Calcareous sand two-dimensional porous microstructure reconstruction processing method, system and platform based on diffusion model and storage medium

Abstract

The invention discloses a calcareous sand two-dimensional porous microstructure reconstruction processing method, system and platform based on a diffusion model and a storage medium. High-fidelity reconstruction and generation of a calcareous sand microstructure with an extremely complex form are realized by integrating principal component analysis directional alignment and a v prediction diffusion model; wherein the generated two-dimensional microstructure image is not only highly matched with a real CT slice in vision, but also shows high consistency in statistical distribution of 14 key morphology parameters such as porosity, fractal dimension, skeleton complexity and the like, and verifies the physical authenticity of the two-dimensional microstructure image. The method has dual capabilities of unconditional generation and conditional reconstruction, can synthesize a large number of statistical reasonable digital samples from zero to expand a scarce data set, and can intelligently enhance low-quality experimental images. And a stable, efficient and extensible digital material source is provided for discrete element numerical simulation, permeability characteristic prediction and microstructure-oriented constitutive model development of the calcareous sand.

Description

Technical Field

[0001] This invention belongs to the field of digital geotechnical engineering and artificial intelligence technology, specifically relating to a method, system, platform and storage medium for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model. Background Technology

[0002] Calcareous sand is a biogenic granular material widely distributed in tropical and subtropical seas, and is a key construction material for marine engineering projects such as artificial islands and reefs and subsea foundations. Unlike terrigenous quartz sand, calcareous sand particles have extremely irregular morphologies, rough surfaces, and multi-scale pores, resulting in unique engineering mechanical behaviors such as high compressibility, fragility, and complex hydraulic properties. Revealing the micromechanical mechanisms of these macroscopic properties depends on the precise characterization of the particle-scale morphology (including external geometry and internal pore structure).

[0003] X-ray micro-computed tomography (microCT) is currently the primary method for non-destructive observation of the three-dimensional internal structure of calcareous sand. However, this technique is costly, has a long data processing cycle, and a limited field of view per scan, resulting in a severe shortage of high-quality, representative datasets of calcareous sand microstructures. This data scarcity significantly restricts the development of statistical analysis based on large datasets, calibration of discrete element method (DEM) numerical simulations, and data-driven constitutive models.

[0004] To overcome these bottlenecks, researchers have attempted to reconstruct the microstructure of porous media using numerical methods. Traditional process simulation methods struggle to reproduce the complex porous systems unique to biological debris particles; while deep learning methods based on generative adversarial networks (GANs) often face problems such as training instability and pattern collapse, and are unable to faithfully reconstruct the fine geometric details (such as small throats and non-convex pores) that are crucial to mechanical and hydraulic properties.

[0005] Denoising diffusion probabilistic models are a class of deep generative models that have emerged in recent years. They fit complex data distributions by learning an inverse, stepwise denoising process. These models offer advantages such as stable training, high-quality generation, and the ability to effectively capture complex geometries and spatial variability, achieving significant success in image generation. However, how to systematically apply diffusion models to the microstructure reconstruction of calcareous sand, one of the most morphologically complex natural granular materials, remains a challenge, lacking in-depth research and feasible technical solutions.

[0006] Therefore, in view of the above-mentioned technical problems and defects, there is an urgent need to design and develop a method, system, platform and storage medium for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model. Summary of the Invention

[0007] To overcome the shortcomings and difficulties of the existing technology, the purpose of this invention is to provide a method, system, platform and storage medium for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model, so as to solve the problem that it is difficult to obtain a large number of representative calcareous sand microstructure samples due to the scarcity of CT scan data in the existing technology.

[0008] The first objective of this invention is to provide a method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model; the second objective of this invention is to provide a system for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model; the third objective of this invention is to provide a platform for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model; and the fourth objective of this invention is to provide a computer-readable storage medium.

[0009] The first objective of this invention is achieved as follows: the method comprises: First data corresponding to calcareous sand particles is created and acquired; the first data is preprocessed and second data corresponding to a single calcareous sand particle is generated; wherein, the first data is microscopic CT scan three-dimensional image data of calcareous sand particles; and the second data is binarized three-dimensional voxel characterization data. The second data is spatially oriented and aligned to generate and acquire third data corresponding to the directional cross section, and a first dataset corresponding to calcareous sand is constructed based on the third data; wherein, the third data is standardized two-dimensional slice image data of a specific directional cross section after alignment; the third data is a training dataset of calcareous sand microstructure; A first model is created based on the U-Net architecture. The first model is trained and processed using the first dataset, and a second model is constructed and generated accordingly. The first model is a denoising diffusion probability model, and the second model is a pre-trained diffusion model. Using the second model and combined with the reverse denoising process, fourth data corresponding to calcareous sand is reconstructed; wherein, the fourth data is two-dimensional porous microstructure image data.

[0010] The second objective of this invention is achieved as follows: the system is used to implement the diffusion-based method for reconstructing the two-dimensional porous microstructure of calcareous sand, the system comprising: A data creation and generation unit is used to create and acquire first data corresponding to calcareous sand particles, preprocess the first data, and generate second data corresponding to a single calcareous sand particle; wherein, the first data is microscopic CT scan three-dimensional image data of calcareous sand particles; and the second data is binarized three-dimensional voxel characterization data. The data processing and generation unit is used to spatially oriented and align the second data, generate and acquire third data corresponding to the directional cross section, and construct a first dataset corresponding to the calcareous sand based on the third data; wherein, the third data is standardized two-dimensional slice image data along a specific directional cross section after alignment processing; the third data is a training dataset of the microstructure of calcareous sand. The model creation and generation unit is used to create and generate a corresponding first model based on the U-Net architecture, train and process the first model according to the first dataset, and construct and generate a corresponding second model; wherein, the first model is a denoising diffusion probability model; and the second model is a trained diffusion model. The data reconstruction generation unit is used to reconstruct and generate fourth data corresponding to calcareous sand through the second model and in combination with the reverse denoising process; wherein the fourth data is two-dimensional porous microstructure image data.

[0011] The third objective of this invention is achieved as follows: it includes a processor, a memory, and a control program for a diffusion-model-based two-dimensional porous microstructure reconstruction processing platform for calcareous sand; wherein the diffusion-model-based two-dimensional porous microstructure reconstruction processing platform control program is executed on the processor, the diffusion-model-based two-dimensional porous microstructure reconstruction processing platform control program is stored in the memory, and the diffusion-model-based two-dimensional porous microstructure reconstruction processing platform control program implements the diffusion-model-based two-dimensional porous microstructure reconstruction processing method for calcareous sand.

[0012] The fourth objective of this invention is achieved as follows: the computer-readable storage medium stores a control program for a two-dimensional porous microstructure reconstruction processing platform for calcareous sand based on a diffusion model, and the control program for the two-dimensional porous microstructure reconstruction processing platform for calcareous sand based on a diffusion model implements the method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model.

[0013] This invention creates and acquires first data corresponding to calcareous sand particles through a method, preprocesses the first data, and generates second data corresponding to a single calcareous sand particle; wherein, the first data is microscopic CT scan three-dimensional image data of calcareous sand particles; the second data is binarized three-dimensional voxel characterization data; the second data is spatially oriented and aligned, generating and acquiring third data corresponding to directional sections, and constructing a first dataset corresponding to calcareous sand based on the third data; wherein, the third data is standardized two-dimensional slice image data along a specific directional section after alignment; the third data is a training dataset for the microstructure of calcareous sand; based on the U-Net architecture... A first model is generated, and the first model is trained and processed based on the first dataset to generate a corresponding second model. The first model is a denoised diffusion probability model, and the second model is a trained diffusion model. Through the second model and combined with the reverse denoising process, a fourth dataset corresponding to calcareous sand is reconstructed. The fourth dataset is two-dimensional porous microstructure image data, along with the corresponding system, platform, and storage medium to generate high-fidelity digital samples of the two-dimensional microstructure of calcareous sand. This solves the problem of insufficient microstructure data due to limitations in experimental methods and provides a reliable data foundation for numerical simulation and mechanism research in marine geotechnical engineering.

