These lecture materials are openly available to everyone.
For students: You are encouraged to use these materials to support your studies.
For instructors: You are welcome to use, modify, and distribute these materials in your teaching.
No credit or reference to us is required.
This course introduces the methodological transition from classical numerical analysis to AI-based scientific computing. Focusing on PDE-based problems, it covers the core principles, training frameworks, limitations, and advanced extensions of Neural ODEs, Physics-Informed Neural Networks, and Operator Learning, together with emerging topics such as hybrid workflows and equation discovery. The course aims to develop AX-oriented AI modeling capabilities for the analysis, prediction, surrogate modeling, and model discovery of complex physical systems.
Topics HTML Colab Slides PowerPoints PS Solution
Foundations of Scientific Machine Learning iColab
Numerical Analysis Fundamentals iColab
Neural ODEs iColab
PINN: Introduction iColab
PINN: Limitations and Extensions iColab
Operator Learning: DeepONet iColab
Operator Learning: FNO iColab
Midterm Exam
Introduction to Hybrid Workflows iColab
Equation Discovery: Sparse Identification of Nonlinear Dynamics iColab
Generative AI: Diffusion Models iColab
Transformers in Scientific Machine Learning iColab
Term Project