Element-wise Multiplication Based Deeper Physics-Informed Neural Networks

TL;DR

This paper introduces Deeper-PINN, a novel physics-informed neural network architecture that uses element-wise multiplication to improve expressiveness and address initialization issues in solving complex PDEs.

Contribution

The paper proposes a new Deeper-PINN model utilizing element-wise multiplication to enhance expressiveness and mitigate initialization problems in PINNs.

Findings

Deeper-PINNs effectively resolve initialization pathologies.

Deeper-PINNs demonstrate strong expressive ability on benchmarks.

Deeper-PINNs outperform traditional PINNs in complex PDEs.

Abstract

As a promising framework for resolving partial differential equations (PDEs), Physics-Informed Neural Networks (PINNs) have received widespread attention from industrial and scientific fields. However, lack of expressive ability and initialization pathology issues are found to prevent the application of PINNs in complex PDEs. In this work, we propose Deeper Physics-Informed Neural Network (Deeper-PINN) to resolve these issues. The element-wise multiplication operation is adopted to transform features into high-dimensional, non-linear spaces. Benefiting from element-wise multiplication operation, Deeper-PINNs can alleviate the initialization pathologies of PINNs and enhance the expressive capability of PINNs. The proposed structure is verified on various benchmarks. The results show that Deeper-PINNs can effectively resolve the initialization pathology and exhibit strong expressive ability.