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Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics

Akian, J.-L. and Bonnet, L. and Owhadi, H. and Savin, É. (2022) Learning "best" kernels from data in Gaussian process regression. With application to aerodynamics. Journal of Computational Physics, 470 . Art. No. 111595. ISSN 0021-9991. doi:10.1016/

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This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert Spaces (RKHS), to solve the problem of approximating a regular target function given observations of it, i.e. supervised learning. A first class of algorithms is kernel flow, which was introduced in the context of classification in machine learning. It can be seen as a cross-validation procedure whereby a "best" kernel is selected such that the loss of accuracy incurred by removing some part of the dataset (typically half of it) is minimized. A second class of algorithms is called spectral kernel ridge regression, and aims at selecting a "best" kernel such that the norm of the function to be approximated is minimal in the associated RKHS. Within Mercer's theorem framework, we obtain an explicit construction of that "best" kernel in terms of the main features of the target function. Both approaches of learning kernels from data are illustrated by numerical examples on synthetic test functions, and on a classical test case in turbulence modeling validation for transonic flows about a two-dimensional airfoil.

Item Type:Article
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Owhadi, H.0000-0002-5677-1600
Savin, É.0000-0002-3767-0281
Record Number:CaltechAUTHORS:20221020-727675300.1
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ID Code:117504
Deposited By: Research Services Depository
Deposited On:28 Oct 2022 15:29
Last Modified:28 Oct 2022 15:29

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