The data-driven localized wave solutions of the derivative nonlinear Schrödinger equation by using improved PINN approach

DOI10.1016/j.wavemoti.2021.102823OpenAlexW3197053878MaRDI QIDQ2124077

JunCai Pu, Yong Chen, Wei-Qi Peng

Publication date: 14 April 2022

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.14493

zbMATH Keywords

derivative nonlinear Schrödinger equationdata-driven localized wave solutionsimproved physics-informed neural networks

Mathematics Subject Classification ID

Fluid mechanics (76-XX) Partial differential equations (35-XX)

Related Items (8)

Data-driven modeling of two-dimensional detonation wave fronts ⋮ Neural networks enforcing physical symmetries in nonlinear dynamical lattices: the case example of the Ablowitz-Ladik model ⋮ The Fermi-Pasta-Ulam-Tsingou recurrence for discrete systems: cascading mechanism and machine learning for the Ablowitz-Ladik equation ⋮ A deep learning method for solving high-order nonlinear soliton equations ⋮ Data-driven forward-inverse problems for Yajima-Oikawa system using deep learning with parameter regularization ⋮ Rational and semi‐rational solutions for a (3 + 1)‐dimensional generalized KP–Boussinesq equation in shallow water wave ⋮ Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm ⋮ The nonlinear wave solutions and parameters discovery of the Lakshmanan-Porsezian-Daniel based on deep learning

Uses Software

• L-BFGS
• ImageNet
• Omniglot
• AlexNet
• PRMLT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the limited memory BFGS method for large scale optimization
• On the derivative nonlinear Schrödinger equation
• Rogue waves in the generalized derivative nonlinear Schrödinger equations
• The derivative nonlinear Schrödinger equation with zero/nonzero boundary conditions: inverse scattering transforms and \(N\)-double-pole solutions
• Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
• Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning
• Rogue waves generation through multiphase solutions degeneration for the derivative nonlinear Schrödinger equation
• The hierarchy of higher order solutions of the derivative nonlinear Schrödinger equation
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Modified Nonlinear Schrödinger Equation for Alfvén Waves Propagating along the Magnetic Field in Cold Plasmas
• Multi-Soliton Solutions of a Derivative Nonlinear Schrödinger Equation
• Human-level concept learning through probabilistic program induction
• The Darboux transformation of the derivative nonlinear Schrödinger equation
• Alfven solitons
• Large Sample Properties of Simulations Using Latin Hypercube Sampling
• An exact solution for a derivative nonlinear Schrödinger equation
• The hierarchy of multi-soliton solutions of the derivative nonlinear Schr dinger equation
• Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
• Learning representations by back-propagating errors
• On improving the effectiveness of periodic solutions of the NLS and DNLS equations
• Solving second-order nonlinear evolution partial differential equations using deep learning
• A deep learning method for solving third-order nonlinear evolution equations

This page was built for publication: The data-driven localized wave solutions of the derivative nonlinear Schrödinger equation by using improved PINN approach