Porous medium internal structure reconstruction method based on attenuation condition diffusion model

Abstract

The invention discloses a porous medium internal structure reconstruction method based on an attenuation condition diffusion model. The internal structure of the porous medium is reconstructed by constructing the attenuation condition diffusion model. The attenuation condition diffusion model takes a denoising diffusion probability model DDPM as a generation framework and a three-dimensional U-Net network as a reverse denoising network. The method comprises the following steps: inputting three mutually vertical outer surface images of a three-dimensional porous medium sample and corresponding porosity values and specific surface area values as input conditions into an attenuation condition diffusion model, introducing an axially related attenuation weight in a reverse generation process of a denoising diffusion probability model DDPM, and adaptively fusing surface information through a three-dimensional U-Net network, and the voxel-level feature generation is guided, so that the internal microstructure can be accurately reconstructed only by depending on the outer surface. According to the method, high-fidelity and low-uncertainty reconstruction results can be obtained under different porosity and heterogeneous conditions, and the method is widely applied to the fields of digital rock physics, geoscience modeling and the like.

Description

Technical Field

[0001] This invention relates to the fields of rock physics and deep learning image processing technology, specifically a method for reconstructing the internal structure of porous media based on an attenuation conditional diffusion model. Background Technology

[0002] Porous media are widely found in nature and engineering materials. Their internal pore structure determines macroscopic behaviors such as fluid flow, solute transport, heat conduction, and mechanical properties, and has important applications in fields such as groundwater environments, oil and gas exploration, geological energy storage, pollution remediation, and the design of new energy materials. The three-dimensional pore geometry is complex and diverse, including porosity, pore throat size distribution, connectivity, and anisotropy, which directly affect the permeability, dispersion coefficient, and mechanical strength of underground media. Therefore, accurately obtaining the three-dimensional microstructure of porous media is crucial for understanding the physicochemical processes of the media, conducting digital rock physics simulations, predicting macroscopic properties, and designing materials.

[0003] Traditional methods for obtaining the internal structure of porous media rely on X-ray microcomputed tomography. Focused ion beam scanning electron microscope Non-destructive imaging techniques such as nuclear magnetic resonance imaging can be used to provide three-dimensional voxel data of the interior of the medium. However, high-resolution imaging is often expensive, time-consuming, and complex to process, and has strict requirements on sample size and material, thus limiting the amount of large-scale high-quality data that can be obtained. In addition, due to the high spatial heterogeneity and multi-scale structure of rock reservoirs and engineering materials, a single sample is difficult to represent the entire distribution, and the scarcity of data leads to uncertainty in digital rock analysis and statistical inference. In current research, microstructure characterization and reconstruction (MCR) methods usually include two categories: (1) using physical descriptors such as correlation functions, porosity distribution, and specific surface area to statistically analyze porous structures, and then generating three-dimensional samples that meet these statistical characteristics through random optimization algorithms or simulated annealing; (2) using methods such as spectral texture analysis, morphological description, Gaussian random fields, or multi-point statistics to simulate pore space. Although these methods can generate structures that meet statistical constraints to a certain extent, they require a large number of high-order statistics, have high computational costs, and perform poorly when dealing with complex anisotropic and highly heterogeneous structures.

[0004] In recent years, deep generative models have emerged as a new tool for digital rock analysis. Variational Autoencoders (VAEs) learn the latent space distribution of training samples through probabilistic encoding, enabling rapid generation of porous media with statistical consistency. However, they are prone to oversmoothing and feature blurring. Generative Adversarial Networks (GNNs) generate realistic images through adversarial training, but often suffer from training instability, mode collapse, and difficulty in controlling output, and are prone to losing details in high-resolution 3D reconstruction. In contrast, diffusion models, as a novel probabilistic generative framework, model data distribution using forward noise addition and backward denoising, offering advantages such as stable training, high sample diversity, and high detail fidelity. Diffusion models have demonstrated superior performance compared to VAEs and GANs in tasks such as image generation, material structure super-resolution, semantic segmentation, and porous media expansion.

[0005] To infer complete 3D structures from limited observational information, researchers have developed conditional generative models, which generate 3D porous media that meet given material parameters, 2D slices, or external properties. Methods such as SliceGAN, BicycleGAN, and SPGAN use single or multiple 2D slices as conditions to generate 3D volumes through VAE or GAN frameworks; however, due to limitations in their model architecture, it is difficult to maintain both local and global structural consistency simultaneously. Micro3Diff, based on a 2D diffusion model, has... Reconstruction attempts are made, but their performance depends on the diversity of training samples and the location of slices, and they are prone to breakage or artifacts in complex topological structures.

