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dc.contributor.authorZavar Moosavi, Azam Sadaten_US
dc.date.accessioned2018-03-14T08:00:37Z
dc.date.available2018-03-14T08:00:37Z
dc.date.issued2018-03-13
dc.identifier.othervt_gsexam:14411en_US
dc.identifier.urihttp://hdl.handle.net/10919/82491
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_US
dc.format.mediumETDen_US
dc.publisherVirginia Techen_US
dc.rightsThis item is protected by copyright and/or related rights. Some uses of this item may be deemed fair and permitted by law even without permission from the rights holder(s), or the rights holder(s) may have licensed the work for use under certain conditions. For other uses you need to obtain permission from the rights holder(s).en_US
dc.subjectUncertainty Quantificationen_US
dc.subjectUncertainty Reductionen_US
dc.subjectStochastic Simulation of Chemical Reactionsen_US
dc.subjectReduced-Order Modelsen_US
dc.subjectStructural Uncertaintyen_US
dc.subjectData Assimilationen_US
dc.subjectNumerical Weather Prediction Modelsen_US
dc.subjectMachine Learningen_US
dc.titleProbabilistic and Statistical Learning Models for Error Modeling and Uncertainty Quantificationen_US
dc.typeDissertationen_US
dc.contributor.departmentComputer Scienceen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineComputer Science and Applicationsen_US
dc.contributor.committeechairSandu, Adrianen_US
dc.contributor.committeememberGugercin, Serkanen_US
dc.contributor.committeememberHuang, Berten_US
dc.contributor.committeememberRibbens, Calvin J.en_US
dc.contributor.committeememberArchibald, Ricken_US


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