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Anisotropic permeability tensor prediction from porous media microstructure: A physics-informed MaxViT
1Faculty of Mathematics and Natural Sciences, University of Oslo, PO Box 1047, Blindern, 0316, Oslo, Norway.
Summary
Physics-informed deep learning accelerates subsurface flow modeling by accurately predicting permeability tensors from microstructures. This framework offers a three-orders-of-magnitude speedup over traditional methods, enabling efficient uncertainty quantification.
Area of Science:
- Geophysics
- Computational Science
- Materials Science
Background:
- Accurate permeability tensor prediction is crucial for subsurface flow modeling.
- Direct numerical simulations are computationally expensive, limiting uncertainty quantification.
- Pore-scale microstructure dictates flow properties.
Purpose of the Study:
- To develop a physics-informed deep learning framework for rapid and accurate permeability tensor prediction.
- To overcome the computational bottleneck of traditional simulation methods.
- To establish transferable principles for scientific machine learning in geoscience.
Main Methods:
- Utilized a MaxViT hybrid CNN-Transformer for multi-axis attention to capture spatial hierarchies.
- Implemented a differentiable physics-aware loss function enforcing Onsager reciprocity and thermodynamic positive-definiteness.
- Employed a D4-equivariant augmentation strategy for consistent tensor label transformation.
Main Results:
- Achieved a variance-weighted R²=0.9960 on 2D sandstone microstructures.
- Demonstrated a speedup of three orders of magnitude (120 ms/sample) compared to lattice-Boltzmann methods.
- Attained mean symmetry error of εsym=3.95×10⁻⁷ with 100% constraint satisfaction.
Conclusions:
- The physics-informed deep learning framework significantly reduces computational cost for permeability prediction.
- The approach establishes transferable principles for scientific machine learning, including visual pretraining and differentiable physical constraints.
- Future work includes 3D micro-CT extension and real-core validation for operational deployment.