Estimating the uncertainty in underresolved nonlinear dynamics

TL;DR

This paper uses the Mori-Zwanzig formalism to quantify uncertainty in underresolved nonlinear dynamical systems, revealing that the resulting noise is typically non-Markovian and non-Gaussian, which is a common scenario.

Contribution

It introduces a general approach to estimate uncertainty in nonlinear dynamics under resolution limitations, highlighting the nature of the noise as non-Markovian and non-Gaussian.

Findings

The noise modeling uncertainty is neither Markovian nor Gaussian.

The approach is demonstrated on a simple example.

Non-Markovian and non-Gaussian noise are typical in such systems.

Abstract

The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise term that describes the uncertainty turns out to be neither Markovian nor Gaussian. It is argued that this is the general situation.