the entity parts are all connected, and the gaps are not necessarily connected) by screening out the structures with fully connected entity parts and good boundary links.

[0120] Figure 2 Part a in the figure shows an optimized data set containing 21,620 data points, which covers doubly connected and non-connected microstructures in the void phase. The outermost six faces of all microstructures are the same as the mask1 image in the upper right corner. The relationship between Young's modulus, Poisson's ratio and Zener ratio is shown in the figure. Each microstructure is represented as a cube, whose size reflects the porosity and the color represents the volume surface ratio (S / V). The red cube highlights the specific microstructure instance indicated by the arrow. The bottom and right projections show the relationship between Young's modulus and Poisson's ratio, and Poisson's ratio and Zener ratio, respectively.

[0121] Figure 2 Part b in Fig. 2 shows the relationship between Young's modulus, Poisson's ratio, and Zener ratio in the optimized dataset under the second boundary condition (mask2). The optimized dataset contains 28,767 data points. Figure 2 Part c in the figure shows the relationship between Young's modulus, Poisson's ratio, and Zener ratio in the optimized data set under the third boundary condition (mask3). The optimized data set contains 26,532 data points. Figure 2 Part d in Figure 4 shows the relationship between Young's modulus, Poisson's ratio, and Zener ratio in the optimized data set under the fourth boundary condition (mask4). The optimized data set contains 14,930 data points.

[0122] In order to expand and enrich the data set, this paper proposes an active learning strategy based on the diffusion model, such as Figure 3 As shown, in order to improve the quality of diffusion model generation, an adaptive method is used, which uses a denoising function It will forward estimate and the sample x at the current time step t t As input. During the training process, Let f(x t ,0,t), the probability is 50%, otherwise it is set to 0. Considering that the microstructure of the present invention is a three-dimensional symmetrical voxel structure, only Single cell.

[0123] To generate microstructures with specific boundaries and moduli, the present invention uses boundary constraints and three independent components C in the elastic tensor matrix C: 1111 ,C 1122 ,C 1212 As conditions, these conditions are introduced into each layer of U-Net through the adaptive instance normalization technique.

[0124] During the training process, the AdamW optimizer is used to optimize the denoising loss function, and the learning rate is set to 10 -4 , with a batch size of 24 and a total of 510 training cycles. The loss calculation is performed by minimizing the mean squared error between the model output and the target value over noise and time steps, so that the model gradually learns to generate microstructures with specified boundaries under given conditions.

[0125] During the generation process, the diffusion model produces a variety of three-dimensional microstructures under the specified boundary and elastic tensor matrix conditions. In order to cover a wide range of modulus properties, the present invention calculates the signed distance function (SDF) value of each node on the Cartesian grid in the attribute space of the training dataset, and samples in the area where the SDF value is less than 0, ensuring that the sampling range extends beyond the coverage of the training dataset. These elastic tensor matrix components, together with the encoding of the target boundary, are input into the network, and 50 steps of DDPM sampling are used to generate microstructures.

[0126] In order to obtain a large-scale bicontinuous dataset with consistent boundaries, an active learning strategy is adopted in the embodiment of the present invention. Initially, the adaptive diffusion model is trained using the optimized initial dataset. Then, the generated bicontinuous microstructures are added to the dataset, and the spatial density is adjusted to ensure the uniform distribution of data points. Structures that do not meet the biconnectivity standard and low quality are iteratively removed. This process ultimately forms a large-scale, boundary-consistent and bicontinuous microstructure (LBBM) dataset. Figure 4As shown in part a of FIG, the LBBM data set using mask1 as the boundary condition is shown, which contains 107,383 high-quality biconnected data, and the relationship between its Young's modulus, Poisson's ratio and Zener ratio is shown. For the other three boundaries with Mask2-Mask4 as the boundary, the embodiment of the present invention uses the active learning network framework in turn, and finally obtains 192,925, 75,660 and 79,744 high-quality biconnected microstructures, respectively. The relationship between their Young's modulus, Poisson's ratio and Zener ratio is shown as follows: Figure 4 As shown in parts b, c, and d.

[0127] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0128] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for constructing a biconnected three-dimensional microstructure dataset with the same boundary, characterized in that: The following steps are involved: Step S1: Determine four boundary types through test analysis, and reconstruct the microstructure using the four boundary types as constraints on the six faces of the cube; Step S2: for each boundary type, using the LIVE3D framework, using the maximum bulk modulus, the maximum shear modulus, the maximum Young's modulus and the five-mode structure as optimization objectives, and creating an initial data set according to the corresponding constraints; Step S3: Generative AI is used for structure generation to expand the attribute space of the microstructure. The generative model adopts a diffusion model, the network structure uses Unet, and the loss function is MSE loss. On this basis, the initial data set in S2 is used to train the Unet network, and an active learning strategy is used to iteratively expand the data set. Step S4: Identify and retain structures with biconnectivity characteristics through a connected component labeling algorithm, remove disconnected structures, and construct a data set with the same boundary and biconnectivity under the boundary type described in step S1.

