Respecting causality for training physics-informed neural networks

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing...

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Veröffentlicht in:Computer methods in applied mechanics and engineering Jg. 421; H. C; S. 116813
Hauptverfasser: Wang, Sifan, Sankaran, Shyam, Perdikaris, Paris
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Netherlands Elsevier B.V 01.03.2024
Elsevier
Schlagworte:
Chaotic systems
Computational physics
Deep learning
Partial differential equations
Deep learning
Computational physics
Partial differential equations
Chaotic systems
ISSN:0045-7825, 1879-2138
Online-Zugang:Volltext
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Zusammenfassung:While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this work we attribute this shortcoming to the inability of existing PINNs formulations to respect the spatio-temporal causal structure that is inherent to the evolution of physical systems. We argue that this is a fundamental limitation and a key source of error that can ultimately steer PINN models to converge towards erroneous solutions. We address this pathology by proposing a simple re-formulation of PINNs loss functions that can explicitly account for physical causality during model training. We demonstrate that this simple modification alone is enough to introduce significant accuracy improvements, as well as a practical quantitative mechanism for assessing the convergence of a PINNs model. We provide state-of-the-art numerical results across a series of benchmarks for which existing PINNs formulations fail, including the chaotic Lorenz system, the Kuramoto–Sivashinsky equation in the chaotic regime, and the Navier–Stokes equations. To the best of our knowledge, this is the first time that PINNs have been successful in simulating such systems, introducing new opportunities for their applicability to problems of industrial complexity.
Bibliographie:USDOE Advanced Research Projects Agency - Energy (ARPA-E)
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2024.116813