Neural oscillators for generalization of physics-informed machine learning

TL;DR

This paper introduces neural oscillators to enhance the generalization of physics-informed machine learning models, enabling better extrapolation and prediction in complex PDE problems by capturing long-term dependencies and addressing gradient issues.

Contribution

The paper proposes integrating neural oscillators with PIML to improve generalization, leveraging causality and temporal features of PDEs for better long-term predictions.

Findings

Neural oscillators outperform existing methods on benchmark PDE problems.

The approach effectively captures long-time dependencies in PDE solutions.

Enhanced generalization in PIML for complex physical systems.

Abstract

A primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs). This paper aims to enhance the generalization capabilities of PIML, facilitating practical, real-world applications where accurate predictions in unexplored regions are crucial. We leverage the inherent causality and temporal sequential characteristics of PDE solutions to fuse PIML models with recurrent neural architectures based on systems of ordinary differential equations, referred to as neural oscillators. Through effectively capturing long-time dependencies and mitigating the exploding and vanishing gradient problem, neural oscillators foster improved generalization in PIML tasks. Extensive experimentation involving time-dependent nonlinear PDEs and biharmonic beam equations demonstrates the efficacy of the proposed approach. Incorporating neural oscillators outperforms existing state-of-the-art methods on benchmark problems across various metrics. Consequently, the proposed method improves the generalization capabilities of PIML, providing accurate solutions for extrapolation and prediction beyond the training data.