Regression on Parametric Manifolds: Estimation of Spatial Fields, Functional Outputs, and Parameters from Noisy Data
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 Offine 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 30, 2012
- Accession Number
- ADA560131
Entities
People
- Anthony T. Patera
- Einar M. Ronquist
Organizations
- Massachusetts Institute of Technology