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

• URL: http://arxiv.org/abs/2112.14040v1
• Date: Tue, 28 Dec 2021 08:41:40 GMT
• Title: Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons
• Authors: Zijian Zhou, Li Wang, and Zhenya Yan
• Abstract summary: 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.
• Score: 6.529583356640745
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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