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Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach
Shaoxuan Chen, Su Yang, Panayotis G. Kevrekidis, Wei Zhu
https://arxiv.org/abs/2506.05245

Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach
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 necessitate densely sampled data and are sensitive to noise, our approach based on Neural ODEs directly models moment trajectories, enabling robust learning from sparse and potentially irregular time series. Using as an application platform the nonlinear Schrödinger equation, the framework accurately recovers govern…