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A-WPINN algorithm for the data-driven vector-soliton solutions and parameter discovery of general coupled nonlinear equations
- Source :
- Physica D: Nonlinear Phenomena. 443:133562
- Publication Year :
- 2023
- Publisher :
- Elsevier BV, 2023.
-
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.
- Subjects :
- FOS: Computer and information sciences
Nuclear Theory
FOS: Mathematics
Computer Science - Neural and Evolutionary Computing
FOS: Physical sciences
Statistical and Nonlinear Physics
Mathematics - Numerical Analysis
Numerical Analysis (math.NA)
Neural and Evolutionary Computing (cs.NE)
Computational Physics (physics.comp-ph)
Condensed Matter Physics
Physics - Computational Physics
Subjects
Details
- ISSN :
- 01672789
- Volume :
- 443
- Database :
- OpenAIRE
- Journal :
- Physica D: Nonlinear Phenomena
- Accession number :
- edsair.doi.dedup.....d31c361b2b97ce28156f757cce389acf