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RAR-PINN algorithm for the data-driven vector-soliton solutions and parameter discovery of coupled nonlinear equations
- Publication Year :
- 2022
-
Abstract
- This work aims to provide an effective deep learning framework to predict the vector-soliton solutions of the coupled nonlinear equations and their interactions. The method we propose here is a physics-informed neural network (PINN) combining with the residual-based adaptive refinement (RAR-PINN) algorithm. Different from the traditional PINN algorithm which takes points randomly, the RAR-PINN algorithm uses an adaptive point-fetching approach to improve the training efficiency for the solutions with steep gradients. A series of experiment comparisons between the RAR-PINN and traditional PINN algorithms are implemented to a coupled generalized nonlinear Schr\"{o}dinger (CGNLS) equation as an example. The results indicate that the RAR-PINN algorithm has faster convergence rate and better approximation ability, especially in modeling the shape-changing vector-soliton interactions in the coupled systems. Finally, the RAR-PINN method is applied to perform the data-driven discovery of the CGNLS equation, which shows the dispersion and nonlinear coefficients can be well approximated.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2205.10230
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.physd.2022.133562