A Layer-Specific Constraint-Based Enriched Physics-Informed Neural Network for Solving Two-Phase Flow Problems in Heterogeneous Porous Media

J.-Q. Lin, X. Yan, E.-Z. Wang, Q. Zhang, K. Zhang, P.-Y. Liu, and L.-M. Zhang

Petroleum Science, 22(11):4714 - 4735, 2025.

Manuscript

Summary

This paper studies how the internal layers of an enriched physics-informed neural network contribute to two-phase-flow prediction in heterogeneous porous media. An interpretation of layer outputs distinguishes dimensional transformations, local potential construction, higher-level feature extraction, and longer-range dependencies. These observations motivate a regularized training strategy that updates different layers at different frequencies. Layers associated more strongly with local fitting are updated less often, encouraging the network to retain features that transfer across time steps. Numerical examples of increasing complexity evaluate the effect on convergence and accuracy. Further analysis examines gradient propagation, equation residuals, and information compression during training. The reported benefits include more structured gradient behavior and more uniform residual distributions. The work connects an interpretable account of network organization with a practical training constraint, aiming to improve generalization without replacing the underlying EPINN flow formulation.