IG-PINNs: Interface-gated physics-informed neural networks for solving elliptic interface problems

TL;DR

This paper introduces IG-PINNs, a neural network approach that effectively solves elliptic interface problems by incorporating an interface-gated mechanism to handle discontinuities, showing improved accuracy over existing PINN methods.

Contribution

The paper presents a novel interface-gated neural network architecture for elliptic interface problems, enhancing accuracy by explicitly modeling interface discontinuities.

Findings

IG-PINNs outperform PINNs, I-PINNs, and M-PINNs in accuracy.

The interface-gated mechanism effectively manages discontinuities.

Numerical experiments validate the method's effectiveness.

Abstract

In this work, we develop interface-gated physics-informed neural networks (IG-PINNs) to solve elliptic interface equations. In IG-PINNs, we use a fully connected neural network to capture the smooth behavior across the entire domain. In each subdomain separated by the interface, an interface-gated network is utilized to provide corrections at the interface. In the architectural design of the interface-gated network, we introduce a gating mechanism and a level-set function derived from the interface. This design enables the interface-gated network to effectively handle discontinuous jumps across the interface. Some numerical experiments have confirmed the effectiveness of the IG-PINNs, demonstrating higher accuracy compared with PINNs, interface PINNs (I-PINNs) and multi-domain PINNs (M-PINNs).