[0014] In other words, this invention integrates principal component analysis-based directional alignment with a v-predictive diffusion model to achieve high-fidelity reconstruction and generation of the extremely complex microstructure of calcareous sand. The generated two-dimensional microstructure images not only visually closely match real CT slices but also exhibit high consistency in the statistical distribution of 14 key morphological parameters, including porosity, fractal dimension, and skeletal complexity, thus verifying their physical authenticity. This invention also possesses dual capabilities of unconditional generation and conditional reconstruction, capable of synthesizing a large number of statistically reasonable digital samples from scratch to expand scarce datasets, and intelligently enhancing low-quality experimental images. It provides a stable, efficient, and scalable digital material source for discrete element numerical simulation, permeability prediction, and microstructure-oriented constitutive model development of calcareous sand, overcoming the bottlenecks of traditional experimental methods in terms of data acquisition cost, scale, and efficiency. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1This is a schematic diagram illustrating the typical morphological characteristics of natural calcareous sand particles in a method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model, according to the present invention. Figure 2 This is a schematic diagram illustrating the workflow of a method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model, specifically a method for constructing a microstructure dataset based on micro-CT scanning. Figure 3 This is a schematic diagram of the forward (noise addition) and reverse (noise removal) processes in the diffusion model of the diffusion model-based method for reconstructing the two-dimensional porous microstructure of calcareous sand according to the present invention. Figure 4 This is a schematic diagram of the U-Net architecture of a diffusion-based method for reconstructing the two-dimensional porous microstructure of calcareous sand according to the present invention. Figure 5 This is a training set generated for a diffusion-based method for reconstructing the two-dimensional porous microstructure of calcareous sand according to the present invention; wherein, a visual comparison diagram of the real training sample (left) and the synthetic sample generated by the diffusion model (right) is shown. Figure 6 This is a schematic diagram demonstrating the forward diffusion, reverse denoising, and unconditional trajectory generation based on a synthetic porous disk model, a two-dimensional porous microstructure reconstruction method for calcareous sand based on a diffusion model according to the present invention. Figure 7 This is a schematic diagram comparing the generation convergence of datasets with different sample sizes in the method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model according to the present invention; wherein, (a) figure shows 2000 random samples; (b) figure shows 20000 random samples; Figure 8 This is a schematic diagram of the forward noise addition and conditional inverse reconstruction process of a real calcareous sand slice in the present invention, which is a method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model. Four images are provided for reference, where the top left image of each image is the original image, the leftmost image of each row is the noise addition effect at the current stage, and each row from left to right is the evolution process of the image obtained after denoising the image under the current noise. Figure 9 This is a schematic diagram of multiple unconditional generation trajectories of real calcareous sand microstructure based on pure noise, which is a method for reconstructing two-dimensional porous microstructures of calcareous sand based on a diffusion model according to the present invention. Figure 10 This is a visual comparison diagram of a real microscopic CT slice (left) and a randomly generated synthetic slice (right) in the present invention, which is a method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model. Figure 11This diagram illustrates the visual evolution of the microstructure generated during the initial training phase (rounds 2-20) of a diffusion-based method for reconstructing two-dimensional porous microstructures of calcareous sand according to the present invention, showing the rapid transformation from a noisy state to a structured calcareous sand morphology. Figure 12 This diagram illustrates the evolution trend of four training and reconstruction error indices during the diffusion model training process of a diffusion model-based method for reconstructing the two-dimensional porous microstructure of calcareous sand according to the present invention; corresponding to the three indices in Table 2, where (a) is the v-prediction loss; (b) the mean square error of noise consistency (MSE); and (c) the structural similarity index (SSIM). Figure 13 This is a mirror histogram comparing the distribution of seven particle boundary characterization parameters of a real calcareous sand slice (blue) and a slice generated by the diffusion model (red) in the present invention, which is a method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model. The parameters in each figure correspond to the indicators in Table 3. Figure 14 This is a violin diagram showing the distribution of seven intraparticle porosity characterization parameters of a real calcareous sand slice and a slice generated by the diffusion model, in relation to a diffusion-based method for reconstructing the two-dimensional porous microstructure of calcareous sand according to the present invention; where each figure corresponds to the index in Table 3. Figure 15 This is a schematic diagram of the process steps of a method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model according to the present invention. Figure 16 This is a schematic diagram of the architecture of a two-dimensional porous microstructure reconstruction system for calcareous sand based on a diffusion model, according to the present invention. Figure 17 This is a schematic diagram of the architecture of a two-dimensional porous microstructure reconstruction and processing platform for calcareous sand based on a diffusion model according to the present invention. Figure 18 This is a schematic diagram of a computer-readable storage medium architecture in one embodiment of the present invention. Detailed Implementation

[0017] To facilitate a clearer understanding of the objectives, technical solutions, and advantages of this invention, the invention will be further described below in conjunction with the accompanying drawings and specific embodiments. Those skilled in the art can easily understand other advantages and effects of this invention from the content disclosed in this specification.

[0018] This invention can also be implemented or applied through other different specific examples, and various details in this specification can also be modified and changed based on different viewpoints and applications without departing from the spirit of this invention.

[0019] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0020] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Secondly, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0021] Preferably, the diffusion-based method for reconstructing the two-dimensional porous microstructure of calcareous sand according to the present invention is applied in one or more terminals or servers. The terminal is a device capable of automatically performing numerical calculations and / or information processing according to pre-set or stored instructions. Its hardware includes, but is not limited to, microprocessors, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), digital signal processors (DSPs), embedded devices, etc.

[0022] The terminal can be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal can interact with the customer via a keyboard, mouse, remote control, touchpad, or voice control device.

[0023] This invention provides a method, system, platform, and storage medium for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model.

[0024] like Figure 15 The diagram shown is a flowchart of the two-dimensional porous microstructure reconstruction method for calcareous sand based on a diffusion model provided in an embodiment of the present invention.

[0025] In this embodiment, the two-dimensional porous microstructure reconstruction method of calcareous sand based on diffusion model can be applied to terminals or fixed terminals with display functions. The terminals are not limited to personal computers, smartphones, tablets, desktop computers or all-in-one computers with cameras, etc.

[0026] The diffusion-based method for reconstructing the two-dimensional porous microstructure of calcareous sand can also be applied to a hardware environment consisting of a terminal and a server connected to the terminal via a network. The network includes, but is not limited to, a wide area network (WAN), a metropolitan area network (MAN), or a local area network (LAN). The diffusion-based method for reconstructing the two-dimensional porous microstructure of calcareous sand in this embodiment can be executed by the server, by the terminal, or by both the server and the terminal.

[0027] For example, for a terminal requiring diffusion-based reconstruction of the two-dimensional porous microstructure of calcareous sand, the diffusion-based reconstruction function provided by the method of this invention can be directly integrated onto the terminal, or a client for implementing the method of this invention can be installed. Alternatively, the method provided by this invention can also run on servers or other devices in the form of a Software Development Kit (SDK). The SDK provides an interface for the diffusion-based reconstruction function of the two-dimensional porous microstructure of calcareous sand, allowing the terminal or other devices to implement the diffusion-based reconstruction function through this interface. The invention will be further described below with reference to the accompanying drawings.

