Randomized Algorithms for Non-Intrusive Parametric Reduced Order Modeling

This paper demonstrates the development of purely data-driven, nonintrusive parametric reduced-order models for the emulation of high-dimensional field outputs using randomized linear algebra techniques. Typically, low-dimensional representations are built using the proper orthogonal decomposition combined with interpolation/regression in the latent space via supervised learning. However, even moderately large simulations can lead to data sets on which the cost of computing the proper orthogonal decomposition becomes intractable due to storage and computational complexity of the numerical procedure. In an attempt to reduce the offline cost, the proposed method demonstrates the application of randomized singular value decomposition and sketching-based randomized singular value decomposition to compute the proper orthogonal decomposition basis. The predictive capability of reduced-order models resulting from regular singular value decomposition 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 reduced-order models constructed using randomized methods are competitive in their predictive accuracy with reduced-order models that employ the conventional deterministic method. Through this new method, it is expected that truly large-scale parametric reduced-order models can be constructed under a significantly limited computational resource budget.