Probabilistic and Statistical Learning Models for Error Modeling and Uncertainty Quantification

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dc.contributor.authorZavar Moosavi, Azam Sadaten
dc.contributor.committeechairSandu, Adrianen
dc.contributor.committeememberGugercin, Serkanen
dc.contributor.committeememberHuang, Berten
dc.contributor.committeememberRibbens, Calvin J.en
dc.contributor.committeememberArchibald, Ricken
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2018-03-14T08:00:37Zen
dc.date.available2018-03-14T08:00:37Zen
dc.date.issued2018-03-13en
dc.description.abstractSimulations and modeling of large-scale systems are vital to understanding real world phenomena. However, even advanced numerical models can only approximate the true physics. The discrepancy between model results and nature can be attributed to different sources of uncertainty including the parameters of the model, input data, or some missing physics that is not included in the model due to a lack of knowledge or high computational costs. Uncertainty reduction approaches seek to improve the model accuracy by decreasing the overall uncertainties in models. Aiming to contribute to this area, this study explores uncertainty quantification and reduction approaches for complex physical problems. This study proposes several novel probabilistic and statistical approaches for identifying the sources of uncertainty, modeling the errors, and reducing uncertainty to improve the model predictions for large-scale simulations. We explore different computational models. The first class of models studied herein are inherently stochastic, and numerical approximations suffer from stability and accuracy issues. The second class of models are partial differential equations, which capture the laws of mathematical physics; however, they only approximate a more complex reality, and have uncertainties due to missing dynamics which is not captured by the models. The third class are low-fidelity models, which are fast approximations of very expensive high-fidelity models. The reduced-order models have uncertainty due to loss of information in the dimension reduction process. We also consider uncertainty analysis in the data assimilation framework, specifically for ensemble based methods where the effect of sampling errors is alleviated by localization. Finally, we study the uncertainty in numerical weather prediction models coming from approximate descriptions of physical processes.en
dc.description.degreePh. D.en
dc.format.mediumETDen
dc.identifier.othervt_gsexam:14411en
dc.identifier.urihttp://hdl.handle.net/10919/82491en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectUncertainty Quantificationen
dc.subjectUncertainty Reductionen
dc.subjectStochastic Simulation of Chemical Reactionsen
dc.subjectReduced-Order Modelsen
dc.subjectStructural Uncertaintyen
dc.subjectData Assimilationen
dc.subjectNumerical Weather Prediction Modelsen
dc.subjectMachine learningen
dc.titleProbabilistic and Statistical Learning Models for Error Modeling and Uncertainty Quantificationen
dc.typeDissertationen
thesis.degree.disciplineComputer Science and Applicationsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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