Description: Traditional machine learning (ML) methods can efficiently approximate complex relationships, handle sparse datasets, and serve as powerful surrogate for expensive numerical simulations. However, when used as purely black-box predictors, these models risk producing unphysical or unreliable results, particularly in highly heterogenous subsurface environments, where governing equations are well established but data are sparse. To overcome these limitations, physics-informed machine learning (PIML) integrates physical laws such as mass and momentum conservation and constitutive relationships into the learning processes. The fusion of physics with machine learning enables models that are not only data-efficient and computational scalable but also consistent with the fundamental governing physics. This seminar course explores the theoretical foundations and recent advances in PIML for subsurface fluid flow, including physics-informed neural networks (PINNs), neural operators (DeepONet, Fourier Neural Operators) through group discussions. Through weekly discussions of cutting-edge research papers and open-source codes, students will critically evaluate the role of PIML in subsurface fluid flow prediction. Recommended Prerequisite(s): Calculus and basic familiarity with differential equations (ODE and PDE), MATH 101, MATH102, MATH 211, MATH 212, PHYS 101; basic knowledge of ML methods and coding with Python