Neural Oscillators for Generalization of Physics-Informed Machine Learning

Taniya Kapoor, Abhishek Chandra, Daniel M. Tartakovsky, Hongrui Wang, Alfredo Nunez, Rolf Dollevoet

Research output: Contribution to journalConference articleScientificpeer-review

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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.

Original languageEnglish
Pages (from-to)13059-13067
Number of pages9
JournalProceedings of the AAAI Conference on Artificial Intelligence
Volume38
Issue number12
DOIs
Publication statusPublished - 2024
Event38th AAAI Conference on Artificial Intelligence, AAAI 2024 - Vancouver, Canada
Duration: 20 Feb 202427 Feb 2024

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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