Physics-informed neural networks method in high-dimensional integrable systems

Abstract

In this paper, the physics-informed neural networks (PINN) is applied to high-dimensional system to solve the (N+1)-dimensional initial boundary value problem with 2N+1 hyperplane boundaries. This method is used to solve the most classic (2+1)-dimensional integrable Kadomtsev-Petviashvili (KP) equation and (3+1)-dimensional reduced KP equation. The dynamics of (2+1)-dimensional local waves such as solitons, breathers, lump and resonance rogue are reproduced. Numerical results display that the magnitude of the error is much smaller than the wave height itself, so it is considered that the classical solutions in these integrable systems are well obtained based on the data-driven mechanism.

References in corpus (6)

• Recurrent Neural Network Regularization
• Inferring solutions of differential equations using noisy multi-fidelity data
• A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions
• Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN
• Solving localized wave solutions of the derivative nonlinear Schrodinger equation using an improved PINN method
• Construction of a tensor product algebra with a multicentric functional calculus

Cited by in corpus (5)

• Data-driven vector localized waves and parameters discovery for Manakov system using deep learning approach
• Physics-informed neural network methods based on Miura transformations and discovery of new localized wave solutions
• Data-driven discoveries of Bäcklund transforms and soliton evolution equations via deep neural network learning schemes
• RAR-PINN algorithm for the data-driven vector-soliton solutions and parameter discovery of coupled nonlinear equations
• Discovery of Quasi-Integrable Equations from traveling-wave data using the Physics-Informed Neural Networks