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Explore uncertainty quantification in physics-informed machine learning through this comprehensive lecture. Delve into two key approaches: Physics-informed Architecture (PIA) and Physics-informed Learning (PIL). Discover how PIA hard-encodes physics knowledge into neural network architectures to produce meaningful uncertainty estimates, illustrated through a case study on lake temperature modeling with monotonicity constraints. Examine the more versatile PIL approach, focusing on its integration with generative adversarial networks (PID-GAN) for uncertainty quantification in scenarios involving closed-form equations or partial differential equations. Learn about an extension of PID-GAN designed for real-world applications where available physics equations are based on simplified assumptions. Gain insights into the critical importance of uncertainty quantification as deep learning increasingly influences scientific applications, and understand how incorporating physics knowledge enhances the consistency and generalizability of machine learning models in scientific contexts.
