Controlled Generation of 3D Porous Media Structures Based on a Continuous Regression Generative Adversarial Network

The design and optimization of porous media require a large number of three-dimensional (3D) candidate structures covering a broad range of structural parameters. However, experimentally acquired physical samples are usually limited in number, and 3D structures with prescribed parameters are difficult to obtain on demand. To address this issue, a controllable generation method for 3D pore structures of Bentheimer sandstone is proposed based on a continuous regression generative adversarial network (CR-GAN). Porosity and specific surface area are selected as continuous conditioning variables. Auxiliary regression supervision is used to constrain the generated structures to the prescribed parameter values, while adaptive instance normalization (AdaIN)-based feature modulation introduces the continuous conditioning information into the generation process. In this way, the model realizes parameter-constrained generation and continuous condition regulation within the training range, allowing the conditioning variables to vary continuously and guide the generated structures to corresponding parameter states. The model is trained using local structures with a size of 64³ voxels. By enlarging the spatial size of the latent noise field, the fully convolutional generator can directly output 3D structures with a size of 480³ voxels, thereby realizing large-scale structure generation from small-scale training samples. This strategy enables the generation scale to be enlarged directly while retaining the parameter-conditioned generation mechanism learned from the local training structures. The controllable generation performance is evaluated in both densely sampled and sparsely sampled regions of the parameter space. The results show that, in both regions, the relative errors of the porosity and specific surface area of the generated structures are below 2%, indicating that the model can maintain accurate parameter control under different levels of training-data coverage and possesses high adaptability to variations in data coverage. When the generation scale is increased, the dispersion of the generated structural parameters is further reduced, resulting in more concentrated parameter distributions at the larger scale. Analyses based on the integral mean curvature and Euler characteristic show that different target parameters correspond to distinct interfacial morphologies and topological features. In addition, the largest connected cluster fractions of both the pore phase and the solid phase exceed 99%. Pore network model calculations further show that the absolute permeability of the high-parameter group is consistently higher than that of the low-parameter group, demonstrating that structures generated under different target parameters exhibit clearly different transport responses. Overall, the proposed method can expand the design space of candidate structures of Bentheimer sandstone under continuous parameter control. Its applicability to other 3D porous materials with substantially different morphologies and topologies remains to be further explored.