Physics-informed Neural Networks for Heterogeneous Poroelastic Media

TL;DR

This paper introduces a physics-informed neural network framework with a composite architecture and interface-specific activation functions to accurately model heterogeneous poroelastic media, significantly improving accuracy and computational efficiency.

Contribution

The study develops a novel CoNN with I-PINNs framework that effectively handles material interfaces in heterogeneous media, outperforming existing PINN and XPINN methods.

Findings

Achieves RMSE two orders of magnitude lower than conventional PINNs.

At least 40 times faster than single neural network approaches.

Outperforms XPINNs with at least one order of magnitude better RMSE.

Abstract

This study presents a novel physics-informed neural network (PINN) framework for modeling poroelasticity in heterogeneous media with material interfaces. The approach introduces a composite neural network (CoNN) where separate neural networks predict displacement and pressure variables for each material. While sharing identical activation functions, these networks are independently trained for all other parameters. To address challenges posed by heterogeneous material interfaces, the CoNN is integrated with the Interface-PINNs or I-PINNs framework (Sarma et al. 2024, https://dx.doi.org/10.1016/j.cma.2024.117135), allowing different activation functions across material interfaces. This ensures accurate approximation of discontinuous solution fields and gradients. Performance and accuracy of this combined architecture were evaluated against the conventional PINNs approach, a single neural network (SNN) architecture, and the eXtended PINNs (XPINNs) framework through two one-dimensional benchmark examples with discontinuous material properties. The results show that the proposed CoNN with I-PINNs architecture achieves an RMSE that is two orders of magnitude better than the conventional PINNs approach and is at least 40 times faster than the SNN framework. Compared to XPINNs, the proposed method achieves an RMSE at least one order of magnitude better and is 40% faster.