[0028] like Figures 1-15 As shown, this invention provides a method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model. The method includes the following steps: S01. Create and acquire first data corresponding to calcareous sand particles, preprocess the first data and generate second data corresponding to a single calcareous sand particle; wherein, the first data is microscopic CT scan three-dimensional image data of calcareous sand particles; the second data is binarized three-dimensional voxel characterization data; S02. Spatial orientation alignment processing of the second data is performed to generate and acquire third data corresponding to the directional cross section, and a first dataset corresponding to the calcareous sand is constructed based on the third data; wherein, the third data is standardized two-dimensional slice image data along a specific directional cross section after alignment processing; the third data is a training dataset of the microstructure of calcareous sand. S03. Based on the U-Net architecture, create and generate a corresponding first model, train and process the first model according to the first dataset, and construct and generate a corresponding second model; wherein, the first model is a denoising diffusion probability model; and the second model is a trained diffusion model. S04. Using the second model and combined with the reverse denoising process, a fourth set of data corresponding to the calcareous sand is reconstructed; wherein the fourth set of data is a two-dimensional porous microstructure image data.

[0029] The spatial orientation alignment process for the second data, generating and acquiring third data corresponding to the directional cross-section, and constructing a first dataset corresponding to calcareous sand based on the third data, further includes: S021. Construct a covariance matrix corresponding to the particle voxels, decompose the covariance matrix to generate fifth data corresponding to the particle voxels, and use the plane of the fifth data as a reference plane to create a corresponding two-dimensional slice plane; wherein, the fifth data is the principal feature vector. S022. Create a two-dimensional slice image corresponding to the calcareous sand particles, construct a corresponding standard-sized image using a zero-value filling method, and linearly normalize the pixel values ​​of the standard-sized image to a preset numerical range.

[0030] The process of creating and generating a corresponding first model based on the U-Net architecture, training and processing the first model using the first dataset, and constructing and generating a corresponding second model further includes: S031. Using the v-prediction parameterization method, construct and generate the first model; wherein, the model prediction target is defined as a linear combination of the source signal and the injected noise, and the specific expression is: (7) In the formula, For pure microscopic structure images, For noise, and To be consistent with diffusion time step Correlation coefficients; the model training objective function is prediction speed. The mean square error between the target velocity and the target velocity.

[0031] The process of creating and generating a corresponding first model based on the U-Net architecture, training and processing the first model using the first dataset, and constructing and generating a corresponding second model further includes: S032. The noise addition intensity at different time steps during the forward diffusion process is controlled by cosine scheduling, and sampling processing is performed during the reverse denoising process according to the DDPM or DDIM algorithm. S033. The model is trained by combining the time step embedding vectors, and the time step embedding vectors are incorporated into the convolutional blocks of the U-Net architecture; wherein the U-Net architecture includes an encoding path, a decoding path, and skip connections connecting the two.

[0032] The process of reconstructing and generating fourth data corresponding to calcareous sand using the second model and in conjunction with a reverse denoising process also includes: S041. Based on the second model, starting from random noise conforming to a Gaussian distribution and combining it with the reverse diffusion trajectory, a sixth data corresponding to calcareous sand is created; wherein, the sixth data is a novel two-dimensional porous microstructure image data of calcareous sand.

[0033] The process of reconstructing and generating fourth data corresponding to calcareous sand using the second model and in conjunction with a reverse denoising process also includes: S042. Generate and acquire the seventh data corresponding to the calcareous sand; wherein, the seventh data is noisy calcareous sand microstructure image data; S043. Based on the seventh data, according to the second model, and in conjunction with the conditional inverse denoising process, a fourth data with high clarity corresponding to the calcareous sand is reconstructed.

[0034] Specifically, in this embodiment of the invention, a diffusion model-based framework is constructed to generate realistic and reliable two-dimensional microstructure slices of calcareous sand. Before model training, principal component analysis (PCA) is first used to orient and align the high-resolution three-dimensional voxelized particles obtained from microscopic CT scans, and then representative two-dimensional slices are extracted to establish a standardized dataset. Subsequently, a v-predictive diffusion model integrating a U-Net network backbone is trained to capture the potential statistical distribution patterns of the microstructure. This scheme will verify the model performance through denoised trajectories, visual comparison, and comprehensive quantitative evaluation based on 14 morphological description indicators. Simultaneously, kernel density estimation and Jensen-Shannon divergence are used to verify the similarity between the generated samples and the real samples at the distribution level.

[0035] In the dataset and preprocessing, the microstructure dataset used in this scheme is derived from high-resolution X-ray micro-computed tomography (micro-CT) imaging of natural calcareous sand. For example... Figure 1 As shown, calcareous sand particles exhibit highly irregular external morphology and numerous internal pores, characteristics stemming from biological growth processes, mechanical abrasion, and fragmentation. These formation mechanisms create the unique multi-scale geometric heterogeneity of calcareous sand, distinguishing it from terrigenous quartz sand. Therefore, to achieve accurate numerical modeling, a refined characterization of its microstructure is essential.

[0036] The voxel resolution of micro-CT scanning is 40 micrometers, which is sufficient to clearly distinguish the outer boundaries and internal pore systems of particles. After image acquisition, the raw CT volume data is sequentially processed by denoising, thresholding, and region segmentation to obtain a binary voxel representation of a single particle. In this representation, a voxel value of 1 represents the solid phase region, and a voxel value of 0 represents the pore space. This binarization process effectively eliminates grayscale artifacts while preserving the true geometry of particle boundaries and internal pores.

[0037] To ensure rotational consistency and generate standardized microstructure slices suitable for diffusion model training, this scheme employs principal component analysis (PCA) to orient and align each segmented particle. For voxelized point clouds... (in The formula for calculating its covariance matrix is: (1) In the formula, This is the data of the voxelized point cloud, where N is the total number of particles and C is the formula for the calculated covariance matrix.

[0038] Subsequently, the matrix is ​​decomposed into eigenvalues ​​and eigenvectors. The principal eigenvector corresponding to the largest eigenvalue is then calculated. This characterizes the dominant geometric orientation of the particles. Instead of rotating the entire volume data, this scheme constructs a model based on the following formula... Orthogonal slicing planes: (2) The method can stably extract two-dimensional slices along the main axis of structural variation, ensuring that the obtained image can present the pore network to the greatest extent and that the geometric morphology between different particles is comparable.

[0039] Subsequently, the nearest neighbor interpolation method was used to rasterize each slice to preserve the clear solid-pore interface characteristic of calcareous sand. This is due to the different cross-sectional areas of the particles. Due to existing differences, this solution employs a zero-fill strategy to embed the effective region into a fixed 128×128 grid, thus standardizing the slices. (Slices after filling) Defined as: (3) In the formula, This is the original cropped slice. This embedding method avoids the geometric distortions that scaling operations typically cause, while also meeting the uniform input dimension requirement of neural networks.

[0040] Finally, all voxel values ​​were linearly scaled to the [-1,1] interval to match the normalized input space of the generative diffusion model standard. The resulting dataset retains the rich morphological variability of the original CT scans, including irregular particle outlines, multi-scale pore clusters, and complex connectivity patterns, laying a solid foundation for the subsequent training and evaluation of the generative model.

[0041] The diffusion model fits complex data distributions by learning a reverse, stepwise noise-addition process. For a given slice of observed microstructure... The forward diffusion process will occur T Gaussian noise is gradually added to the perturbation process within each time step, while the trained inverse process restores the structural information through a series of denoising operations. This framework possesses stable optimization characteristics and high-fidelity generation capabilities, making it suitable for characterizing the multi-scale porous morphology of calcareous sands. The forward and reverse diffusion trajectories used in this scheme strictly adhere to... Figure 3 Implemented as shown.

