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Anisotropic Permeability Tensor Prediction from Porous Media Microstructure via Physics-Informed Progressive Transfer Learning with Hybrid CNN-Transformer

Accurate prediction of permeability tensors from pore-scale microstructure images is essential for subsurface flow modeling, yet direct numerical simulation requires hours per sample, fundamentally limiting large-scale uncertainty quantification and reservoir optimization workflows. A physics-informed deep learning framework is presented that resolves this bottleneck by combining a MaxViT hybrid CNN-Transformer architecture with progressive transfer learning and differentiable physical constraints. MaxViT's multi-axis attention mechanism simultaneously resolves grain-scale pore-throat geometry via block-local operations and REV-scale connectivity statistics through grid-global operations, providing the spatial hierarchy that permeability tensor prediction physically requires. Training on 20000 synthetic porous media samples spanning three orders of magnitude in permeability, a three-phase progressive curriculum advances from an ImageNet-pretrained baseline with D4-equivariant augmentation and tensor transformation, through component-weighted loss prioritizing off-diagonal coupling, to frozen-backbone transfer learning with porosity conditioning via Feature-wise Linear Modulation (FiLM). Onsager reciprocity and positive definiteness are enforced via differentiable penalty terms. On a held-out test set of 4000 samples, the framework achieves variance-weighted R2 = 0.9960 (R2_Kxx = 0.9967, R2_Kxy = 0.9758), a 33% reduction in unexplained variance over the supervised baseline. The results offer three transferable principles for physics-informed scientific machine learning: large-scale visual pretraining transfers effectively across domain boundaries; physical constraints are most robustly integrated as differentiable architectural components; and progressive training guided by diagnostic failure-mode analysis enables unambiguous attribution of performance gains across methodological stages.

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