Machine Learning Study through Physics-Informed Neural Networks: Analysis of the Stable Vortices in Quasi-Integrable Systems

Vortices in the nonlinear equations, including Zakharov-Kuznetsov (ZK) equation and the regularized long-wave (RLW) equation are studied. The Physics-Informed Neural Networks solve these equations in the forward process and obtain the solutions. In the inverse process, the proper equations can successfully be derived from a given training data. However, between the ZK equation and the RLW equation, sometimes serious misidentification occurs. In order to improve the resolution of the identification, we introduce two methods: a friction method and deformations of the initial profile which offers a nice discrimination of the equations.