Neuro-Spectral Architectures with Time-Domain Decomposition

Vitor Balestro, Márcio Marques, Leonardo Mendonça, Leonardo M. Moreira, Christian Júnior de Oliveira, Francisco Ganacim, Tiago Novello, Pavel Petrov, Daniel Yukimura, Lucas Nissenbaum

Keywords: scientific machine learning, physics-informed neural networks, time domain decomposition, neuro-spectral architectures

TL;DR: We apply time domain decomposition strategies to neuro-spectral architectures in order to generate new physics-informed neural networks that can be trained faster, are able to deal with complex dynamics, and are less prone to stiffness.

Abstract:

Physics-informed neural networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) within the framework of scientific machine learning. However, despite their flexibility, PINNs often struggle with certain issues such as spectral bias and difficulties in capturing temporal causality. Recently, neuro-spectral architectures (NeuSA) were proposed as an alternative strategy that successfully deals with some of these problems. In this study, a modified D-NeuSA architecture is introduced. By contrast to the original one, D-NeuSA performs a decomposition of the time domain in order to increase robustness of the resulting neuro-spectral model.
D-NeuSA consistently outperforms NeuSA and other baseline models in terms of both predictive accuracy and training efficiency across a wide range of problems. Moreover, D-NeuSA is able to produce reliable solutions in scenarios where NeuSA and other established PINN methods fail to converge.

Submission Number: 89