Model Order Reduction Techniques for the Stochastic Finite Volume Method

TL;DR

This paper introduces a reduced order modeling approach with hyper-reduction techniques to significantly decrease computational costs in the stochastic finite volume method for high-dimensional uncertainty quantification.

Contribution

It combines interpolation-based ROM and Q-DEIM hyper-reduction to improve efficiency in SFV methods for high-dimensional stochastic problems.

Findings

Reduces computational cost and memory requirements for high-dimensional stochastic spaces.

Demonstrates effectiveness through numerical experiments.

Achieves high-order accuracy in uncertainty quantification.

Abstract

The stochastic finite volume method (SFV method) is a high-order accurate method for uncertainty quantification (UQ) in hyperbolic conservation laws. However, the computational cost of SFV method increases for high-dimensional stochastic parameter spaces due to the curse of dimensionality. To address this challenge, we incorporate interpolation-based reduced order model (ROM) techniques that reduce the cost of computing stochastic integrals in the SFV method. Further efficiency gains are achieved through hyper-reduction with a QR factorization-based discrete empirical interpolation method (Q-DEIM). Numerical experiments suggest that this approach can lower both computational cost and memory requirements for high-dimensional stochastic parameter spaces.