[0042] In this scheme, the forward diffusion process is formally represented by a Markov chain, which progressively corrupts the image according to the transfer kernel function. (4) In the formula, Indicates the current image. This represents the image from the previous step. A scheduling scheme for controlling noise intensity. Leveraging the properties of a Gaussian distribution, this multi-step process can be directly derived from the initial slice using a closed-form expression. Sampling at any time step corresponding slices : (5) This scheme employs a cosine noise scheduling method. Unlike linear scheduling schemes, cosine scheduling generates gradually changing noise at the initial time step. However, the time step will increase in the later stages. The increment. This design is crucial for preserving structural details in the initial stages of image destruction, while ensuring a smooth evolution of variance, thereby enabling more stable model training and improving the reconstruction of small pore boundaries.

[0043] For the inverse denoising process, the generative (i.e., inverse) diffusion process is modeled as a parameterized Gaussian transfer process: (6) In the formula, the mean term By neural network Approximate fitting. To improve numerical stability, this scheme employs the v-prediction parameterization method. The target variable is defined as a linear combination of the source signal and noise: (7) In the formula, This represents injected noise. (Model predictions) It can simultaneously achieve the following: and The reconstruction. Compared to direct The prediction method, with its parameterized form, exhibits superior numerical stability and is particularly suitable for datasets containing significant high-frequency spatial features, such as the typical serrated profile and sharp pore boundaries of calcareous sand.

[0044] The reverse sampling process follows the standard Denoising Diffusion Probability Model (DDPM) process, while incorporating optional randomness and adaptive exponential moving average (EMA) weights to optimize the quality of the generated results.

[0045] For network architecture, the core denoising function of the backdiffusion process A two-dimensional U-Net architecture is used for parameterization. This architecture was chosen because it can simultaneously capture multi-scale contextual features and local spatial details. Figure 4 The schematic diagram shown illustrates that the U-Net consists of an encoder-decoder structure with the addition of symmetrical skip connections (i.e., the U-Net architecture is a multi-level encoder-decoder structure equipped with skip connections for feature fusion).

[0046] In the encoding path, a series of convolutional blocks progressively downsample the input slice. This hierarchical extraction method captures coarse-scale topographic information, such as the elongation morphology of particles, overall geometry, and large clusters of pores. Subsequently, the decoding path restores spatial resolution through transposed convolution. Crucially, skip connections enable the direct transfer of high-frequency spatial information from the encoding to the decoding path. This mechanism ensures that minute pore boundaries, jagged outer contours, and other fine microstructural details are effectively preserved throughout the denoising process.

[0047] To integrate temporal information, this scheme maps the temporal embedding vector obtained based on sinusoidal position encoding through a multilayer perceptron (MLP) and incorporates it into each convolutional block, enabling the network to adjust according to specific diffusion time steps. It dynamically adjusts its noise reduction behavior.

[0048] In the training strategy and implementation details, the model training adopts the v prediction objective function, which has been proven to improve model stability and reconstruction fidelity, especially in high time step regions. Given a noisy slice and its corresponding time step The network will affect the speed variable Make predictions. The optimization process aims to minimize the mean squared error (MSE) between the predicted velocity and the target velocity. (8) Model optimization was performed using the AdamW optimizer, with a base learning rate of 1×10⁻⁶. −4 A cosine learning rate decay strategy was employed to promote model convergence. All input slices were normalized to the [-1,1] interval and processed in batches of 128 samples. The basic training process consisted of 200 training epochs, with an additional 400 epochs of extended training to verify the model's convergence characteristics. The total number of diffusion time steps was fixed at T=1000, consistent with the cosine noise scheduling scheme used in the forward diffusion process.

[0049] To ensure computational efficiency and numerical robustness, mixed-precision training (AMP) was used, and the gradient norm was clipped to 1.0 to prevent gradient explosion. Furthermore, the model parameters were maintained using an exponential moving average (EMA) throughout training, with a decay rate of 0.9995. This EMA model will be used in the final inference stage, as it typically produces clearer and more stable results. The complete hyperparameters and numerical settings of the diffusion model are summarized in Table 1.

[0050] After training, synthetic microstructure slices can be generated by executing a reverse diffusion trajectory starting from pure Gaussian noise. The model generation performance will be evaluated using both the standard DDPM sampling algorithm and the accelerated DDIM sampling algorithm. To monitor the training process, a fixed 36-sample grid is generated after each training epoch, serving as a unified visual benchmark for evaluating reconstruction fidelity and the emergence of statistically effective pore structures. These samples will be used as the basis for qualitative analysis, and this approach will also incorporate morphological description metrics for rigorous quantitative evaluation.

[0051] Table 1 Hyperparameters for Diffusion Model Training

[0052] For results and evaluation, preliminary validation was conducted using synthetic porous disks. Before applying the proposed framework to the complex microstructure of calcareous sand, preliminary validation was performed using synthetic porous disks. This stage aimed to verify the correctness of the forward-backward diffusion mechanism and evaluate the model's ability to learn geometric distribution patterns from randomly generated data. To construct a controllable real-world reference dataset, a synthetic dataset was built using a random generation process: each sample contained a standardized circular boundary with 6 to 12 randomly positioned circular pores of varying radii. This design ensured that each image corresponded to a unique geometric configuration, forcing the model to learn underlying generation patterns rather than memorizing specific templates.

[0053] After training, the fidelity of the model generation was first qualitatively evaluated by directly comparing the visual effects of the random training dataset with those of the model-generated samples. The results are as follows: Figure 5 As shown in the figure, the left image is a representative subset of the real reference images used for training, and the right image is the sample generated after the diffusion model converges. It can be observed that the synthesized microstructures are visually indistinguishable from the real training data: the model not only successfully captures the clear solid-pore interface, but also accurately reproduces the random variability of pore size and location; in addition, the generated samples exhibit a rich variety of pore configurations and do not completely overlap with any training image, indicating that the network has mastered the underlying geometric probability distribution.

[0054] In addition to the final output, such as Figure 6 As shown, the internal dynamics of the diffusion process are also revealed. The figure depicts the trajectories of forward diffusion, deterministic restoration, and stochastic generation. The first row shows the forward diffusion process, where Gaussian noise is progressively injected into a reference disk sample. As the number of diffusion steps increases, the morphological features are gradually masked, eventually converging into an isotropic noise field, which verifies that the forward mechanism can effectively push the data toward the prior distribution. The second row presents the deterministic inverse denoising process, where the model iteratively restores the underlying structure from the corrupted state. The re-emergence of the circular contours and pore locations indicates that the network has successfully fitted the transition probabilities. The third line illustrates the unconditional generation process, with the reverse process starting from pure Gaussian noise for initialization. Despite the absence of specific structural prior information, the trajectory converges to a reasonable porous disk structure with clear boundaries, confirming that the model has obtained robust generative priors for the porous disk microstructure manifold.

[0055] To evaluate the impact of dataset size on training stability, this approach underwent further validation. Two differentiated datasets were constructed for the experiment: a small dataset containing 2000 independent images and a large dataset containing 20000 independent images. Figure 7 As shown, the generation results of the two datasets at different training epochs are compared. For the 2000-sample dataset (left figure a), the generation results in the early stages of training (epochs 1, 100, and 200) are dominated by noise and degradation artifacts. It is not until about 300–400 epochs that a clear and distinguishable porous micromorphology can be generated. In contrast, the 20000-sample dataset (right figure b) shows a significantly faster convergence speed: after only 30–50 epochs of training, a coherent disk geometry with a regular pore distribution can be generated, and a rapid transition from pure noise to the target micromorphology is achieved in the initial training stage.

[0056] The comparative results above demonstrate that larger-scale and more diverse training data can significantly accelerate model convergence, stabilize training dynamics, and enable the model to effectively learn the geometric generation rules behind microstructures. Comprehensive analysis shows that the proposed diffusion model architecture possesses high-fidelity microstructure generation capabilities, and its performance gains significantly depend on data diversity, laying a solid foundation for its subsequent application in the analysis of real calcareous sand microstructures.