[0006] Therefore, designing a method that can both utilize the rich information contained in the external surface and achieve stable training and high-precision reconstruction within a deep diffusion framework is a key challenge in the field of microstructure reconstruction. Summary of the Invention

[0007] The purpose of this invention is to provide a method for reconstructing the internal structure of porous media based on an attenuation conditional diffusion model. This method utilizes three mutually perpendicular outer surface images of a three-dimensional porous media sample as conditional inputs. Axially correlated attenuation weights are introduced during the inverse generation process of the denoising diffusion probability model (DDPM). The network adaptively fuses surface information to guide the generation of voxel-level features, thereby accurately reconstructing the internal microstructure by relying solely on the outer surface.

[0008] To solve the above-mentioned technical problems, the present invention provides the following technical solution: A method for reconstructing the internal structure of porous media based on an attenuation-conditional diffusion model includes the following steps: Data acquisition involved collecting synthetic porous media datasets and real core datasets. The synthetic porous media dataset used the DeePore dataset as the primary training data source, while the real core datasets included Berea Upper Gray Sandstone and Claystone. The former exhibits homogeneous texture and stable pore connectivity, while the latter displays a distinct layered structure and a porous system with low connectivity.

[0009] Data preprocessing involves downsampling and normalizing both the synthetic porous media dataset and the real core dataset, followed by data augmentation. Specifically, to adapt to diffusion model training, the synthetic porous media dataset samples are downsampled and normalized. Simultaneously, for each 3D sample, from... Three two-dimensional images are obtained by taking a slice of the outer surface along each of the three axes. These slice images contain boundary information, pore distribution, and local texture of the three-dimensional structure. Their porosity and specific surface area values ​​are calculated and then used as input conditions for the model. Data augmentation method: To enhance training diversity, during preprocessing, three mutually perpendicular outer surfaces are randomly selected from six outer surfaces for any given core sample, resulting in eight possible surface condition combinations for the same core. This strategy significantly increases the size of the effective dataset and enables the model to capture anisotropy in structural reconstruction. Once trained, the model can randomly reconstruct 3D volumes under any orthogonal surface set, ensuring strong generalization ability in different directions.

[0010] A decay-conditional diffusion model is constructed, using the Denoising Diffusion Probability Model (DDPM) as the generation framework. The forward diffusion process progressively adds Gaussian noise to the training samples, while the reverse diffusion process... Predict noise and combine it with conditional information to recover a clear 3D structure; Model training employed the Adam optimizer to train a decaying conditional diffusion model. To avoid instability in the early stages of training, cosine annealing was used for learning rate scheduling. Random sampling was implemented during training. This ensures that the model learns noise prediction at each time step; The internal structure reconstruction of porous media involves inputting three mutually perpendicular outer surface images of a 3D porous media sample, along with their corresponding porosity and specific surface area values, into an attenuation-conditional diffusion model. Axially correlated attenuation weights are introduced during the inverse generation of the denoising diffusion probability model (DDPM). This is achieved through 3D... The network adaptively fuses surface information to guide voxel-level feature generation, resulting in a reconstructed internal structure of the porous medium. The attenuation weights are automatically learned during model training, and their magnitude decreases exponentially with the voxel distance from feature points at different levels to the outer surface. Different attenuation scales can be learned for different axes. The outer surface image is used to extract features via a 2D convolutional encoder, then copied along an axis perpendicular to the surface to form a 3D feature tensor. A projection operation is then performed to adjust the number of channels to match the surface's dimensions. The feature dimensions of different layers are consistent, and conditional fusion is achieved by adding the current feature map to each layer.

[0011] According to the above technical solution, the three-dimensional U-Net network includes an input layer, an encoder, a bottleneck layer, a decoder, and an output layer; The bottleneck layer includes several conditional residual convolutional blocks and an attention module; the conditional residual convolutional block includes a convolutional layer and an adder block with axial decay weights; The decoder and the encoder employ symmetrical sampling layers followed by conditional residual convolutional blocks. The cross-resolution skip connection connects the encoder and the corresponding layers of the decoder, and through an adder block with axial attenuation weights, the conditional guidance information is continuously fused at each layer. The bottleneck layer includes several conditional residual convolutional blocks and an attention module.

