Scientific Machine Learning for Physical Modeling and Discovery
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.
Topics
- Explain the mathematical and computational principles underlying both physics-based solvers (PDE operators, discretization, numerical solution) and AI-based approaches for physical systems.
- Compare and critique physics-based vs. AI-based approaches in terms of accuracy, scalability, generalizability, robustness, and uncertainty quantification.
- Implement and evaluate neural-operator / deep-learning models for spatiotemporal physical dynamics, and assess generalization behavior on unseen conditions.
- Develop hybrid scientific-AI models by integrating physical laws/constraints into ML, and use them to solve forward prediction tasks and inverse parameter/model-inference problems.
- Design, run, and interpret computational experiments (training, validation, ablation, error diagnostics) to justify modeling choices and trade-offs for real applications in fluids/solids/heat transfer.
Official roster learning outcomes
Prerequisites & course information
CS 1110 or CS 1112.
Sources
- Course catalogue ↗2026-2027