Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls
In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analo- gous to our previously proposed approach [1, 2], for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary value problems when the boundary dat...
| Main Authors: | , , , , |
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| Format: | Article |
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IOP Publishing
2018
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| Online Access: | https://eprints.nottingham.ac.uk/51562/ |
| _version_ | 1848798524386312192 |
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| author | Iglesias, Marco Sawlan, Zaid Scavino, Marco Tempone, Raul Woodard, Christopher |
| author_facet | Iglesias, Marco Sawlan, Zaid Scavino, Marco Tempone, Raul Woodard, Christopher |
| author_sort | Iglesias, Marco |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analo- gous to our previously proposed approach [1, 2], for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary value problems when the boundary data are noisy. We apply EnMKF to infer the thermal properties of building walls and to estimate the corresponding heat flux from real and synthetic data. Compared with a modified Ensemble Kalman Filter (EnKF) that is not marginalized, EnMKF reduces the bias error, avoids the collapse of the ensemble without needing to add in- flation, and converges to the mean field posterior using 50% or less of the ensemble size required by EnKF. According to our results, the marginalization technique in EnMKF is key to performance improvement with smaller ensembles at any fixed time. |
| first_indexed | 2025-11-14T20:21:08Z |
| format | Article |
| id | nottingham-51562 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:21:08Z |
| publishDate | 2018 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-515622020-05-04T19:37:05Z https://eprints.nottingham.ac.uk/51562/ Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls Iglesias, Marco Sawlan, Zaid Scavino, Marco Tempone, Raul Woodard, Christopher In this work, we present the ensemble-marginalized Kalman filter (EnMKF), a sequential algorithm analo- gous to our previously proposed approach [1, 2], for estimating the state and parameters of linear parabolic partial differential equations in initial-boundary value problems when the boundary data are noisy. We apply EnMKF to infer the thermal properties of building walls and to estimate the corresponding heat flux from real and synthetic data. Compared with a modified Ensemble Kalman Filter (EnKF) that is not marginalized, EnMKF reduces the bias error, avoids the collapse of the ensemble without needing to add in- flation, and converges to the mean field posterior using 50% or less of the ensemble size required by EnKF. According to our results, the marginalization technique in EnMKF is key to performance improvement with smaller ensembles at any fixed time. IOP Publishing 2018-05-22 Article PeerReviewed Iglesias, Marco, Sawlan, Zaid, Scavino, Marco, Tempone, Raul and Woodard, Christopher (2018) Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls. Inverse Problems, 34 (7). 075008. ISSN 0266-5611 http://iopscience.iop.org/article/10.1088/1361-6420/aac224 doi:10.1088/1361-6420/aac224 doi:10.1088/1361-6420/aac224 |
| spellingShingle | Iglesias, Marco Sawlan, Zaid Scavino, Marco Tempone, Raul Woodard, Christopher Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls |
| title | Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls |
| title_full | Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls |
| title_fullStr | Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls |
| title_full_unstemmed | Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls |
| title_short | Ensemble-marginalized Kalman filter for linear time-dependent PDEs with noisy boundary conditions: application to heat transfer in building walls |
| title_sort | ensemble-marginalized kalman filter for linear time-dependent pdes with noisy boundary conditions: application to heat transfer in building walls |
| url | https://eprints.nottingham.ac.uk/51562/ https://eprints.nottingham.ac.uk/51562/ https://eprints.nottingham.ac.uk/51562/ |