Dimension reduction of the input parameter space of vector-valued functions

Olivier Zahm 1
1 AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows
Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology, UGA - Université Grenoble Alpes, LJK - Laboratoire Jean Kuntzmann, Inria Grenoble - Rhône-Alpes
Abstract : Approximation of multivariate functions is a difficult task when the number of input parameters is large. Identifying the directions where the function does not significantly vary is a key step for complexity reduction. Among other dimension reduction techniques, the Active Subspace method uses gradients of a scalar valued function to reduce the parameter space. In this talk, we extend this methodology for vector-valued functions, including multiple scalar-valued functions and functions taking values in functional spaces. Numerical examples reveals the importance of the choice of the metric to measure errors and compare it with the commonly used truncated Karhunen-Loeve decomposition.
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Conference papers
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https://hal.inria.fr/hal-01955795
Contributor : Olivier Zahm <>
Submitted on : Friday, December 14, 2018 - 3:56:17 PM
Last modification on : Friday, February 8, 2019 - 8:14:02 AM

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Olivier Zahm. Dimension reduction of the input parameter space of vector-valued functions. SIAM-UQ 2018 - SIAM Conference on Uncertainty Quantification, Apr 2018, Los Angeles, United States. ⟨hal-01955795⟩

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