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.