Data driven localized wave solution of the Fokas-Lenells equation using modified PINN
This work addresses the challenge of simulating nonlinear wave phenomena in fields like optics, but it is incremental as it builds on existing PINN methods with specific enhancements.
The researchers tackled the problem of finding localized wave solutions for the Fokas-Lenells equation by modifying a physics-informed neural network (PINN) with control parameters and conserved quantities in the loss function, resulting in bright and dark soliton solutions with improved accuracy as measured by relative L2 error.
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