Sahar Bakhshian

This course provides a comprehensive introduction to fundamental principles governing fluid flow in porous media, combined with different hands-on coding exercises for students to understand how to implement computational techniques such as lattice Boltzmann modeling to solve the governing equations. Cross-list: EEPS 631. Mutually Exclusive: Cannot register for EEPS 431 if student has credit for EEPS 631.

Advanced work in Earth science adapted to the needs of individual graduate students. Repeatable for Credit.

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

This course provides a comprehensive introduction to fundamental principles governing fluid flow in porous media, combined with different hands-on coding exercises for students to understand how to implement computational techniques such as lattice Boltzmann modeling to solve the governing equations. Cross-list: EEPS 431. Recommended Prerequisite(s): calculus and basic familiarity with differential equations, basic knowledge of coding with MATLAB; MATH 101, MATH102, MATH 211, MATH 212, PHYS 101 or equivalents from previous institutions Mutually Exclusive: Cannot register for EEPS 631 if student has credit for EEPS 431.

Thesis research. Recommended Prerequisite(s): Students must pass the preliminary exam before taking this course. Repeatable for Credit.