Learning effective dynamics from data-driven stochastic systems
Abstract
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to investigating the effective dynamics for slow-fast stochastic dynamical systems. Given observation data on a short-term period satisfying some unknown slow-fast stochastic systems, we propose a novel algorithm including a neural network called Auto-SDE to learn invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also validated to be accurate, stable and effective through numerical experiments under various evaluation metrics.
Cite
@article{arxiv.2205.04151,
title = {Learning effective dynamics from data-driven stochastic systems},
author = {Lingyu Feng and Ting Gao and Min Dai and Jinqiao Duan},
journal= {arXiv preprint arXiv:2205.04151},
year = {2024}
}