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Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons

arXiv 2112.14040 ↗First posted 28 Dec 2021nlin.PS cs.LG math-phcited by 0

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Abstract (arXiv)

In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional KP-I equation and spin-nonlinear Schr"odinger (spin-NLS) equation via the deep neural networks leaning. Moreover, the inverse problems of the (2+1)-dimensional KP-I equation and spin-NLS equation are studied via deep learning. The main idea of the data-driven forward and inverse problems is to use the deep neural networks with the activation function to approximate the solutions of the considered (2+1)-dimensional nonlinear wave equations by optimizing the chosen loss functions related to the considered nonlinear wave equations.

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References · 15

  1. 2017DGM: A deep learning algorithm for solving partial differential equationscited by 674
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3 more
  1. 2020Data-driven rogue waves and parameter discovery in the defocusing NLS equation with a potential using the PINN deep learningcited by 12
  2. 2021Data-driven peakon and periodic peakon travelling wave solutions of some nonlinear dispersive equations via deep learningcited by 6
  3. 2021Deep learning neural networks for the third-order nonlinear Schrodinger equation: Solitons, breathers, and rogue wavescited by 4

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