Universal Upper Estimate for Prediction Errors under Moderate Model Uncertainty

TL;DR

This paper presents universal, optimal upper bounds on prediction errors caused by moderate model uncertainty, based on the known invariants of the Cauchy-Green strain tensor, and introduces the Model Sensitivity as a practical assessment tool.

Contribution

It derives universal, optimal upper estimates for prediction errors under model uncertainty using invariants of the Cauchy-Green tensor and introduces the Model Sensitivity for global uncertainty assessment.

Findings

Bounds are optimal and cannot be improved for general systems.

Model Sensitivity effectively assesses the impact of uncertainties.

Finite-Time Lyapunov Exponents do not fully capture sensitivity to modeling errors.

Abstract

We derive universal upper estimates for model-prediction error under moderate but otherwise unknown model uncertainty. Our estimates give upper bounds on the leading order trajectory-uncertainty arising along model trajectories, solely as functions of the invariants of the known Cauchy-Green strain tensor of the model. Our bounds turn out to be optimal, which means that they cannot be improved for general systems. The quantity relating the leading-order trajectory-uncertainty to the model uncertainty is the Model Sensitivity, which we find to be a useful tool for a quick global assessment of the impact of modeling uncertainties in various domains of the phase space. Examining the expectation that Finite-Time Lyapunov Exponents capture sensitivity to modeling errors, we show that this does not generally follow. However, we find that certain important features of the FTLE persist in the MS field.