Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-informed Neural Networks Framework for Interface Problems

TL;DR

AdaI-PINNs is an advanced physics-informed neural network framework that adaptively trains activation function slopes to efficiently solve complex interface problems with discontinuities, outperforming previous methods in speed and accuracy.

Contribution

The paper introduces AdaI-PINNs, a fully automated PINNs framework that adaptively trains activation slopes, eliminating the need for preset functions and enhancing performance on interface problems.

Findings

AdaI-PINNs reduce computational costs by 2-6 times.

AdaI-PINNs achieve similar or better accuracy than I-PINNs.

The framework is effective for 1D, 2D, and 3D interface problems.

Abstract

We present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of interface problems with discontinuous coefficients and/or interfacial jumps. This framework is an enhanced version of its predecessor, Interface PINNs or I-PINNs (Sarma et al.; https://dx.doi.org/10.2139/ssrn.4766623), which involves domain decomposition and assignment of different predefined activation functions to the neural networks in each subdomain across a sharp interface, while keeping all other parameters of the neural networks identical. In AdaI-PINNs, the activation functions vary solely in their slopes, which are trained along with the other parameters of the neural networks. This makes the AdaI-PINNs framework fully automated without requiring preset activation functions. Comparative studies on one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs outperform I-PINNs, reducing computational costs by 2-6 times while producing similar or better accuracy.