3 papers
nlin.PS2025
Data-driven Soliton Manifold Approximations for Dark and Bright Waves: Some Prototypical 1d Case Examples
Su Yang, Shaoxuan Chen, Wei Zhu +1
In this paper, we revisit the investigation of solitary-wave interactions in the nonlinear Schrödinger model, both in the presence and absence of a parabolic trapping potential. W…
nlin.PS2025
Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach
Shaoxuan Chen, Su Yang, Panayotis G. Kevrekidis +1
We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which…
nlin.PS2024
Data-Driven Discovery of Conservation Laws from Trajectories via Neural Deflation
Shaoxuan Chen, Panayotis G. Kevrekidis, Hong-Kun Zhang +1
In an earlier work by a subset of the present authors, the method of the so-called neural deflation was introduced towards identifying a complete set of functionally independent co…