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.
翻译:这项工作侧重于解决使用多种随机系数的大规模不确定性量化(UQ)问题的空间-时间减序模型(ROM)方法(ROM),与传统的空间-时间模型(ROM)方法(Space-ROM方法,该方法在空间层面的尺寸减少)相比,空间-时间-ROM方法在空间和时空领域都具有尺寸减少的作用,从而能够以低成本实现准确的近似解决办法。我们把空间-时间光谱战略与各种传统的随机UQ传播方法(如Stochatic Galerkin和Monte Carlo)结合起来。数字结果表明,与最先进的ROM方法相比,我们的方法具有重大的计算优势。通过测试近似误差,我们表明,由于计算效率高,对空间-时间光谱的模拟准确性没有明显损失。