Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data
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...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Elsevier,
2015-10-21T14:47:18Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | 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. United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0613) United States. Office of Naval Research (Grant N00014-11-0713) Norwegian University of Science and Technology |
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