[0012] Among them, the 3D U-Net network is used as the reverse denoising network. The network integrates hierarchical convolutional coding, multi-scale latent representation and symmetric decoding structure with skip connections. The network is specially designed with an integration mechanism of temporal embedding and surface conditional embedding, which can maintain the temporal consistency in the diffusion process and realize spatial anisotropy guidance by utilizing boundary prior knowledge. The encoder downsamples the volume data step by step through a series of conditional residual convolutional blocks (ResBlocks). Each module of the encoder includes: (1) 3D convolutional layer followed by GroupNorm normalization and Swish / SiLU activation function; (2) temporal step conditional bias injection mechanism; (3) conditional residual injection implemented by the addition module, that is, adding the embedding vector from the surface at each resolution level; The decoder employs an architecture symmetrical to the encoder, consisting of upsampling layers (trilinear interpolation or transposed convolution) followed by conditional residual convolutional blocks. Cross-resolution jumps connect corresponding layers in the encoder and decoder, ensuring that fine-grained structural information is transmitted throughout the network.

[0013] According to the above technical solution, the axial attenuation weight is defined as follows: ,in Let be the distance between the voxel and the outer surface along a certain axis. The attenuation coefficient is learned along this axis. The outer surface image is mapped to a feature map using a 2D convolutional encoder. After being resized using bilinear interpolation, it is copied along the corresponding axis to form a 3D tensor, which is then multiplied by a decay weight and injected. The feature map enables spatial consistency fusion of information on conditions with different axes.

[0014] A series of learnable axial attenuation weights are introduced into the feature maps at each scale to perform distance-weighted attenuation of the outer surface information at different depths.

[0015] According to the above technical solution, the adder block with axial attenuation weight is at each level For any axial direction Apply guidance separately: ; in, Indicates from the surface a Extracted two-dimensional conditional tensor; It is a lightweight 2D convolutional encoder that projects surface conditions into 2D feature maps; Perform bilinear interpolation to match the first Spatial resolution of conditional residual convolution blocks; Along with the surface a orthogonal axes a Copy the binary feature map to generate a size of The three-dimensional tensor; Project the conditional channels onto the feature dimensions of the conditional residual convolutional block. , Then it means the first The attenuation weight in the stage depends on the axial direction.

[0016] Through additive blocks with axial attenuation weights, conditional guidance information is continuously fused at each level, enabling surface condition information to be injected into the latent representation space in a distance-aware manner.

[0017] According to the above technical solution, the three-dimensional U-Net network in Hierarchical feature maps The added total guide is the sum of contributions in all three axes. : ; ; In the formula, Show Contribution on the axis Indicates in Contribution on the axis Indicates in Contribution on the axis This represents the current feature map.

[0018] According to the above technical solution, a positional encoding function is used to map the time step into a high-dimensional vector, and the above-mentioned... The input layer of the network is concatenated with the feature map.

[0019] According to the above technical solution, the step of reconstructing the internal structure of the porous medium includes: Using three mutually perpendicular outer surface images of a three-dimensional porous medium sample, along with their corresponding porosity and specific surface area values, as input conditions, a forward diffusion process is gradually applied to the sample using a denoised diffusion probability model. Adding noise to generate pure noise ; Pure noise The input is fed into a 3D U-Net, where the encoder maps the outer surface image into a feature map. After being resized using bilinear interpolation, it is copied along the corresponding axis as a 3D tensor. A positional encoding function is then used to map the time steps into a high-dimensional vector, which is concatenated with the feature map in the input layer of the U-Net network to enhance temporal information. Finally, it is multiplied by the decay weights in an additive block with axial decay weights and then injected. The feature map is used to perform distance-weighted attenuation of the outer surface information at different depths. Conditional guidance information is continuously fused at each level to achieve spatial consistency fusion of conditional information across different axes, and the output prediction noise is then generated. ; By using the reverse sampling formula of DDPM to gradually reverse the forward noise addition, the reconstructed internal structure of the porous medium is obtained.

[0020] According to the above technical solution, the back sampling formula of DDPM is: ; In the formula, Indicates from time step The previous time step obtained by backsampling The sample, Indicates time step Noisy samples at that location Indicates time step Noise, z Represents a random variable that follows a standard normal distribution. ; This represents the standard deviation of the random noise added during the backsampling process. This refers to a noise predictor (i.e., U-Net). y This indicates surface guidance information.

