Data-driven rogue waves and parameter discovery in the defocusing nonlinear Schrödinger equation with a potential using the PINN deep learning

2020/12/18 by Li Wang, Zhenya Yan · 144 citations
Computer Science · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Artificial intelligence #Artificial neural network #Boundary value problem #Computer science #Deep learning #Fractional Differential Equations Solutions #Function (biology) #Gaussian #Mathematical analysis #Mathematics #Meteorological Phenomena and Simulations #Model Reduction and Neural Networks #Nonlinear Schrödinger equation #Nonlinear system #Partial differential equation #Physics #Quantum mechanics #Rogue wave #Schrödinger equation #cs.LG #nlin.PS #quant-ph

paper · pdf · doi:10.1016/j.physleta.2021.127408

published in Physics Letters A 404, 127408 (Elsevier BV) · 12 pages, 5 figures

arxiv created 2020/12/18 · openalex created_date 2021/01/05 · openalex publication_date 2021/05/06 · arxiv updated 2021/11/19 · openalex updated_date 2026/08/05

Abstract

The physics-informed neural networks (PINNs) can be used to deep learn the nonlinear partial differential equations and other types of physical models. In this paper, we use the multi-layer PINN deep learning method to study the data-driven rogue wave solutions of the defocusing nonlinear Schrödinger (NLS) equation with the time-dependent potential by considering several initial conditions such as the rogue wave, Jacobi elliptic cosine function, two-Gaussian function, or three-hyperbolic-secant function, and periodic boundary conditions. Moreover, the multi-layer PINN algorithm can also be used to learn the parameter in the defocusing NLS equation with the time-dependent potential under the sense of the rogue wave solution. These results will be useful to further discuss the rogue wave solutions of the defocusing NLS equation with a potential in the study of deep learning neural networks.

Citations

• Modulation instability: The beginning
• On the limited memory BFGS method for large scale optimization
• Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
• ImageNet classification with deep convolutional neural networks
• Human-level concept learning through probabilistic program induction
• Understanding Deep Convolutional Networks
• On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groups
• N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
• Large Sample Properties of Simulations Using Latin Hypercube Sampling

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