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: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Elsevier
2015
|
| Online Access: | http://hdl.handle.net/1721.1/99385 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1826206039460020224 |
|---|---|
| author | Patera, Anthony T. Ronquist, Einar M. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Patera, Anthony T. Ronquist, Einar M. |
| author_sort | Patera, Anthony T. |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T13:23:03Z |
| format | Article |
| id | mit-1721.1/99385 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T13:23:03Z |
| publishDate | 2015 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/993852022-10-01T14:54:08Z Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data Patera, Anthony T. Ronquist, Einar M. Massachusetts Institute of Technology. Department of Mechanical Engineering Patera, Anthony T. 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 2015-10-21T14:47:18Z 2015-10-21T14:47:18Z 2012-05 2012-03 Article http://purl.org/eprint/type/JournalArticle 1631073X http://hdl.handle.net/1721.1/99385 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. https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1016/j.crma.2012.05.002 Comptes Rendus Mathematique Creative Commons Attribution-Noncommercial-NoDerivatives http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier MIT Web Domain |
| spellingShingle | Patera, Anthony T. Ronquist, Einar M. Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data |
| title | Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data |
| title_full | Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data |
| title_fullStr | Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data |
| title_full_unstemmed | Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data |
| title_short | Regression on parametric manifolds: Estimation of spatial fields, functional outputs, and parameters from noisy data |
| title_sort | regression on parametric manifolds estimation of spatial fields functional outputs and parameters from noisy data |
| url | http://hdl.handle.net/1721.1/99385 https://orcid.org/0000-0002-2631-6463 |
| work_keys_str_mv | AT pateraanthonyt regressiononparametricmanifoldsestimationofspatialfieldsfunctionaloutputsandparametersfromnoisydata AT ronquisteinarm regressiononparametricmanifoldsestimationofspatialfieldsfunctionaloutputsandparametersfromnoisydata |