[0021] According to the above technical solution, the loss function for training the attenuation conditional diffusion model is the improved mean squared error (MSE): ; in, For noise samples in forward diffusion, y Information is provided for the three outer surfaces.

[0022] The training objective is to make the noise predicted by the U-Net network closely resemble the actual noise.

[0023] The evaluation metrics of this invention include: calculating structural similarity (SSIM) and mean squared similarity on the validation and test sets. Coefficient of determination R 2 and two-point correlation functions Simultaneously, the porosity distribution, standard deviation, and specific surface area of ​​the reconstructed volume were statistically analyzed to assess the model's generalization ability across different porosity ranges.

[0024] According to another aspect of the present invention, the present invention further provides an electronic device, comprising: one or more processors; and a storage device for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to perform a method for reconstructing the internal structure of a porous medium based on an attenuation conditional diffusion model as described in any of the above technical solutions.

[0025] According to another aspect of the present invention, the present invention further provides a storage medium storing at least one instruction, which is loaded and executed by a processor to implement the method for reconstructing the internal structure of a porous medium based on a decay conditional diffusion model as described in any of the above technical solutions.

[0026] Compared with existing technologies, the beneficial effects achieved by this invention are as follows: This invention utilizes three mutually perpendicular outer surface images of a three-dimensional porous medium sample as conditional inputs. Axially correlated attenuation weights are introduced during the reverse generation process of the Denoising Diffusion Probability Model (DDPM). Surface information is adaptively fused through a three-dimensional U-Net network to guide voxel-level feature generation, thereby accurately reconstructing the internal microstructure based solely on the outer surface. Compared with traditional MCR methods and unconditional or conditional models based on GAN / VAE, this invention has the advantages of stable training, high reconstruction accuracy, and the ability to accurately infer the three-dimensional structure without internal slicing. Users can infer the internal pore geometry based solely on surface information, opening up new pathways for understanding and designing porous materials and potentially improving the level of underground reservoir exploration and geological resource management. Attached Figure Description

[0027] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of the steps of a method for reconstructing the internal structure of porous media based on an attenuation condition diffusion model according to the present invention. Figure 2 These are diagrams showing eight different surface condition combinations corresponding to the same core sample. Figure 3 The implementation examples demonstrate the reconstruction performance on the DeePore dataset (SSIM, MS-SSIM, and...). R 2 ); Figure 4 It is the two-point correlation function of the implementation example on the DeePore dataset. ; Figure 5 This is the reconstruction result of the implementation example on the Berea Upper Gray Sandstone and Claystone datasets. Detailed Implementation

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] This embodiment reduces the sample size of the DeePore dataset by 64 times (256) through downsampling. 3 Up to 64 3 At the same time, the spatial structure and texture of the porous medium were meticulously preserved. Berea Upper Gray Sandstone and Claystone core samples underwent similar processing, with sizes ranging from 500... 3 Compress to 100 3 The sample dataset used is shown in Table 1: Table 1 Sample Dataset

[0030] The model was trained and tested on large-scale synthetic datasets (DeePore) and real core samples (such as Berea Upper Gray Sandstone and Claystone) to verify its reconstruction accuracy and generalization ability under different porosity ranges, rock types, and heterogeneity levels, achieving a level where the structural similarity of individual samples is close to 1 and the two-point correlation functions are highly consistent. Specific steps include: S1. Obtain a large-scale synthetic dataset (DeePore) and real core samples (such as Berea Upper Gray Sandstone, Claystone, etc.). For the DeePore dataset, this example selects 15,000 volumes with porosity values ​​between 0.1 and 0.4, evenly distributed across three intervals (0.1-0.2, 0.2-0.3, and 0.3-0.4; 5,000 volumes per interval). Each interval is divided into training and testing sets in an 8:2 ratio, resulting in a total of 12,000 training volumes and 3,000 testing volumes. The training and testing sets are further expanded to 96,000 and 24,000 volumes, respectively.

[0031] For the Berea Upper Gray Sandstone and Claystone core samples, this embodiment constructed two datasets containing 216 sub-volumes, of which 175 sub-volumes were used for training (expanded to 1400 volumes after data augmentation), and the rest were used for testing.

