Learning effective dynamics from data-driven stochastic systems

Lingyu Feng; Ting Gao; Min Dai; Jinqiao Duan

doi:10.1063/5.0126667

Learning effective dynamics from data-driven stochastic systems

Chaos. 2023 Apr 1;33(4):043131. doi: 10.1063/5.0126667.

Authors

Lingyu Feng^{1

2}, Ting Gao^{1

2}, Min Dai³, Jinqiao Duan⁴

Affiliations

¹ School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
² Center for Mathematical Science, Huazhong University of Science and Technology, Wuhan 430074, China.
³ School of Science, Wuhan University of Technology, Wuhan 430070, China.
⁴ College of Science, Great Bay University, Dongguan, Guangdong 523000, China.

PMID: 37097942
DOI: 10.1063/5.0126667

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 an 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.