A bridge between invariant dynamical structures and uncertainty quantification

TL;DR

This paper introduces a new phase space-based uncertainty quantifier for dynamical system trajectories, linking it to invariant structures and enabling quantitative comparison of transport in ocean data sets.

Contribution

It develops a novel uncertainty quantifier connected to dynamical systems structures, facilitating data-driven analysis and comparison of transport phenomena.

Findings

The uncertainty quantifier reveals rich structure related to hyperbolic trajectories.

Application to ocean data sets demonstrates effective transport comparison.

Methodology bridges invariant structures with practical uncertainty assessment.

Abstract

We develop a new quantifier for forward time uncertainty for trajectories that are solutions of models generated from data sets. Our uncertainty quantifier is defined on the phase space in which the trajectories evolve and we show that it has a rich structure that is directly related to phase space structures from dynamical systems theory, such as hyperbolic trajectories and their stable and unstable manifolds. We apply our approach to an ocean data set, as well as standard benchmark models from deterministic dynamical systems theory. A significant application of our results, is that they allow a quantitative comparison of the transport performance described from different ocean data sets. This is particularly interesting nowadays when a wide variety of sources are available, since our methodology provides avenues for assessing the effective use of these data sets in a variety of situations.