A new framework for extracting coarse-grained models from time series with multiscale structure

TL;DR

This paper introduces a novel inference framework for deriving coarse-grained models from single time series data of multiscale systems, overcoming biases of traditional estimators and enabling effective model extraction.

Contribution

The work presents a new parametric inference method for multiscale systems that avoids bias and systematically derives coarse-grained models from partial observations.

Findings

The proposed method reduces bias in parameter estimation.

It effectively derives coarse-grained models from limited data.

Demonstrated success across diverse multiscale examples.

Abstract

In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales. In this work we consider the inference problem of identifying an appropriate coarse-grained model from a single time series of a multiscale system. It is known that estimators such as the maximum likelihood estimator or the quadratic variation of the path estimator can be strongly biased in this setting. Here we present a novel parametric inference methodology for problems with linear parameter dependency that does not suffer from this drawback. Furthermore, we demonstrate through a wide spectrum of examples that our methodology can be used to derive appropriate coarse-grained models from time series of partial observations of a multiscale system in an effective and systematic fashion.