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Data-Driven Model Reduction, Scientific Frontiers, and Applications ()

Suman Chakravorty, Department of Aerospace Engineering
Randomized Model Reduction for Large Scale Systems


In this work, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a randomized balanced proper orthogonal decomposition (RPOD*) technique to obtain the reduced order model by perturbing the primal and adjoint system using Gaussian white noise. We obtain rigorous probabilistic error bounds on the impulse response of the obtained reduced order models. We show that computations required by the RPOD* algorithm is orders of magnitude lower while its performance is much better than other state of the art algorithms. We shall also relate the RPOD* algorithm to Krylov subspace methods and show that it constitutes an alternative randomized approach to any computational linear algebra problems utilizing Krylov subspace methods.