A Computationally Optimal Randomized Proper Orthogonal Decomposition Technique
Abstract
In this paper, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a computationally optimal randomized proper orthogonal decomposition (RPOD*) technique to obtain the reduced order model by perturbing the primal and adjoint system using Gaussian white noise. We show that the computations required by the RPOD* algorithm is orders of magnitude cheaper when compared to the balanced proper orthogonal decomposition (BPOD) algorithm and BPOD output projection algorithm while the performance of the RPOD* algorithm is much better than BPOD output projection algorithm. It is optimal in the sense that a minimal number of snapshots is needed. We also relate the RPOD* algorithm to random projection algorithms. The method is tested on two advection-diffusion equations.
Cite
@article{arxiv.1509.05705,
title = {A Computationally Optimal Randomized Proper Orthogonal Decomposition Technique},
author = {Dan Yu and Suman Chakravorty},
journal= {arXiv preprint arXiv:1509.05705},
year = {2016}
}