2 research outputs found
A Computationally Optimal Randomized Proper Orthogonal Decomposition Technique
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
Efficient Algorithms for Eigensystem Realization using Randomized SVD
Eigensystem Realization Algorithm (ERA) is a data-driven approach for
subspace system identification and is widely used in many areas of engineering.
However, the computational cost of the ERA is dominated by a step that involves
the singular value decomposition (SVD) of a large, dense matrix with block
Hankel structure. This paper develops computationally efficient algorithms for
reducing the computational cost of the SVD step by using randomized subspace
iteration and exploiting the block Hankel structure of the matrix. We provide a
detailed analysis of the error in the identified system matrices and the
computational cost of the proposed algorithms. We demonstrate the accuracy and
computational benefits of our algorithms on two test problems: the first
involves a partial differential equation that models the cooling of steel
rails, and the second is an application from power systems engineering