[0032] S2. Downsample and normalize the samples in the large-scale synthetic dataset DeePore to 64. 3 The size is within the range of 0–1, where the porous phase is marked with a non-zero value and the solid phase is marked with a zero value.

[0033] For each 3D sample, from Three two-dimensional images are obtained by taking a slice of the outer surface along each of the three axes. These slice images contain boundary information, pore distribution, and local texture of the three-dimensional structure. Their porosity and specific surface area values ​​are calculated and then used as input conditions for the model.

[0034] Meanwhile, to enhance the diversity of training, during the preprocessing process, three mutually perpendicular outer surfaces were randomly selected from six outer surfaces for any core sample, resulting in a total of eight surface condition combinations corresponding to the same core sample. Figure 2 This strategy significantly increases the size of the effective dataset and enables the model to capture anisotropy in structural reconstruction. Once trained, the model can randomly reconstruct 3D volumes under any orthogonal surface set, thus ensuring strong generalization ability in different directions.

[0035] S3. Construct an attenuation conditional diffusion model, using the denoising diffusion probability model DDPM as the generation framework and a three-dimensional U-Net network as the inverse denoising network.

[0036] Wherein, the original data distribution is assumed to be The forward diffusion process gradually moves towards the sample. Add noise generation Specifically ,in , , This is a noise scheduling sequence. The number of noise steps is set. T With linear or cosine noise scheduling, the smoothness of forward diffusion can be controlled; The 3D U-Net network includes an input layer, encoder, bottleneck layer, decoder and output layer, and a series of learnable axial attenuation weights are introduced on the feature maps at each scale to perform distance-weighted attenuation of the outer surface information at different depths. The decoder and encoder employ symmetrical sampling layers followed by conditional residual convolutional blocks; cross-resolution jumps connect the encoder and decoder to their corresponding layers, and through adder blocks with axial attenuation weights, conditional guidance information is continuously fused at each layer. The bottleneck layer includes several conditional residual convolutional blocks and attention modules. Axial attenuation weight is defined as ,in Let be the distance between the voxel and the outer surface along a certain axis. The attenuation coefficient is learned along this axis. The outer surface image is mapped into a feature map using a two-dimensional convolutional encoder. After being resized by bilinear interpolation, it is copied into a three-dimensional tensor along the corresponding axis. This tensor is then multiplied by the attenuation weights and injected into the feature map of U-Net, achieving spatial consistency fusion of information under different axial conditions.

[0037] S4. The Adam optimizer is used to train the decay-based conditional diffusion model.

[0038] For the DeePore dataset, the decay conditional diffusion model was trained in parallel for 160 epochs on four NVIDIA RTX 4090 GPUs with a batch size of 16. On average, it trained 64... 3 Sampling (inference) of the volume under surface conditions takes approximately 16 seconds. For a broader evaluation, this embodiment additionally extracted 2000 DeePore volumes with porosities between 0.40 and 0.45, applied the same enhancement method, and performed 16,000 reconstructions. On a single NVIDIA A100 GPU, each 64 3 The average reasoning time for volume is approximately 25 seconds.

[0039] For the Berea Upper Gray Sandstone and Claystone core samples, training was performed on four NVIDIA RTX 4090 GPUs with a batch size of 4, while inference was benchmarked on a single NVIDIA A100 GPU.

[0040] The heterogeneous core structures of Berea Upper Gray Sandstone and Claystone show that the former exhibits stronger connectivity, relatively uniform pore distribution, consistent grain size, and a more homogeneous overall structure. The latter, however, displays a significant layered, dense structure with irregular pore morphology, reflecting strong microscopic heterogeneity and anisotropy. The characteristic scales of the two differ by more than two orders of magnitude (approximately 1125 μm and 5 μm, respectively). In this embodiment, 20 random samples were performed on each of the two datasets, and the results are as follows: Figure 5 As shown in A and B in the diagram.

[0041] S5. The three mutually perpendicular outer surface images of the three-dimensional porous medium sample, along with their corresponding porosity and specific surface area values, are input into the attenuation-conditional diffusion model. Axially correlated attenuation weights are introduced during the reverse generation process of the denoising diffusion probability model DDPM. Surface information is adaptively fused through a three-dimensional U-Net network to guide voxel-level feature generation, resulting in the reconstructed internal structure of the porous medium. Specific steps include: Using three mutually perpendicular outer surface images of a three-dimensional porous medium sample, along with their corresponding porosity and specific surface area values, as input conditions, a forward diffusion process is gradually applied to the sample using a denoised diffusion probability model. Adding noise to generate pure noise ; Pure noise Input into a 3D U-Net outputs predicted noise Meanwhile, a positional encoding function is used to map the time steps into high-dimensional vectors, which are then concatenated with the feature maps in the input layer of the U-Net network.

