Closure Term Estimation in Spatiotemporal Models of Dynamical Systems

TL;DR

This paper introduces a new, efficient method for estimating closure terms in spatiotemporal dynamical systems that includes uncertainty quantification and works well with noisy or sparse data.

Contribution

The paper presents a novel closure modeling approach that is computationally efficient, provides uncertainty quantification, and handles noisy or sparse observations effectively.

Findings

Effective in one and two spatial dimensions

Demonstrated on Fisher-KPP and advection-diffusion equations

Handles noisy and sparse data well

Abstract

Closure modeling - the statistical modeling of missing dynamics in the natural sciences and engineering - is a growing and active area of research. Existing methods for closure modeling are often computationally prohibitive, lack uncertainty quantification, or require noise-free observations of the temporal derivatives over the system state. We propose a novel, computationally efficient approach for the modeling and estimation of closure terms over the spatiotemporal domain that provides uncertainty quantification and is effective even when the observations of the system state are sparse or contain moderate levels of noise. The efficacy of our approach is demonstrated in both one and two spatial dimensions through numerical experiments using the Fisher-KPP reaction-diffusion equation and the advection-diffusion equation as exemplars.