Data-driven Effective Modeling of Multiscale Stochastic Dynamical Systems

TL;DR

This paper introduces a data-driven numerical approach to model the effective dynamics of slow variables in unknown multiscale stochastic systems, using observation data to construct accurate generative models.

Contribution

It proposes a novel method that learns the slow dynamics directly from data without knowing the governing equations, applicable to multiscale stochastic systems.

Findings

Successfully captures the distribution of slow variables

Demonstrates effectiveness through numerical examples

Provides a generative model for unknown multiscale systems

Abstract

We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are available. By utilizing the observation data, our proposed method is capable of constructing a generative stochastic model that can accurately capture the effective dynamics of the slow variables in distribution. We present a comprehensive set of numerical examples to demonstrate the performance of the proposed method.