Low-Rank Tensor Methods for Model Order Reduction

Anthony Nouy ()
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Anthony Nouy: GeM, Ecole Centrale Nantes, Department of Computer Science and Mathematics

Chapter 25 in Handbook of Uncertainty Quantification, 2017, pp 857-882 from Springer

Abstract: Abstract Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems, or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many instances of the input parameters, which may be intractable for complex numerical models. A possible remedy consists in replacing the model by an approximate model with reduced complexity (a so-called reduced order model) allowing a fast evaluation of output variables of interest. This chapter provides an overview of low-rank methods for the approximation of functions that are identified either with order-two tensors (for vector-valued functions) or higher-order tensors (for multivariate functions). Different approaches are presented for the computation of low-rank approximations, either based on samples of the function or on the equations that are satisfied by the function, the latter approaches including projection-based model order reduction methods. For multivariate functions, different notions of ranks and the corresponding low-rank approximation formats are introduced.

Keywords: High-dimensional problems; Low-rank approximation; Model order reduction; Parameter-dependent equations; Stochastic equations; Uncertainty quantification (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-12385-1_21

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