Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)

TL;DR

This paper introduces IDPINN, a novel physics-informed neural network framework that enhances initialization and employs domain decomposition to significantly improve prediction accuracy in solving forward problems.

Contribution

The paper presents a new IDPINN framework that combines improved initialization with domain decomposition, leading to better accuracy in physics-informed neural network predictions.

Findings

IDPINN outperforms traditional PINNs in accuracy.

Enhanced initialization reduces training time.

Domain decomposition improves local solution quality.

Abstract

We propose a new physics-informed neural network framework, IDPINN, based on the enhancement of initialization and domain decomposition to improve prediction accuracy. We train a PINN using a small dataset to obtain an initial network structure, including the weighted matrix and bias, which initializes the PINN for each subdomain. Moreover, we leverage the smoothness condition on the interface to enhance the prediction performance. We numerically evaluated it on several forward problems and demonstrated the benefits of IDPINN in terms of accuracy.