Deep neural networks for solving forward and inverse problems of (2+1)-dimensional nonlinear wave equations with rational solitons
This work addresses computational challenges in solving complex wave equations for physics and engineering applications, but it appears incremental as it applies existing deep learning methods to new data.
The paper tackles forward and inverse problems for (2+1)-dimensional nonlinear wave equations (KP-I and spin-NLS) with rational solitons using deep neural networks, achieving solutions by optimizing loss functions to approximate these equations.
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 Schrödinger (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.