Self-adaptive physics-informed neural network for forward and inverse problems in heterogeneous porous flow

TL;DR

This paper introduces a self-adaptive physics-informed neural network framework that effectively solves forward and inverse problems in heterogeneous porous media, accurately predicting flow and permeability without mesh dependence.

Contribution

The work presents a novel self-adaptive PINN with region-aware permeability parameterization and automatic loss balancing, enhancing robustness and accuracy in complex porous media problems.

Findings

Accurate velocity and pressure prediction in heterogeneous media.

Reliable permeability inversion from flow data.

Stable and accelerated training with combined optimization strategies.

Abstract

We develop a self-adaptive physics-informed neural network (PINN) framework that reliably solves forward Darcy flow and performs accurate permeability inversion in heterogeneous porous media. In the forward setting, the PINN predicts velocity and pressure for discontinuous, piecewise-constant permeability; in the inverse setting, it identifies spatially varying permeability directly from indirect flow observations. Both models use a region-aware permeability parameterization with binary spatial masks, which preserves sharp permeability jumps and avoids the smoothing artifacts common in standard PINNs. To stabilize training, we introduce self-learned loss weights that automatically balance PDE residuals, boundary constraints, and data mismatch, eliminating manual tuning and improving robustness, particularly for inverse problems. An interleaved AdamW-L-BFGS optimization strategy further accelerates and stabilizes convergence. Numerical results demonstrate accurate forward surrogates and reliable inverse permeability recovery, establishing the method as an effective mesh-free solver and data-driven inversion tool for porous-media systems governed by partial differential equations.