[0057] Regarding the model's performance in generating real calcareous sand microstructures, based on the validation using synthetic data, this scheme further systematically explored the diffusion model's ability to characterize complex natural micromorphologies. The experimental data used were microstructure images of real calcareous sand. Figure 8 As shown, the evolution of a representative micro-CT slice during forward noise addition and conditional inverse reconstruction is illustrated in matrix visualization. The vertical axis of the matrix corresponds to the forward diffusion process: starting from the original microstructure image (top left corner), Gaussian noise is gradually applied according to a cosine noise scheduling strategy, eventually causing the particle boundaries and pore network contours to gradually blur until they are completely obliterated.

[0058] For the different noise levels shown in the first column, the model calculates and displays the corresponding inverse denoising trajectories along the horizontal direction. Experimental results show that under low to moderate noise pollution levels, the model can achieve high-fidelity microstructure reconstruction—not only are irregular particle outlines accurately restored, but the main pore structure inside the particles also highly consistent with the real sample. The intermediate process of inverse denoising exhibits a hierarchical recovery pattern: the model prioritizes reconstructing the macroscopic geometry of the sand body, and then gradually refines the microscopic details of the pores. However, as the initial noise pollution level increases, the model's reconstruction behavior changes significantly: although the final generated result still converges to the realistic and reliable morphology of calcareous sand particles, the specific distribution of pores can no longer be completely consistent with the original CT slices. This deviation reflects the inherent randomness of the diffusion model: when the original signal is significantly masked by noise, multiple different microstructures can statistically match the contaminated state. In this case, the model no longer performs a strictly defined inverse reconstruction operation, but instead synthesizes reasonable pore details that conform to the microscopic characteristics of calcareous sand based on the prior knowledge learned during training.

[0059] Appendix Figure 8 The focus is on verifying the reconstruction stability of the model, while... Figure 9This visually demonstrates the model's unconditional generation capability. Each row in the figure corresponds to an independent reverse diffusion trajectory, with all trajectories using a pure Gaussian noise field as the initial input. The image sequence clearly tracks the gradual evolution and manifestation of microstructural features during the denoising process. In different generation instances, the particle morphology, pore distribution frequency, and spatial arrangement of the final output image all exhibit significant diversity. Despite this variability, all generated samples consistently present the core morphological features of calcareous sand, such as non-convex particle boundaries and complex intragranular pore structures.

[0060] This result confirms that the proposed diffusion model is not limited to mechanical memorization of a single sample in the training set, but has successfully learned robust generative priors covering the real microstructure manifold, providing a reliable model basis for subsequent quantitative analysis and performance prediction of calcareous sand microstructure.

[0061] To further verify the visual realism of the synthetic data, such as Figure 10 As shown, a direct qualitative comparative analysis was conducted. The left side of the figure displays a batch of randomly selected real micro-CT slices, while the right side presents an equal number of samples generated by a trained diffusion model. The generated images accurately reproduce the typical morphological features of calcareous sand, including rough and irregular particle outlines and multi-scale internal porosity. Furthermore, the inter-sample variability of the synthetic dataset is comparable to the variability level of the real physical dataset.

[0062] The above visual comparison results show that the proposed diffusion model has fully captured the core geometric features and pore scale statistical regularities of the microstructure of calcareous sand.

[0063] For training convergence and parameter analysis, to rigorously evaluate the numerical stability and learning dynamics of the diffusion model, this scheme employs a multi-dimensional monitoring strategy throughout the training phase. This strategy selects four complementary error metrics for tracking and analysis: virtual prediction loss (v-prediction loss), L1 reconstruction loss, inversion consistency loss, and structural loss based on the structural similarity index (SSIM). These metrics quantify model performance from different dimensions, ranging from pixel-level accuracy to high-level structural fidelity. The mathematical definitions and physical meanings of each metric are detailed in Table 2.

[0064] Table 2 defines and explains the four error metrics used to evaluate model training and reconstruction performance.

[0065] Loss function definition: ; Symbol explanation: For the first Noisy images at each diffusion time step; Index for discrete diffusion time steps; For a neural network model with parameter θ; For the diffusion rate variable, it is defined as follows: ; For true, noise-free original images; Gaussian noise sampled from a standard normal distribution; noise domain defined as: In the formula, This is the actual noise added during forward diffusion; This represents the noise predicted by the model during the backdiffusion process. Image domain definition: The initial image is obtained through the inversion process; structural similarity is defined as: ; Symbol explanation: It represents the average value within a local image window; Local standard deviation For covariance; This is a constant used for numerical stability.

[0066] Qualitative analysis results of the training process, such as Figure 11 As shown in the figure, this visualization illustrates the gradual improvement in the quality of the generated images during the initial training phase (rounds 2 to 20). In the initial training phase (rounds 2–6), the generated results were dominated by high-frequency noise and discrete artifacts, making it difficult for the model to effectively distinguish between solid regions and the background. During rounds 8–14, the model exhibited a significant structural transformation: coherent particle boundaries began to appear, and the characteristic "cluster-like" morphology of calcareous sand gradually became discernible, although the internal pore structure remained blurred. By rounds 16–20, the model had converged to a high-fidelity microstructure representation level, with generated images displaying clear particle boundaries and a fully resolved internal pore network. This rapid visual convergence demonstrates that the virtual prediction (v-prediction) parameterization method can efficiently capture the underlying geometric distribution patterns of the calcareous sand microstructure.

[0067] The quantitative evolution process of the model is in Figure 12The figure illustrates this, tracking various metrics on the training and validation sets to evaluate the model's generalization ability. The primary training objective, v-prediction loss, decreases sharply within the first 10 epochs and stabilizes after approximately 40 epochs. Crucially, the validation loss is closely correlated with the training loss, showing a minimal discrepancy, indicating that the model generalizes well to unseen microstructures without significant overfitting. The noise consistency mean squared error (MSE) exhibits a similar trend, serving as an indicator of the stability of the backdiffusion trajectory. The convergence of the validation curves demonstrates the statistical robustness of the learned denoising dynamics across the entire dataset. Finally, the structural similarity index (SSIM) shows a monotonically increasing trend, reaching a high similarity value of approximately 0.7 on both datasets. The high agreement between the SSIM curves on the training and validation sets confirms that the model can capture structural features of coral sand (e.g., pore connectivity and particle boundaries), rather than simply memorizing pixel-level noise patterns. Overall, the consistency of the training and validation set metrics demonstrates the numerical stability and representational power of the proposed framework.

[0068] Based on the variation patterns of various loss indicators, it can be seen that the proposed diffusion model can effectively learn the global geometric features and local topological properties required for the reconstruction of the microstructure of real calcareous sand, providing quantitative support for the reliability of the model performance.

[0069] To rigorously verify whether the diffusion model simultaneously captures the visual appearance and intrinsic statistical regularities of the microstructure of calcareous sand, this method calculated fourteen morphological characterization parameters for both real microscopic CT slices and model-generated synthetic slices. These parameters were divided into two categories: one category consists of particle boundary characterization parameters used to characterize the external morphology of particles, and the other category consists of intraparticle porosity characterization parameters used to quantify the internal pore structure of particles. The mathematical definitions of the two categories of parameters are summarized in Table 3.

