KA-GAN: Kolmogorov-Arnold Generative Adversarial Networks for Reconstruction of 3D Porous Media

Summary

3D reconstruction of porous media plays a crucial role in materials science and petroleum engineering, particularly for pore structure characterization and physical-mechanical property prediction. Although deep learning–based generative models have emerged as promising tools for 3D porous media reconstruction, challenges remain, including inadequate feature representation, training instability, and limited generation diversity. To address these issues, we propose the Kolmogorov-Arnold (KA) generative adversarial network (GAN) (KA-GAN) for 3D reconstruction of porous media, where an improved KA convolutional layer is incorporated in the generator. Moreover, KA-GAN employs grouped convolution mechanisms and phase-controlled activation functions to enhance spatial structure preservation and generation diversity while mitigating geometric distortions. The discriminator integrates gradient penalty (GP) regularization to improve training stability. Comprehensive experiments were conducted on diverse porous media data sets, including heterogeneous sandstone and structurally complex carbonate rocks. Qualitative results show accurate visual resemblance to ground truth (GT), while quantitative evaluations demonstrate improvements in porosity, throat geometry, connectivity metrics, and absolute permeability, confirming that KA-GAN outperforms existing state-of-the-art methods. The source code for this paper is publicly available at https://github.com/HoneyOrangeSummer/ka-gan/.