  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.
