Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons
Pattern Formation and Solitons
2021-12-30 v1 Machine Learning
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Computational Physics
Abstract
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.
Keywords
Cite
@article{arxiv.2112.14040,
title = {Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons},
author = {Zijian Zhou and Li Wang and Zhenya Yan},
journal= {arXiv preprint arXiv:2112.14040},
year = {2021}
}
Comments
15 pages, 6 figures