Anisotropic permeability tensor prediction from porous media microstructure: A physics-informed MaxViT CNN-Transformer framework.
Accurate permeability tensor prediction from pore-scale microstructure is essential for subsurface flow modeling, yet direct numerical simulation requires hours per sample, fundamentally constraining large-scale uncertainty quantification. The proposed physics-informed deep learning framework resolves this computational bottleneck through three integrated contributions. First, a MaxViT hybrid CNN-Transformer leverages multi-axis attention to simultaneously resolve grain-scale geometry via block-local operations and representative elementary volume connectivity through grid-global operations, supplying the spatial hierarchy required for anisotropic prediction. Second, a differentiable physics-aware loss function penalizes violations of Onsager reciprocity and thermodynamic positive-definiteness, achieving a mean symmetry error of εsym=3.95×10-7 and 100 % constraint satisfaction without post-hoc correction. Third, a D4-equivariant augmentation strategy introduces a consistent second-order tensor label transformation that eliminates the label-image mismatch typical of naive augmentation. Evaluated on 20,000 synthetic 2D binary sandstone microstructures spanning three orders of magnitude in permeability, the framework achieves a variance-weighted R2=0.9960 ( [Formula: see text] , [Formula: see text] ) on a 4,000-sample test set, a significant reduction in unexplained variance over supervised baselines, with every reported metric improving monotonically across phases. Inference requires 120 ms per sample, a speedup of three orders of magnitude over lattice-Boltzmann references, while integrated Monte Carlo Dropout provides per-sample confidence estimates. Three-dimensional micro-CT extension and real-core validation are identified as the critical next steps toward operational deployment. Ultimately, these results establish transferable principles for scientific machine learning: visual pretraining generalizes across domain boundaries, physical constraints function best as differentiable architectural components, and progressive training guided by failure-mode analysis isolates precise structural performance drivers.