Data driven localized wave solution of the Fokas-Lenells equation using modified PINN
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Abstract (arXiv)
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
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References · 8
- 2017Attention Is All You Needcited by 60,361
- 2014Adam: A Method for Stochastic Optimizationcited by 37,240
- 2021Learning the solution operator of parametric partial differential equations with physics-informed DeepOnetscited by 540
- 2015Recent Advances in Convolutional Neural Networkscited by 360
- 2020hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decompositioncited by 236
- 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 233
- 2022Respecting causality is all you need for training physics-informed neural networkscited by 156
- 2019An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applicationscited by 118
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