[0070] This scheme uses mirrored histograms combined with kernel density estimation (KDE) curves to visualize and analyze the statistical distribution characteristics of the above-mentioned characterization parameters. The results are shown in the appendix. Figure 13 (Particle boundary parameters) and attachments Figure 14(Porosity scale parameters) are shown. In each statistical chart, the left vertical axis, represented by a blue curve, shows the parameter distribution characteristics of real calcareous sand particles, while the right vertical axis, represented by a red curve, shows the parameter distribution characteristics of model-generated particles. To quantitatively measure the similarity of their distributions, this scheme calculates and labels the Jensen-Shannon divergence (JS-D) between the real and generated distributions. The lower the divergence value, the greater the statistical consistency between the real and synthetic datasets. For particle boundary characterization parameters, the mirror histogram shows a high degree of symmetry in the parameter distributions of the real and generated samples. The distribution curves of area, perimeter, roundness, aspect ratio, convexity, and fractal dimension all show significant overlap, and the kernel density fitting curve of the generated samples closely matches the distribution contour of the real samples. This consistency indicates that the diffusion model can accurately reproduce the core scale characteristics of calcareous sand particles, including key attributes such as particle size range, elongation, boundary irregularity, and multi-scale roughness. The low Jensen-Shannon divergence (JS-D) values ​​corresponding to the above parameters further confirm that the model captures the global morphological variability of natural calcareous sand particles.

[0071] Only minor differences were observed in the number of skeleton branches, primarily in the tail region of the distribution curve. This parameter is highly sensitive to the high-frequency fluctuations in particle profiles, and the generated data exhibits a wider distribution range, indicating that the model introduces a moderate amount of additional variability in the undulating morphology of the fine particle boundaries. This phenomenon is entirely consistent with the stochastic nature of the generative model.

[0072] Table 3. Morphological and porosity-related descriptors used for quantitative evaluation of porous microstructures.

[0073] In summary, the quantitative comparison results show that the proposed diffusion model can accurately capture the core statistical laws of the microstructure of calcareous sand in two dimensions: particle-scale geometric features and pore-scale heterogeneity. The distributions of most characterization parameters are highly consistent, and the generated samples exhibit rich diversity. This indicates that the model does not mechanically memorize individual slices from the training set, but rather learns a reliable approximation of the potential probability distribution of the microstructure. The results of this approach lay a solid foundation for the application of the microstructures generated by the diffusion model in downstream analyses, such as discrete element method (DEM) numerical simulations and the construction of constitutive models based on microstructures.

[0074] This study demonstrates that the diffusion model can serve as a robust generative framework for the reconstruction and synthesis of complex calcareous sand microstructures. Compared to traditional process-based numerical simulation methods or adversarial learning models (such as Generative Adversarial Networks, GANs), the diffusion model's paradigm offers significant methodological advantages in geoscientific material applications. These advantages include stable training dynamics, a mathematically sound probabilistic sampling mechanism, and the inherent ability to characterize multi-scale spatial variability without concern for pattern collapse.

[0075] This study yielded a key conclusion from the experiments: the forward-reverse dynamics of the diffusion model can naturally reproduce the hierarchical organizational characteristics of the microstructure of calcareous sand. During the forward noise addition process, micro-scale features such as pore boundaries are masked by noise early on, while the macroscopic morphology of the particles is preserved at higher noise levels. Conversely, the reverse noise reduction process follows a pattern of first reconstructing the global geometry and then gradually refining high-frequency pore details. This characteristic is highly consistent with the physical nature of biodetrital calcareous sand particles—the macroscopic contours of such particles are relatively stable, while the arrangement of internal pores exhibits significant random fluctuations. (Appendix) Figure 8 - Appendix Figure 9 The visualization reconstruction results show that the model can achieve high-fidelity particle-scale structure reconstruction under moderate noise levels; while when the initial noise pollution level is high, the model can effectively utilize the learned real-world priors to synthesize reasonable structures that conform to the microscopic characteristics of calcareous sand. This consistency confirms that the model has successfully internalized the complex geometric laws governing the formation of natural calcareous sand.

[0076] Quantitative validation further corroborates the visual fidelity of the model's generated results. The 14 morphological characterization parameters selected in the scheme cover multiple dimensions, including particle external size indices, morphological roughness, porosity, and pore size distribution, and their statistical distributions are highly consistent with the real dataset. However, parameters sensitive to topological details or long-range spatial correlations (such as Euler number and two-point correlation function) remain unchanged. A slight bias was observed in the sample. This reflects the inherent challenge of capturing complex pore connectivity in two-dimensional slices—such topological features are highly sensitive to pixel-level perturbations. Nevertheless, the parameter distribution of the generated samples remains within the characteristic range of natural calcareous sand, faithfully reproducing the statistical heterogeneity observed in micro-CT images.

[0077] This paper proposes a generative framework based on a diffusion probability model for the reconstruction and synthesis of two-dimensional microstructures of calcareous sand. This framework combines a principal component analysis (PCA)-guided registration process with a virtual prediction (v-prediction) diffusion architecture, effectively standardizing particle orientation and learning complex reverse diffusion dynamics based on high-resolution micro-CT data. This method can perform high-precision reconstruction of noisy-contaminated slices and unconditionally generate realistic calcareous sand microstructures starting from pure Gaussian noise.

[0078] Experimental results show that the proposed model achieves stable convergence under various noise conditions and accurately reproduces multi-scale morphological features ranging from irregular particle boundaries to complex internal pores. Quantitative evaluation based on 14 morphological characterization parameters shows a high degree of statistical consistency between the real and generated datasets. The model faithfully reproduces the core geometric properties of calcareous sand, including macroscopic particle geometry, pore size distribution, and solid-pore distribution patterns. Although slight deviations were observed in indicators sensitive to microscopic topological features, the overall characteristics of the generated samples remain within the variability range of natural calcareous sand.

[0079] The results of the above scheme verify the reliability of the diffusion model as a digital material reconstruction tool, providing an scalable solution to the problem of data scarcity in geomechanical analysis. Future directions will focus on three aspects: first, extending the framework to three-dimensional microstructure reconstruction; second, introducing a conditional generation mechanism to achieve customized microstructures based on performance control; and third, embedding the synthesized microstructures into discrete element method (DEM) or computational fluid dynamics (CFD) simulations to explore their mechanical and hydraulic properties. Overall, the framework proposed in this scheme provides a flexible and physically plausible method for simulating the complex heterogeneity of biogenic geological materials.

[0080] To achieve the above objectives, the present invention also provides a two-dimensional porous microstructure reconstruction system for calcareous sand based on a diffusion model, such as... Figure 16 As shown, the system is applied to the diffusion-based two-dimensional porous microstructure reconstruction method for calcareous sand, and the system includes: A data creation and generation unit is used to create and acquire first data corresponding to calcareous sand particles, preprocess the first data, and generate second data corresponding to a single calcareous sand particle; wherein, the first data is microscopic CT scan three-dimensional image data of calcareous sand particles; and the second data is binarized three-dimensional voxel characterization data. The data processing and generation unit is used to spatially oriented and align the second data, generate and acquire third data corresponding to the directional cross section, and construct a first dataset corresponding to the calcareous sand based on the third data; wherein, the third data is standardized two-dimensional slice image data along a specific directional cross section after alignment processing; the third data is a training dataset of the microstructure of calcareous sand. The model creation and generation unit is used to create and generate a corresponding first model based on the U-Net architecture, train and process the first model according to the first dataset, and construct and generate a corresponding second model; wherein, the first model is a denoising diffusion probability model; and the second model is a trained diffusion model. The data reconstruction generation unit is used to reconstruct and generate fourth data corresponding to calcareous sand through the second model and in combination with the reverse denoising process; wherein the fourth data is two-dimensional porous microstructure image data.

