Scientific Machine Learning for Physical Modeling and Discovery

Catalog description

This senior/graduate elective rigorously explores the interplay between conventional physics-based methods and modern data-driven AI approaches for modeling and discovering complex physical systems, including fluid dynamics, solid mechanics, and heat transfer. Students will build a deep understanding of the mathematical foundations and computational principles behind both physics-based solvers (e.g., finite-difference and finite-volume methods) and AI techniques (e.g., neural operators, generative models, and symbolic AI). Emphasis is placed on hybrid scientific AI frameworks that unify physical laws with data-driven models to solve forward and inverse problems in scientific computing, including predictive modeling, parameter inference, and equation discovery. Through theoretical analysis, algorithm development, and hands-on case studies, students will critically evaluate trade-offs in accuracy, scalability, robustness, and uncertainty quantification, and develop practical skills to innovate at the intersection of scientific computing and AI.