2. The method for constructing a biconnected three-dimensional microstructure dataset with the same boundary according to claim 1, characterized in that: In the objective function of the optimization target in step S2, ρ is the density of the structure, C(ρ) is the flexibility when the structure density is ρ, and the specific objective function is as follows: The objective function for maximizing the bulk modulus is: C 1111 With C 1122 are the two components in the elastic tensor matrix C; The objective function for maximizing the shear modulus is: f(C(ρ)) = C 1212 , where C 1212 is a component of the elastic tensor matrix C; The purpose function that maximizes Young's modulus is: The objective function of the five-module structure is: The bulk modulus K is given by the formula Definition: Shear modulus G is given by the formula G = C 1212 Definition: K0 and G0 are the initial values ​​of bulk modulus and shear modulus obtained by random initial calculation, respectively.

3. The method for constructing a biconnected three-dimensional microstructure dataset with the same boundary according to claim 1, characterized in that: The constraint conditions in step S2 specifically refer to: Equilibrium equation constraint: K(ρ)u=f, where K(ρ) is the stiffness matrix, u is the displacement vector, and f is the applied external force; Volume fraction constraint: Where M is the total number of discrete elements of the material, v e and ρ e are the volume fraction and density of the material at the eth position, respectively, and |Ω| represents the volume of the microstructure design domain. This constraint ensures that the total volume of the material does not exceed V during the optimization process; Boundary condition constraints: During the optimization process, ensure that the boundary b1 is as close to the boundary b2 as possible, and ε is the allowable convergence error; Isotropic constraint: Poisson's ratio constraint: Where v0 is the specified initial Poisson's ratio; Density variable constraint: 0≤ρ e ≤1, M is the total number of discrete units of the material, that is, among the total discrete units, any unit ρ e The material density is between [0,1].

4. The method for constructing a biconnected three-dimensional microstructure dataset with the same boundary according to claim 1, characterized in that: The diffusion model in step S3 includes a forward denoising process and a reverse denoising process. The forward denoising process is calculated by equation Step by step to x t Add noise to the real data x0, where ε t-1 Sampling from a standard Gaussian distribution with parameter α t To control the noise level, the reverse denoising process is to obtain the data x close to pure noise. t First, use a neural network to predict the noise and indirectly recover x t-1 , until the real data x0 is restored.

5. The method for constructing a biconnected three-dimensional microstructure dataset with the same boundary according to claim 1, characterized in that: The loss function of the diffusion model in step S3 trains the network according to the following relationship, which is used to guide the neural network to learn to denoise the noisy data: Where t represents the time step in the diffusion process, t~[1,T] represents the time step t is uniformly sampled from the time interval [1,T], x0 represents a real data in the training data, q(x0) represents the probability distribution of the real data, x0~q(x0) represents randomly sampling a data point x0 from q(x0), that is, selecting a sample from the training data as the input of the diffusion model, ε~N(0,I) represents the noise sampled from the standard normal distribution, with a mean of 0, and the covariance matrix is ​​the unit matrix I, x t is the noisy data of the diffusion process at time t, which is generated by adding noise to the real data x0. θ (x t ,t) represents the predicted value of the neural network model with parameter θ.

6. The method for constructing a biconnected three-dimensional microstructure dataset with the same boundary according to claim 1, characterized in that: In the network training described in step S3, voxels are used to represent all microstructures, that is, each structure is represented as an n×n×n three-dimensional binary matrix. Since the structure has cubic symmetry, only the upper left corner 1 / 8 of the structure needs to be considered as input during training. At the same time, due to symmetry, symmetrical noise is also used in the forward and reverse diffusion processes.

7. The method for constructing a biconnected three-dimensional microstructure dataset with the same boundary according to claim 1, characterized in that: Step S3 adopts a self-conditioning strategy to improve the generation quality, that is, the content currently generated by the network is used as the condition for the next generation.

8. The method for constructing a biconnected three-dimensional microstructure dataset with the same boundary according to claim 1, characterized in that: In terms of the network structure described in step S3, both the U-Net encoder and decoder contain 5 stages, and each stage consists of a Resblock with an attention mechanism.

9. The method for constructing a biconnected three-dimensional microstructure dataset with the same boundary according to claim 1, characterized in that: Step S3 is to construct a large-scale microstructure dataset and use an active learning strategy for iterative training.

10. The method for constructing a biconnected three-dimensional microstructure dataset with the same boundary according to claim 1, characterized in that: The connection component marking algorithm in step S4 specifically includes: First scan: For each pixel point p at the coordinate (i, j), output the image label L(i, j). The calculation process is as follows: Where N(p) represents the neighboring pixels of p. If there are multiple labels in N(p), the smallest label is selected and these labels are recorded as equivalent relations. Second scan: traverse each pixel point p in the image again, update the label to ensure that all equivalent labels are unified into one label: L(i,j)=find(L(i,j)), where the find function finds the minimum label equivalent to L(i,j) to achieve label unification.

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