MAE 4080

Scientific Machine Learning for Physical Modeling and Discovery

Course Description

Course information provided by the 2026-2027 Catalog.

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.

Prerequisites MAE 3200 or equivalent, Students are expected to be able to program in Python.

Last 4 Terms Offered (None)

Learning Outcomes

• 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.

View Enrollment Information