Non-Intrusive Parametric Reduced Order Modeling using Randomized Algorithms

Abstract

This paper demonstrates the creation of purely data-driven, non-intrusive parametric reduced order models (ROMs) for emulation of high-dimensional field outputs using randomized linear algebra techniques. Typically, low-dimensional representations are built using the Proper Orthogonal Decomposition (POD) combined with interpolation/regression in the latent space via machine learning. However, even moderately large simulations can lead to data sets on which the cost of computing the POD becomes intractable due to storage and computational complexity of the numerical procedure. In an attempt to reduce the \textit{offline} cost, the proposed method demonstrates the application of randomized singular value decomposition (SVD) and sketching-based randomized SVD to compute the POD basis. The predictive capability of ROMs resulting from regular SVD and randomized/sketching-based algorithms are compared with each other to ensure that the decrease in computational cost does not result in a loss in accuracy. Demonstrations on canonical and practical fluid flow problems show that the ROMs resulting from randomized methods are competitive with ROMs that employ the conventional deterministic method. Through this new method, it is hoped that truly large-scale parametric ROMs can be constructed under a significantly limited computational budget.