Space-time reduced-order modeling for uncertainty quantification

2021/11/11 by Ruhui Jin, Jin, Ruhui, Francesco Rizzi +3
Computer Science · Decision Sciences · Mathematics · Physics and Astronomy · #Advanced Multi-Objective Optimization Algorithms #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #cs.NA #math.NA

paper · pdf · doi:10.48550/arxiv.2111.06435

arxiv created 2021/11/11 · openalex publication_date 2021/11/11 · arxiv updated 2021/11/15 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

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.

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