Physics-informed Machine Learning with Uncertainty Quantification

Physics 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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Computer Science and Applications

Department dc:contributor.department

Computer Science and Applications

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2024

Author dc:creator

• Daw, Arka

Chair dc:contributor.committeechair

• Karpatne, Anuj

Committee members dc:contributor.committeemember

• Reddy, Chandan K.
• Ramakrishnan, Narendran
• Perdikaris, Paris
• Lourentzou, Ismini

• Deep Learning
• Physics-informed Machine Learning
• Uncertainty Quantification
• Physics-informed Neural Networks.

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

vt_gsexam:39285

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/117966