Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs
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Date
2021
Publication Type
Journal Article
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Abstract
We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-Holm and Benjamin-Ono equations. The stability of solutions of these dispersive PDEs is leveraged to prove rigorous bounds on the resulting error. We present several numerical experiments to demonstrate that PINNs can approximate solutions of these dispersive PDEs very accurately.
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published
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Journal / series
Volume
39 (6)
Pages / Article No.
816 - 847
Publisher
Global Science Press
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Methods
Software
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Subject
Nonlinear dispersive PDEs; Deep learning; Physics Informed Neural Networks
Organisational unit
03851 - Mishra, Siddhartha / Mishra, Siddhartha