Learning effective dynamics from data-driven stochastic systems

TL;DR

This paper introduces Auto-SDE, a neural network-based algorithm that learns invariant slow manifolds in multiscale stochastic systems from short-term observational data, enabling effective modeling of complex slow-fast dynamics.

Contribution

The paper proposes a novel neural network approach, Auto-SDE, for learning effective slow manifold dynamics directly from data in stochastic systems, addressing a key challenge in multiscale modeling.

Findings

Auto-SDE accurately captures slow manifold dynamics.

The method demonstrates stability and effectiveness across various experiments.

Numerical validation confirms the approach's robustness and precision.

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.