Element-Wise Multiplication Based Deeper Physics-Informed Neural Networks

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 power and initialization pathology issues are found to prevent the successful application of PINNs in complex PDEs. In this work, we propose a 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 expressiveness 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 power.

Keywords: Physics-Informed Neural Networks, deep learning, Partial differential equations