Arka Daw - Uncertainty Quantification with Physics-informed Machine Learning

As applications in deep learning (DL) continue to seep into critical scientific use-cases, the importance of performing uncertainty quantification (UQ) with deep learning has become more pressing than ever before. In scientific applications, it is also important to inform the learning of deep learning models with the knowledge of physics of the problem to produce physically consistent and generalized solutions. This is referred to as the emerging field of Physics-informed Machine Learning (PIML). We present two distinct schools of thought for performing uncertainty quantification with physics-informed machine learning: (1) Physics-informed Architecture (PIA), where the physics-knowledge is hard-encoded into the neural network architecture, thereby producing meaning uncertainty estimates, (2) Physics-informed learning (PIL), where the additional physical knowledge is enforced as a soft constraint. We will demonstrate a Physics-informed Architecture approach for a special case of enforcing monotonicity constraints in the context of lake temperature modeling. We would also present a more generic Physics-informed learning (PIL) approach paired with generative adversarial networks (PID-GAN) to perform uncertainty quantifications when the physics-knowledge is found in the form of closed form equations/partial differential equations. We also provide an extension of PID-GAN for applications where the physics-equations available to us are derived using simplistic assumptions of complex real-world phenomena, i.e., the available knowledge is imperfect.