Quantifying model uncertainty in non-Gaussian dynamical systems with observations on mean exit time or escape probability

TL;DR

This paper introduces a novel method for estimating parameters in non-Gaussian dynamical systems using observations of mean exit time or escape probability, avoiding the need for extensive data on system paths or densities.

Contribution

A new inverse problem approach using non-local PDEs and numerical optimization to estimate parameters from limited observations in non-Gaussian systems.

Findings

Effective estimation with small spatial domain data

Reduces data collection requirements compared to existing methods

Applicable to systems with feasible mean exit time or escape probability observations

Abstract

Complex systems are sometimes subject to non Gaussian alpha stable Levy fluctuations. A new method is devised to estimate this uncertain parameter and other system parameters, using observations on either mean exit time or escape probability for the system evolution. It is based on solving an inverse problem for a deterministic, non-local partial differential equation via numerical optimization. The existing methods for estimating parameters require observations on system state sample paths for long time periods or probability densities at large spatial ranges. The method proposed here, instead, requires observations on mean exit time or escape probability only for an arbitrarily small spatial domain. This new method is beneficial to systems for which mean exit time or escape probability is feasible to observe.