Data driven localized wave solution of the Fokas-Lenells equation using modified PINN

TL;DR

This paper introduces a modified physics-informed neural network (PINN) that incorporates control parameters and conserved quantities to accurately compute localized wave solutions of the Fokas-Lenells equation, advancing deep learning applications in nonlinear physics.

Contribution

The paper presents a novel modification to PINN by adding control parameters and conserved quantities as loss terms, improving the accuracy of localized wave solutions for the Fokas-Lenells equation.

Findings

Modified PINN accurately predicts bright and dark solitons.

Conserved quantities loss term enhances solution accuracy.

Source code availability facilitates further research.

Abstract

We investigate data driven localized wave solutions of the Fokas-Lenells equation by using physics informed neural network(PINN). We improve basic PINN by incorporating control parameters into the residual loss function. We also add conserve quantity as another loss term to modify the PINN. Using modified PINN we obtain the data driven bright soliton and dark soliton solutions of Fokas-Lenells equation. Conserved quantities informed loss function achieve more accuracy in terms of relative L2 error between predicted and exact soliton solutions. We hope that the present investigation would be useful to study the applications of deep learning in nonlinear optics and other branches of nonlinear physics. Source codes are available at https://github.com/gautamksaharia/Fokas-Lenells