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Low-rank tensor methods for model order reduction

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.
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Contributor : Anthony Nouy <>
Submitted on : Tuesday, January 26, 2016 - 4:31:32 PM
Last modification on : Tuesday, December 8, 2020 - 9:39:21 AM

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  • HAL Id : hal-01262403, version 1
  • ARXIV : 1511.01555



Anthony Nouy. Low-rank tensor methods for model order reduction. R. Ghanem; D. Higdon; H. Owhadi. Handbook of Uncertainty Quantification, 2016. ⟨hal-01262403⟩



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