Weighted reduced order methods for uncertainty quantification in computational fluid dynamics

TL;DR

This paper introduces and compares weighted reduced order methods for uncertainty quantification in stochastic fluid dynamics problems, addressing high-dimensional parameter spaces and the curse of dimensionality.

Contribution

It develops and analyzes weighted reduced order techniques, including weighted greedy and POD, for stochastic Stokes and Navier-Stokes equations, improving efficiency in high-dimensional settings.

Findings

Weighted methods outperform non-weighted in stochastic scenarios.

Different sampling and weighting strategies help mitigate the curse of dimensionality.

The approach enhances computational efficiency for uncertainty quantification.

Abstract

In this manuscript we propose and analyze weighted reduced order methods for stochastic Stokes and Navier-Stokes problems depending on random input data (such as forcing terms, physical or geometrical coefficients, boundary conditions). We will compare weighted methods such as weighted greedy and weighted POD with non-weighted ones in case of stochastic parameters. In addition we will analyze different sampling and weighting choices to overcome the curse of dimensionality with high dimensional parameter spaces.