Predictability in Spatially Extended Systems with Model Uncertainty

TL;DR

This paper discusses techniques for analyzing the predictability of spatially extended systems modeled by stochastic partial differential equations, focusing on correlation estimation, Lyapunov exponents, and noise impact, relevant across various scientific fields.

Contribution

It provides an overview of methods to understand solution behaviors and predictability in SPDEs with model uncertainty, applicable to physics, geophysics, and biology.

Findings

Techniques for estimating correlations in SPDE solutions

Analysis of Lyapunov exponents in spatial systems

Assessment of noise impact on predictability

Abstract

Macroscopic models for spatially extended systems under random influences are often described by stochastic partial differential equations (SPDEs). Some techniques for understanding solutions of such equations, such as estimating correlations, Liapunov exponents and impact of noises, are discussed. They are relevant for understanding predictability in spatially extended systems with model uncertainty, for example, in physics, geophysics and biological sciences. The presentation is for a wide audience.