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

2021/12/13 by Zheng Wu Miao, Yong Chen
Physics and Astronomy · Computer Science · #Model Reduction and Neural Networks #Neural Networks and Applications #Quantum chaos and dynamical systems

paper · doi:10.1142/s021798492150531x

Abstract

In this paper, the physics-informed neural networks (PINNs) are applied to high-dimensional system to solve the [Formula: see text]-dimensional initial-boundary value problem with [Formula: see text] 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.

Citations

• On the limited memory BFGS method for large scale optimization
• ImageNet classification with deep convolutional neural networks
• An overview of gradient descent optimization algorithms
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations
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