[0042] In the 3D U-Net, the additive block with axial decay weights is at each level. For any axial direction Perform separately: ; in, Indicates from the surface a Extracted two-dimensional conditional tensor; It is a lightweight 2D convolutional encoder that projects surface conditions into 2D feature maps; Perform bilinear interpolation to match the first Spatial resolution of conditional residual convolution blocks; Along with the surface a orthogonal axes a Copy the binary feature map to generate a size of The three-dimensional tensor; Project the conditional channels onto the feature dimensions of the conditional residual convolutional block. , Then it means the first The attenuation weight in the stage depends on the axial direction.

[0043] 3D U-Net network in Hierarchical feature maps The added total guiding condition is the sum of the contributions in all three axes.

[0044] By using the reverse sampling formula of DDPM to gradually reverse the forward noise addition, the reconstructed internal structure of the porous medium is obtained.

[0045] S6. Calculate the structural similarity SSIM, mean squared similarity MS-SSIM, and coefficient of determination on the validation and test sets. R 2 and two-point correlation functions Simultaneously, the porosity distribution, standard deviation, and specific surface area of ​​the reconstructed volume were statistically analyzed to assess the model's generalization ability across different porosity ranges.

[0046] Among them, the reconstruction results on the DeePore dataset (SSIM, as well as R 2 )like Figure 3 As shown. Reconstruction results on the DeePore dataset (two-point correlation function). )like Figure 4 As shown. On the test samples of the DeePore dataset, from Figure 3 It can be seen that the model achieves SSIM and [missing information] within the porosity range of 0.1–0.4. R 2 A score higher than 0.98. As porosity increases, SSIM... and R 2 The mean value shows an upward trend, indicating that the connectivity of highly porous media is more easily captured by the model.

[0047] from Figure 4 As can be seen from this, the correlation function between the two points The results show that at local scales with r < 5 voxels, the reconstructed sample curves closely match the original sample curves. Differences at long-range scales primarily reflect the model's adaptation to non-statistical distribution regions. The model provides a conservative prediction. Across different porosity ranges, the reconstructed porosity distribution exhibits an approximately Gaussian distribution and concentrates near the original sample. For In the interval, the mean porosity of the reconstructed samples is slightly higher; for The mean is slightly lower in the range; for The intervals are almost identical. These phenomena indicate that the model maintains accurate statistical fidelity within the training distribution and exhibits a balanced trend of overestimation and underestimation across different intervals. In intervals outside the training distribution... In the middle, due to the lack of training samples, the model tends to generate structures with low porosity, but the structural similarity index is high.

[0048] Solid-phase two-point correlation function of original and reconstructed samples (average of 20 samples) on the Berea Upper Gray Sandstone and Claystone datasets. like Figure 5 As shown in C and D in the diagram. Berea Upper Gray Sandstone The curves showed a high degree of agreement with the original samples across different scales (r < 50 voxels), indicating that the model can accurately reproduce the correlation and connectivity structure of solid-state space, demonstrating high physical consistency. Claystone's... It maintains a high degree of consistency with the original sample within a short range (r < 10 voxel).

[0049] Depend on Figures 3 to 5 The reconstruction accuracy and generalization ability are evident under different porosity ranges, rock types, and heterogeneity levels. For statistically stable homogeneous Berea Upper Gray Sandstone, the model can stably generate results highly consistent with the original structure under multiple samplings. For highly heterogeneous and anisotropic Claystone, although the generated structure exhibits slight local deviations, it still accurately preserves the overall pore structure and spatial statistical characteristics. This further demonstrates that the model proposed in this invention can achieve high-fidelity reconstruction of pore spatial structure in multi-scale complex media, while maintaining spatial correlation consistent with the real structure at the statistical level.

