Physics-informed Machine Learning with Uncertainty Quantification

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dc.contributor.authorDaw, Arkaen
dc.contributor.committeechairKarpatne, Anujen
dc.contributor.committeememberReddy, Chandan K.en
dc.contributor.committeememberRamakrishnan, Narendranen
dc.contributor.committeememberPerdikaris, Parisen
dc.contributor.committeememberLourentzou, Isminien
dc.contributor.departmentComputer Science and Applicationsen
dc.date.accessioned2024-02-13T09:00:20Zen
dc.date.available2024-02-13T09:00:20Zen
dc.date.issued2024-02-12en
dc.description.abstractPhysics Informed Machine Learning (PIML) has emerged as the forefront of research in scientific machine learning with the key motivation of systematically coupling machine learning (ML) methods with prior domain knowledge often available in the form of physics supervision. Uncertainty quantification (UQ) is an important goal in many scientific use-cases, where the obtaining reliable ML model predictions and accessing the potential risks associated with them is crucial. In this thesis, we propose novel methodologies in three key areas for improving uncertainty quantification for PIML. First, we propose to explicitly infuse the physics prior in the form of monotonicity constraints through architectural modifications in neural networks for quantifying uncertainty. Second, we demonstrate a more general framework for quantifying uncertainty with PIML that is compatible with generic forms of physics supervision such as PDEs and closed form equations. Lastly, we study the limitations of physics-based loss in the context of Physics-informed Neural Networks (PINNs), and develop an efficient sampling strategy to mitigate the failure modes.en
dc.description.abstractgeneralOwing to the success of deep learning in computer vision and natural language processing there is a growing interest of using deep learning in scientific applications. In scientific applications, knowledge is available in the form of closed form equations, partial differential equations, etc. along with labeled data. My work focuses on developing deep learning methods that integrate these forms of supervision. Especially, my work focuses on building methods that can quantify uncertainty in deep learning models, which is an important goal for high-stakes applications.en
dc.description.degreeDoctor of Philosophyen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:39285en
dc.identifier.urihttps://hdl.handle.net/10919/117966en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectDeep Learningen
dc.subjectPhysics-informed Machine Learningen
dc.subjectUncertainty Quantificationen
dc.subjectPhysics-informed Neural Networks.en
dc.titlePhysics-informed Machine Learning with Uncertainty Quantificationen
dc.typeDissertationen
thesis.degree.disciplineComputer Science and Applicationsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.nameDoctor of Philosophyen

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