Speaker: Prof. Yong Chen, East China Normal University

Title: Lax pairs informed neural networks solving integrable systems-(I)

Language: Chinese

Time & Venue: 2024.11.14 19:00-19:40 N402

Abstract: In this talk, we propose the Lax pairs informed neural networks (LPINNs) tailored for integrable systems with Lax pairs by designing novel network architectures and loss functions, comprising LPINN-v1 and LPINN-v2. On the basis of LPINN-v1, we additionally incorporate the compatibility condition/zero curvature equation of Lax pairs in LPINN-v2, its major advantage is the ability to solve and explore high-accuracy data-driven localized wave solutions and associated spectral problems for all integrable systems with Lax pairs. The numerical experiments in this work involve several important and classic low-dimensional and high-dimensional integrable systems, abundant localized wave solutions and their Lax pairs , including the soliton of the KdV equation and modified KdV equation, rogue wave solution of the NLS, kink solution of the sine-Gordon equation, non-smooth peakon solution of the Camassa-Holm equation and pulse solution of the short pulse equation, as well as the line-soliton solution KP equation.