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Active Sampling of Interpolation Points to Identify Dominant Subspaces for Model Reduction by Reddig, Celine; Goyal, Pawan; Duff, Igor Pontes; Benner, Peter is a scholarly article available to read on EtoBox.

What is Active Sampling of Interpolation Points to Identify Dominant Subspaces for Model Reduction about?

Model reduction is an active research field to construct low-dimensional surrogate models of high fidelity to accelerate engineering design cycles. In this work, we investigate model reduction for linear structured systems using dominant reachable and observable subspaces. When the training set $-$ containing all possible interpolation points $-$ is large, then these subspaces can be determined by solving many large-scale linear systems. However, for high-fidelity models, this easily becomes computationally intractable. To circumvent this issue, in this work, we propose an active sampling strategy to sample only a few points from the given training set, which can allow us to estimate those subspaces accurately. To this end, we formulate the identification of the subspaces as the solution of the generalized Sylvester equations, guiding us to select the most relevant samples from the training set to achieve our goals. Consequently, we construct solutions of the matrix equations in low-rank forms, which encode subspace information. We extensively discuss computational aspects and efficient usage of the low-rank factors in the process of obtaining reduced-order models. We illustrate th

Author

Reddig, Celine; Goyal, Pawan; Duff, Igor Pontes; Benner, Peter

Published

2024

Language

EN