A Computationally Optimal Randomized Proper Orthogonal Decomposition Technique
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2016 American Automatic Control Council (AACC). 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 while the performance of the RPOD algorithm is better than BPOD. It is optimal in the sense that a minimal number of snapshots is needed. We also relate the RPOD algorithm to random projection algorithms. One numerical example is given to illustrate the procedure.