[0081] The data processing and generation unit further includes: The first processing module is used to construct a covariance matrix corresponding to the particle voxels, decompose the covariance matrix to generate fifth data corresponding to the particle voxels, and use the plane of the fifth data as a reference plane to create a corresponding two-dimensional slice plane; wherein, the fifth data is the principal feature vector; the first generation module is used to create a two-dimensional slice image corresponding to the calcareous sand particles, construct a corresponding standard-sized image by combining a zero-value filling method, and linearly normalize the pixel values ​​of the standard-sized image to a preset numerical range; And / or, the model creation and generation unit further includes: The second generation module is used to construct the first model using the v-prediction parameterization method; wherein, the model prediction target is defined as a linear combination of the source signal and the injected noise, and the specific expression is: (7) In the formula, For pure microscopic structure images, For noise, and To be consistent with diffusion time step Correlation coefficients; the model training objective function is prediction speed. The mean square error between the target velocity and the target velocity; The second processing module is used to control the noise addition intensity at different time steps during the forward diffusion process through cosine scheduling, and to perform sampling processing in the reverse denoising process according to the DDPM or DDIM algorithm. The model training module is used to train the model by combining the time step embedding vectors and to integrate the time step embedding vectors into the convolutional blocks of the U-Net architecture; wherein, the U-Net architecture includes an encoding path, a decoding path and a skip connection connecting the two. And / or, the data reconstruction generation unit further includes: a third generation module, used to create and generate sixth data corresponding to calcareous sand based on the second model, starting from random noise conforming to a Gaussian distribution and combining it with a reverse diffusion trajectory; wherein the sixth data is a novel two-dimensional porous microstructure image data of calcareous sand; a fourth generation module, used to generate and acquire seventh data corresponding to calcareous sand; wherein the seventh data is a noisy microstructure image data of calcareous sand; and a fifth generation module, used to reconstruct and generate fourth data with high clarity corresponding to calcareous sand based on the seventh data, according to the second model, and combined with a conditional inverse denoising process.

[0082] In the system embodiment of the present invention, the specific details of the method steps involved in the reconstruction of the two-dimensional porous microstructure of calcareous sand based on the diffusion model have been described above. That is to say, the functional modules in the system are used to implement the steps or sub-steps in the above method embodiment, which will not be repeated here.

[0083] To achieve the above objectives, the present invention also provides a two-dimensional porous microstructure reconstruction platform for calcareous sand based on a diffusion model, such as... Figure 17 As shown, the system includes a processor, a memory, and a control program for a diffusion-model-based two-dimensional porous microstructure reconstruction processing platform for calcareous sand. The processor executes the diffusion-model-based control program, which is stored in the memory. This control program implements the steps of the diffusion-model-based two-dimensional porous microstructure reconstruction processing method for calcareous sand. The specific details of these steps have been described above and will not be repeated here.

[0084] In this embodiment of the invention, the processor built into the diffusion-model-based calcareous sand two-dimensional porous microstructure reconstruction processing platform can be composed of integrated circuits, such as a single packaged integrated circuit or multiple integrated circuits with the same or different functions, including combinations of one or more central processing units (CPUs), microprocessors, digital processing chips, graphics processors, and various control chips. The processor connects to various components using various interfaces and lines, and executes programs or units stored in memory, as well as calls data stored in memory, to perform various functions and process data for the diffusion-model-based calcareous sand two-dimensional porous microstructure reconstruction processing. The memory, used to store program code and various data, is installed in the diffusion-model-based two-dimensional porous microstructure reconstruction processing platform for calcareous sand and enables high-speed, automatic access to programs or data during operation. The memory includes read-only memory (ROM), random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), one-time programmable read-only memory (OTPROM), electrically erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, disk storage, magnetic tape storage, or any other computer-readable medium capable of carrying or storing data.

[0085] To achieve the above objectives, the present invention also provides a computer-readable storage medium, such as... Figure 18 As shown, the computer-readable storage medium stores a control program for a diffusion-model-based reconstruction processing platform for the two-dimensional porous microstructure of calcareous sand. This control program implements the steps of the diffusion-model-based reconstruction processing method for the two-dimensional porous microstructure of calcareous sand. The specific details of these steps have been described above and will not be repeated here.

[0086] In the description of embodiments of the present invention, it should be noted that any process or method description in the flowcharts or otherwise described herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing a particular logical function or process, and the scope of the preferred embodiments of the present invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order according to the functions involved, as should be understood by those skilled in the art to which the embodiments of the present invention pertain.

[0087] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processing module, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, a “computer-readable medium” can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, the computer-readable medium can even be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0088] This invention creates and acquires first data corresponding to calcareous sand particles through a method, preprocesses the first data, and generates second data corresponding to a single calcareous sand particle; wherein, the first data is microscopic CT scan three-dimensional image data of calcareous sand particles; the second data is binarized three-dimensional voxel characterization data; the second data is spatially oriented and aligned, generating and acquiring third data corresponding to directional sections, and constructing a first dataset corresponding to calcareous sand based on the third data; wherein, the third data is standardized two-dimensional slice image data along a specific directional section after alignment; the third data is a training dataset for the microstructure of calcareous sand; based on the U-Net architecture... A first model is generated, and the first model is trained and processed based on the first dataset to generate a corresponding second model. The first model is a denoised diffusion probability model, and the second model is a trained diffusion model. Through the second model and combined with the reverse denoising process, a fourth dataset corresponding to calcareous sand is reconstructed. The fourth dataset is two-dimensional porous microstructure image data, along with the corresponding system, platform, and storage medium to generate high-fidelity digital samples of the two-dimensional microstructure of calcareous sand. This solves the problem of insufficient microstructure data due to limitations in experimental methods and provides a reliable data foundation for numerical simulation and mechanism research in marine geotechnical engineering.

[0089] In other words, this invention integrates principal component analysis-based directional alignment with a v-predictive diffusion model to achieve high-fidelity reconstruction and generation of the extremely complex microstructure of calcareous sand. The generated two-dimensional microstructure images not only visually closely match real CT slices but also exhibit high consistency in the statistical distribution of 14 key morphological parameters, including porosity, fractal dimension, and skeletal complexity, thus verifying their physical authenticity. This invention also possesses dual capabilities of unconditional generation and conditional reconstruction, capable of synthesizing a large number of statistically reasonable digital samples from scratch to expand scarce datasets, and intelligently enhancing low-quality experimental images. It provides a stable, efficient, and scalable digital material source for discrete element numerical simulation, permeability prediction, and microstructure-oriented constitutive model development of calcareous sand, overcoming the bottlenecks of traditional experimental methods in terms of data acquisition cost, scale, and efficiency.

[0090] In other words, calcareous sand is a biogenic sediment characterized by highly irregular grain morphology, well-developed multi-scale porosity within the grains, and fragility, which gives it complex mechanical and hydraulic properties in marine geotechnical engineering systems. Although X-ray microcomputed tomography (microCT) technology can directly observe these microstructural features, its high cost and limited scanning volume severely restrict the acquisition of representative datasets. To address this data scarcity issue, this proposal suggests a generative framework based on a diffusion model for reconstructing the two-dimensional porous microstructure of calcareous sand.

[0091] This approach first uses principal component analysis to orient and align 3D calcareous sand particles obtained from CT scans, then extracts representative slices to construct a standardized microstructure dataset. Subsequently, a v-predictive diffusion model is trained using the UNet denoising network as its backbone, enabling it to learn the statistical distribution patterns of porous structures. The model is first validated using a rotation-enhanced baseline morphology, and the results show that it possesses a stable denoised trajectory and orientation invariance. Furthermore, increasing the number of rotational samples improves the model's convergence performance.

[0092] When the model was applied to the reconstruction of real calcareous sand slices, the generated microstructures matched the morphology of the actual CT measurements, and quantitatively reproduced key indicators such as porosity, boundary roughness, number of pores, fractal dimension, and skeletal complexity. Further comparison of the distribution levels based on kernel density estimation and Jensen-Shannon divergence confirmed that the generated samples had a high degree of statistical consistency with the real samples.

[0093] This framework provides an scalable technical approach for digital microstructure reconstruction and has significant application potential in marine geotechnical engineering schemes such as discrete element / finite discrete element (DEM / FDEM) numerical simulation, permeability coefficient estimation, and constitutive model construction based on microstructure.

