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.

Open PDF

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

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Differential Equations
  • Engineering
  • Equations
  • Errors
  • Experimental Data
  • Information Operations
  • Interpolation
  • Inverse Problems
  • Mathematical Analysis
  • Mathematics
  • Measurement
  • Mechanical Engineering
  • Observation
  • Partial Differential Equations
  • Random Variables
  • Standards

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Neural Network Machine Learning.
  • Underwater engineering and Marine Technology.