Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

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dc.contributor.authorPopov, Andrey A.en
dc.contributor.authorSandu, Adrianen
dc.date.accessioned2023-02-27T18:31:02Zen
dc.date.available2023-02-27T18:31:02Zen
dc.date.issued2022-06-02en
dc.date.updated2023-02-25T22:28:19Zen
dc.description.abstractData assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.en
dc.description.versionPublished versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.3389/fams.2022.904687en
dc.identifier.eissn2297-4687en
dc.identifier.issn2297-4687en
dc.identifier.orcidSandu, Adrian [0000-0002-5380-0103]en
dc.identifier.urihttp://hdl.handle.net/10919/113985en
dc.identifier.volume8en
dc.language.isoenen
dc.publisherFrontiersen
dc.rightsCreative Commons Attribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectBayesian inferenceen
dc.subjectControl variatesen
dc.subjectData assimilationen
dc.subjectMultifidelity ensemble Kalman filteren
dc.subjectReduced order modelingen
dc.subjectMachine learningen
dc.subjectSurrogate models frontiersen
dc.titleMultifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencodersen
dc.title.serialFrontiers in Applied Mathematics and Statisticsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherJournal Articleen
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/Engineeringen
pubs.organisational-group/Virginia Tech/Engineering/Computer Scienceen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Engineering/COE T&R Facultyen

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