TY - JOUR
T1 - Neural Oscillators for Generalization of Physics-Informed Machine Learning
AU - Kapoor, Taniya
AU - Chandra, Abhishek
AU - Tartakovsky, Daniel M.
AU - Wang, Hongrui
AU - Nunez, Alfredo
AU - Dollevoet, Rolf
N1 - 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.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85189561109&partnerID=8YFLogxK
U2 - 10.1609/aaai.v38i12.29204
DO - 10.1609/aaai.v38i12.29204
M3 - Conference article
AN - SCOPUS:85189561109
SN - 2159-5399
VL - 38
SP - 13059
EP - 13067
JO - Proceedings of the AAAI Conference on Artificial Intelligence
JF - Proceedings of the AAAI Conference on Artificial Intelligence
IS - 12
T2 - 38th AAAI Conference on Artificial Intelligence, AAAI 2024
Y2 - 20 February 2024 through 27 February 2024
ER -