[0050] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0051] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for reconstructing internal structure of a porous medium based on an attenuating condition diffusion model, characterized in that, The steps include: Data acquisition, including synthetic porous medium data set and real core data set; Data preprocessing, including down-sampling, normalization and data enhancement of synthetic porous medium data set and real core data set; An attenuated condition diffusion model is constructed to denoise the diffusion probability model DDPM as a generation framework, the forward diffusion process gradually adds Gaussian noise to the training sample, and the reverse diffusion process restores the clear three-dimensional structure by predicting the noise and combining the condition information predicting the noise and combining the condition information to restore the clear three-dimensional structure Model training, using Adam optimizer to train the decay condition diffusion model; The internal structure of the porous medium is reconstructed, three mutually perpendicular outer surface images of the three-dimensional porous medium sample and corresponding porosity values and specific surface area values are input into the attenuation condition diffusion model as input conditions, an axial correlation attenuation weight is introduced in the reverse generation process of the denoising diffusion probability model (DDPM), and three-dimensional The network adaptively fuses surface information, guides the generation of voxel-level features, and obtains the reconstructed internal structure of the porous medium.

2. The method of claim 1, wherein, The three-dimensional U-Net network includes an input layer, an encoder, a bottleneck layer, a decoder and an output layer; The bottleneck layer includes a plurality of conditional residual convolution blocks and attention modules; the conditional residual convolution block includes a convolution layer and an addition block with axial decay weight; The decoder and the encoder use symmetric sampling layers followed by conditional residual convolution blocks; the encoder and the decoder are connected through cross-resolution jump.

3. The method of claim 2, wherein, The attenuation weights : ； wherein, is the distance of a voxel from the outer surface in a certain axis, is the attenuation coefficient learned along that axis, ; Wherein, the decay weight is automatically learned in model training, and the size of the decay weight exponentially decays with the increase of the distance from the feature point of different levels to the surface of the porous medium, and different axial directions can learn different decay scales.

4. The method of claim 3, wherein, The adder block with axial attenuation weights computes in each level respectively a steering condition :​​ ； where, represents the two-dimensional conditional tensor extracted from surface a; is a lightweight two-dimensional convolutional encoder that projects the surface condition into a two-dimensional feature map; performing bilinear interpolation to match the spatial resolution of the level condition residual convolutional block; copying the binary feature map along the axis a orthogonal to surface a, resulting in a three-dimensional tensor of size ; projecting the condition channel into the feature dimension of the condition residual convolutional block , where represents the axis-dependent decay weight in the level.

5. The method of claim 4, wherein, The three-dimensional U-Net network in Hierarchical feature maps Added total boot conditions The sum of contributions to the three axial guiding conditions, of which express Contribution on the axis Indicates in Contribution on the axis Indicates in Contribution on the axis.

6. The method of claim 5, wherein the method further comprises: The internal structure reconstruction step of the porous medium includes: Three mutually perpendicular outer surface images of a three-dimensional porous medium sample and their corresponding porosity values and specific surface area values are used as input conditions, and a denoising diffusion probability model is used to forward diffuse the process step by step towards the sample Adding noise generates pure noise ; The pure noise is input into a three-dimensional U-Net, the outer surface image is mapped into a feature map by the encoder, is copied into a three-dimensional tensor along the corresponding axis after adjusting the size by bilinear interpolation, and a position encoding function is used to map the time step into a high-dimensional vector, which is spliced with the feature map in the input layer of the U-Net network to enhance the timing information, and then multiplied by an addition block with an axial attenuation weight to inject the feature map of the outer surface information at different depths, and the conditional guidance information is continuously fused at each level to realize spatial consistency fusion of different axial conditional information, and output the predicted noise ; Using the reverse sampling formula of DDPM to gradually reverse the forward noise to obtain the reconstructed internal structure of the porous medium.

7. The method of claim 6, wherein the method further comprises: The reverse sampling formula of DDPM: ； wherein denotes the sample at time step obtained by backward sampling the previous time step , denotes the noisy sample at time step , denotes the noise at time step , denotes a random variable of a standard normal distribution, ; denotes the standard deviation of the random noise added during the backward sampling process, denotes a noise predictor, y denotes surface guiding information.

8. The method of claim 1, wherein, The loss function of the attenuation condition diffusion model training : ； wherein y is the noise sample in the forward diffusion, and y is the three outer surface steering information.

9. An electronic device, comprising: Including: One or more processors; A storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors execute the method according to any one of claims 1-8.

10. A storage medium, characterized by The storage medium stores at least one instruction, which is loaded and executed by the processor to realize the method according to any one of claims 1-8.

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