Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data
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Patera_Regression on parametric.pdf
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Author(s)
Patera, Anthony T.
Ronquist, Einar M.
Date Issued
May 2012
Journal
Comptes Rendus Mathematique
Publisher
Elsevier
Citation
Patera, Anthony T., and Einar M. Ronquist. “Regression on Parametric Manifolds: Estimation of Spatial Fields, Functional Outputs, and Parameters from Noisy Data.” Comptes Rendus Mathematique 350, no. 9–10 (May 2012): 543–547.
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Author's final manuscript
Abstract
In this Note we extend the Empirical Interpolation Method (EIM) to a regression context which accommodates noisy (experimental) data on an underlying parametric manifold. The EIM basis functions are computed Offline from the noise-free manifold; the EIM coefficients for any function on the manifold are computed Online from experimental observations through a least-squares formulation. Noise-induced errors in the EIM coefficients and in linear-functional outputs are assessed through standard confidence intervals and without knowledge of the parameter value or the noise level. We also propose an associated procedure for parameter estimation from noisy data.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1016/j.crma.2012.05.002
