Data-driven closures for stochastic dynamical systems

TL;DR

This paper introduces a novel data-driven closure method for high-dimensional stochastic dynamical systems that estimates statistical properties from data, independent of system dimension, and assesses data sufficiency using hyperbolic systems.

Contribution

It presents a new dimension-independent closure approximation technique and a paradigm for measuring data information content in reduced-order models.

Findings

Effective in nonlinear dynamical systems

Applicable to systems biology models

Provides a way to evaluate data sufficiency

Abstract

In this paper we develop a new data-driven closure approximation method to compute the statistical properties of quantities of interest in high-dimensional stochastic dynamical systems. The new method relies on estimating conditional expectations from sample paths or experimental data, and it is independent of the dimension of the underlying phase space. We also address the important question of whether enough useful data is being injected into the reduced-order model governing the quantity of interest. To this end, we develop a new paradigm to measure the information content of data based on the numerical solution of hyperbolic systems of equations. The effectiveness of the proposed new methods is demonstrated in applications to nonlinear dynamical systems and models of systems biology evolving from random initial states.