Data driven localized wave solution of the Fokas-Lenells equation using
  modified PINN
Gautam Kumar Saharia Sagardeep Talukdar Riki Dutta Sudipta Nandy
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