[0094] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model, characterized in that, The method includes: First data corresponding to calcareous sand particles is created and acquired; the first data is preprocessed and second data corresponding to a single calcareous sand particle is generated; wherein, the first data is microscopic CT scan three-dimensional image data of calcareous sand particles; and the second data is binarized three-dimensional voxel characterization data. The second data is spatially oriented and aligned to generate and acquire third data corresponding to the directional cross section, and a first dataset corresponding to calcareous sand is constructed based on the third data; wherein, the third data is standardized two-dimensional slice image data of a specific directional cross section after alignment; the third data is a training dataset of calcareous sand microstructure; A first model is created based on the U-Net architecture. The first model is trained and processed using the first dataset, and a second model is constructed and generated accordingly. The first model is a denoising diffusion probability model, and the second model is a pre-trained diffusion model. Using the second model and combined with the reverse denoising process, fourth data corresponding to calcareous sand is reconstructed; wherein, the fourth data is two-dimensional porous microstructure image data.

2. The method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model according to claim 1, characterized in that, The spatial orientation alignment process for the second data, generating and acquiring third data corresponding to the directional cross-section, and constructing a first dataset corresponding to calcareous sand based on the third data, further includes: Construct a covariance matrix corresponding to the particle voxels, decompose the covariance matrix to generate fifth data corresponding to the particle voxels, and use the plane of the fifth data as a reference plane to create a corresponding two-dimensional slice plane; wherein, the fifth data is the principal feature vector. Two-dimensional slice images corresponding to calcareous sand particles are created, and images of corresponding standard sizes are constructed using a zero-value filling method. The pixel values ​​of the standard-size images are then linearly normalized to a preset numerical range.

3. The method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model according to claim 1 or 2, characterized in that, The process of creating and generating a corresponding first model based on the U-Net architecture, training and processing the first model using the first dataset, and constructing and generating a corresponding second model further includes: The first model is constructed using the v-prediction parameterization method; the model prediction target is defined as a linear combination of the source signal and the injected noise, specifically expressed as: (7) In the formula, For pure microscopic structure images, For noise, and To be consistent with diffusion time step Correlation coefficients; the model training objective function is prediction speed. The mean square error between the target velocity and the target velocity.

4. The method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model according to claim 3, characterized in that, The process of creating and generating a corresponding first model based on the U-Net architecture, training and processing the first model using the first dataset, and constructing and generating a corresponding second model further includes: The noise addition intensity at different time steps during the forward diffusion process is controlled by cosine scheduling, and sampling processing is performed during the reverse denoising process according to the DDPM or DDIM algorithm. The model is trained by combining time-step embedding vectors, and the time-step embedding vectors are incorporated into the convolutional blocks of the U-Net architecture; wherein the U-Net architecture includes an encoding path, a decoding path, and skip connections connecting the two.

5. The method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model according to claim 1, characterized in that, The process of reconstructing and generating fourth data corresponding to calcareous sand using the second model and in conjunction with a reverse denoising process also includes: Based on the second model, starting from random noise conforming to a Gaussian distribution and combining it with the reverse diffusion trajectory, a sixth data corresponding to calcareous sand is created; wherein, the sixth data is a novel two-dimensional porous microstructure image data of calcareous sand.

6. A method for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model, as described in claim 1 or 5, characterized in that, The process of reconstructing and generating fourth data corresponding to calcareous sand using the second model and in conjunction with a reverse denoising process also includes: Generate and acquire seventh data corresponding to calcareous sand; wherein, the seventh data is noisy calcareous sand microstructure image data; Based on the seventh data, according to the second model, and combined with the conditional inverse denoising process, a fourth data with high clarity corresponding to the calcareous sand is reconstructed.

7. A system for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model, characterized in that, The system is applied to the diffusion-based two-dimensional porous microstructure reconstruction method for calcareous sand as described in any one of claims 1 to 6, and the system comprises: A data creation and generation unit is used to create and acquire first data corresponding to calcareous sand particles, preprocess the first data, and generate second data corresponding to a single calcareous sand particle; wherein, the first data is microscopic CT scan three-dimensional image data of calcareous sand particles; and the second data is binarized three-dimensional voxel characterization data. The data processing and generation unit is used to spatially oriented and align the second data, generate and acquire third data corresponding to the directional cross section, and construct a first dataset corresponding to the calcareous sand based on the third data; wherein, the third data is standardized two-dimensional slice image data along a specific directional cross section after alignment processing; the third data is a training dataset of the microstructure of calcareous sand. The model creation and generation unit is used to create and generate a corresponding first model based on the U-Net architecture, train and process the first model according to the first dataset, and construct and generate a corresponding second model; wherein, the first model is a denoising diffusion probability model; and the second model is a trained diffusion model. The data reconstruction generation unit is used to reconstruct and generate fourth data corresponding to calcareous sand through the second model and in combination with the reverse denoising process; wherein the fourth data is two-dimensional porous microstructure image data.

8. The system for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model according to claim 7, characterized in that, The data processing and generation unit further includes: The first processing module is used to construct a covariance matrix corresponding to the particle voxels, decompose the covariance matrix to generate fifth data corresponding to the particle voxels, and use the plane of the fifth data as a reference plane to create a corresponding two-dimensional slice plane; wherein, the fifth data is the principal feature vector. The first generation module is used to create a two-dimensional slice image corresponding to the calcareous sand particles, construct a corresponding standard-sized image by combining a zero-value filling method, and linearly normalize the pixel values ​​of the standard-sized image to a preset numerical range. And / or, the model creation and generation unit further includes: The second generation module is used to construct the first model using the v-prediction parameterization method; wherein, the model prediction target is defined as a linear combination of the source signal and the injected noise, and the specific expression is: (7) In the formula, For pure microscopic structure images, For noise, and To be consistent with diffusion time step Correlation coefficients; the model training objective function is prediction speed. The mean square error between the target velocity and the target velocity; The second processing module is used to control the noise addition intensity at different time steps during the forward diffusion process through cosine scheduling, and to perform sampling processing in the reverse denoising process according to the DDPM or DDIM algorithm. The model training module is used to train the model by combining the time step embedding vectors and to integrate the time step embedding vectors into the convolutional blocks of the U-Net architecture; wherein, the U-Net architecture includes an encoding path, a decoding path and a skip connection connecting the two. And / or, the data reconstruction generation unit further includes: The third generation module is used to create a sixth data corresponding to calcareous sand based on the second model, starting from random noise that conforms to a Gaussian distribution and combining it with the reverse diffusion trajectory; wherein, the sixth data is a brand-new two-dimensional porous microstructure image data of calcareous sand. The fourth generation module is used to generate and acquire the seventh data corresponding to the calcareous sand; wherein, the seventh data is noisy calcareous sand microstructure image data; The fifth generation module is used to reconstruct and generate fourth data with high clarity that corresponds to the calcareous sand based on the seventh data, according to the second model, and in combination with the conditional inverse denoising process.

9. A platform for reconstructing the two-dimensional porous microstructure of calcareous sand based on a diffusion model, characterized in that, The system includes a processor, a memory, and a control program for a diffusion-model-based reconstruction processing platform for two-dimensional porous microstructures of calcareous sand. The processor executes the diffusion-model-based control program for the reconstruction processing platform for two-dimensional porous microstructures of calcareous sand, which is stored in the memory. This diffusion-model-based control program implements the diffusion-model-based reconstruction processing method for two-dimensional porous microstructures of calcareous sand as described in any one of claims 1 to 6.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a control program for a diffusion-based two-dimensional porous microstructure reconstruction processing platform for calcareous sand. This diffusion-based two-dimensional porous microstructure reconstruction processing platform control program implements the diffusion-based two-dimensional porous microstructure reconstruction processing method for calcareous sand as described in any one of claims 1 to 6.

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