Certified reduced basis model validation: A frequentistic uncertainty framework
We introduce a frequentistic validation framework for assessment — acceptance or rejection — of the consistency of a proposed parametrized partial differential equation model with respect to (noisy) experimental data from a physical system. Our method builds upon the Hotelling T[superscript 2] stati...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Elsevier
2015
|
| Online Access: | http://hdl.handle.net/1721.1/99387 https://orcid.org/0000-0002-2794-1308 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1811092015142666240 |
|---|---|
| author | Patera, Anthony T. Huynh, Dinh Bao Phuong Knezevic, David Patera, Anthony T. |
| author2 | Massachusetts Institute of Technology. Center for Computational Engineering |
| author_facet | Massachusetts Institute of Technology. Center for Computational Engineering Patera, Anthony T. Huynh, Dinh Bao Phuong Knezevic, David Patera, Anthony T. |
| author_sort | Patera, Anthony T. |
| collection | MIT |
| description | We introduce a frequentistic validation framework for assessment — acceptance or rejection — of the consistency of a proposed parametrized partial differential equation model with respect to (noisy) experimental data from a physical system. Our method builds upon the Hotelling T[superscript 2] statistical hypothesis test for bias first introduced by Balci and Sargent in 1984 and subsequently extended by McFarland and Mahadevan (2008). Our approach introduces two new elements: a spectral representation of the misfit which reduces the dimensionality and variance of the underlying multivariate Gaussian but without introduction of the usual regression assumptions; a certified (verified) reduced basis approximation — reduced order model — which greatly accelerates computational performance but without any loss of rigor relative to the full (finite element) discretization. We illustrate our approach with examples from heat transfer and acoustics, both based on synthetic data. We demonstrate that we can efficiently identify possibility regions that characterize parameter uncertainty; furthermore, in the case that the possibility region is empty, we can deduce the presence of “unmodeled physics” such as cracks or heterogeneities. |
| first_indexed | 2024-09-23T15:11:33Z |
| format | Article |
| id | mit-1721.1/99387 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:11:33Z |
| publishDate | 2015 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/993872022-09-29T13:15:57Z Certified reduced basis model validation: A frequentistic uncertainty framework Patera, Anthony T. Huynh, Dinh Bao Phuong Knezevic, David Patera, Anthony T. Massachusetts Institute of Technology. Center for Computational Engineering Massachusetts Institute of Technology. Department of Mechanical Engineering Huynh, Dinh Bao Phuong Knezevic, David Patera, Anthony T. We introduce a frequentistic validation framework for assessment — acceptance or rejection — of the consistency of a proposed parametrized partial differential equation model with respect to (noisy) experimental data from a physical system. Our method builds upon the Hotelling T[superscript 2] statistical hypothesis test for bias first introduced by Balci and Sargent in 1984 and subsequently extended by McFarland and Mahadevan (2008). Our approach introduces two new elements: a spectral representation of the misfit which reduces the dimensionality and variance of the underlying multivariate Gaussian but without introduction of the usual regression assumptions; a certified (verified) reduced basis approximation — reduced order model — which greatly accelerates computational performance but without any loss of rigor relative to the full (finite element) discretization. We illustrate our approach with examples from heat transfer and acoustics, both based on synthetic data. We demonstrate that we can efficiently identify possibility regions that characterize parameter uncertainty; furthermore, in the case that the possibility region is empty, we can deduce the presence of “unmodeled physics” such as cracks or heterogeneities. United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-1-0613) MIT-Singapore International Design Center 2015-10-21T15:02:42Z 2015-10-21T15:02:42Z 2011-09 2011-07 Article http://purl.org/eprint/type/JournalArticle 00457825 http://hdl.handle.net/1721.1/99387 Huynh, D.B.P., D.J. Knezevic, and A.T. Patera. “Certified Reduced Basis Model Validation: A Frequentistic Uncertainty Framework.” Computer Methods in Applied Mechanics and Engineering 201–204 (January 2012): 13–24. https://orcid.org/0000-0002-2794-1308 https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1016/j.cma.2011.09.011 Computer Methods in Applied Mechanics and Engineering Creative Commons Attribution-Noncommercial-NoDerivatives http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier MIT Web Domain |
| spellingShingle | Patera, Anthony T. Huynh, Dinh Bao Phuong Knezevic, David Patera, Anthony T. Certified reduced basis model validation: A frequentistic uncertainty framework |
| title | Certified reduced basis model validation: A frequentistic uncertainty framework |
| title_full | Certified reduced basis model validation: A frequentistic uncertainty framework |
| title_fullStr | Certified reduced basis model validation: A frequentistic uncertainty framework |
| title_full_unstemmed | Certified reduced basis model validation: A frequentistic uncertainty framework |
| title_short | Certified reduced basis model validation: A frequentistic uncertainty framework |
| title_sort | certified reduced basis model validation a frequentistic uncertainty framework |
| url | http://hdl.handle.net/1721.1/99387 https://orcid.org/0000-0002-2794-1308 https://orcid.org/0000-0002-2631-6463 |
| work_keys_str_mv | AT pateraanthonyt certifiedreducedbasismodelvalidationafrequentisticuncertaintyframework AT huynhdinhbaophuong certifiedreducedbasismodelvalidationafrequentisticuncertaintyframework AT knezevicdavid certifiedreducedbasismodelvalidationafrequentisticuncertaintyframework AT pateraanthonyt certifiedreducedbasismodelvalidationafrequentisticuncertaintyframework |