Robust Estimation of Effective Diffusions from Multiscale Data

TL;DR

This paper introduces a new method using filtered data and moving averages to accurately estimate effective dynamics in multiscale systems, demonstrating improved robustness and less model knowledge requirement compared to traditional subsampling techniques.

Contribution

The paper proposes a semi-parametric approach for estimating coarse-grained dynamics that is asymptotically unbiased and more robust than existing methods like subsampling.

Findings

Method accurately extracts coarse-grained dynamics from multiscale data.

Approach is more robust and requires less prior model knowledge.

Validated through challenging numerical experiments.

Abstract

We present a novel methodology based on filtered data and moving averages for estimating effective dynamics from observations of multiscale systems. We show in a semi-parametric framework of the Langevin type that our approach is asymptotically unbiased with respect to the theory of homogenization. Moreover, we demonstrate on a range of challenging numerical experiments that our method is accurate in extracting coarse-grained dynamics from multiscale data. In particular, the estimators we propose are more robust and require less knowledge of the full model than the standard technique of subsampling, which is widely employed in practice in this setting.