1. Discrete empirical interpolation in the tensor t-product framework
- Author
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Chellappa, Sridhar, Feng, Lihong, and Benner, Peter
- Subjects
Mathematics - Numerical Analysis ,Computer Science - Computational Engineering, Finance, and Science ,Mathematics - Dynamical Systems - Abstract
The discrete empirical interpolation method (DEIM) is a well-established approach, widely used for state reconstruction using sparse sensor/measurement data, nonlinear model reduction, and interpretable feature selection. We introduce the tensor t-product Q-DEIM (t-Q-DEIM), an extension of the DEIM framework for dealing with tensor-valued data. The proposed approach seeks to overcome one of the key drawbacks of DEIM, viz., the need for matricizing the data, which can distort any structural and/or geometric information. Our method leverages the recently developed tensor t-product algebra to avoid reshaping the data. In analogy with the standard DEIM, we formulate and solve a tensor-valued least-squares problem, whose solution is achieved through an interpolatory projection. We develop a rigorous, computable upper bound for the error resulting from the t-Q-DEIM approximation. Using five different tensor-valued datasets, we numerically illustrate the better approximation properties of t-Q-DEIM and the significant computational cost reduction it offers., Comment: 37 pages, 22 figures, 1 table more...
- Published
- 2024