Space-time reduced-order modeling for uncertainty quantification

TL;DR

This paper introduces a space-time reduced-order modeling approach for uncertainty quantification that reduces dimensions in both space and time, leading to efficient and accurate large-scale simulations.

Contribution

The novel space-time ROM method combines spatial and temporal dimension reduction with classical UQ techniques, improving efficiency without sacrificing accuracy.

Findings

Significant computational savings over traditional ROM methods.

High accuracy maintained despite reduced dimensions.

Effective for large-scale uncertainty quantification problems.

Abstract

This work focuses on the space-time reduced-order modeling (ROM) method for solving large-scale uncertainty quantification (UQ) problems with multiple random coefficients. In contrast with the traditional space ROM approach, which performs dimension reduction in the spatial dimension, the space-time ROM approach performs dimension reduction on both the spatial and temporal domains, and thus enables accurate approximate solutions at a low cost. We incorporate the space-time ROM strategy with various classical stochastic UQ propagation methods such as stochastic Galerkin and Monte Carlo. Numerical results demonstrate that our methodology has significant computational advantages compared to state-of-the-art ROM approaches. By testing the approximation errors, we show that there is no obvious loss of simulation accuracy for space-time ROM given its high computational efficiency.