Predicting Uncertainty in Geometric Fluid Mechanics

TL;DR

This paper discusses how stochastic geometric mechanics can be used to integrate observed data into variational principles, enabling the development of data-driven models that account for variability in fluid motion caused by small-scale, rapid phenomena.

Contribution

It introduces a framework for incorporating observed data into stochastic geometric mechanics to derive nonlinear models of fluid variability.

Findings

Framework for data integration into stochastic mechanics

Enhanced models capturing small-scale fluid effects

Potential for improved fluid motion predictions

Abstract

We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable scales of fluid motion, due to unresolvable, small, rapid scales of fluid motion.