S-OPT: A POINTS SELECTION ALGORITHM FOR HYPER-REDUCTION IN REDUCED ORDER MODELS

doi:10.1137/22M1484018

S-OPT: A POINTS SELECTION ALGORITHM FOR HYPER-REDUCTION IN REDUCED ORDER MODELS

2024-07-16

3

OA

AI

DOI：10.1137/22M1484018

Original

Original request for help

Save

Abstract

En 中文

While projection-based reduced order models can reduce the dimension of full order solutions, the resulting reduced models may still contain terms that scale with the full order dimension. Hyper-reduction techniques are sampling-based methods that further reduce this computational complexity by approximating such terms with a much smaller dimension. The goal of this work is to introduce the points selection algorithm developed by Shin and Xiu [SIAM J. Sci. Comput., 38 (2016), pp. A385-A411] as a hyper-reduction method. The selection algorithm was originally proposed as a stochastic collocation method for uncertainty quantification. Since the algorithm aims at maximizing a quantity S that measures both the column orthogonality and the determinant, we refer to the algorithm as S-OPT. Numerical examples are provided to demonstrate the performance of S-OPT and to compare its performance with a gappy proper orthogonal decomposition (POD) algorithm. We found that using the S-OPT algorithm is shown to predict the full order solutions with higher accuracy than gappy POD especially when the number of sampling points is small, although we note that S-OPT shows slow asymptotic convergence with respect to the number of samples for some applications, e.g., Lagrangian hydrodynamics.

Keywords:

reduced order modeling

nonlinear model reduction

Galerkin projection

hyper-reduction

sampling algorithm

S-OPT: A POINTS SELECTION ALGORITHM FOR HYPER-REDUCTION IN REDUCED ORDER MODELS

Abstract

Journal

Organization