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.Â
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
[AI Basics]
[Numerical Analysis]
[PINN]
Part 1: Embedding Physical Knowledge iHTML iColab pdf pptx PS#04
Part 2: Embedding Governing Equations iHTML iColab pdf pptx PS#05
Part 3: Multiple Loss Terms and Weighting iHTML iColab pdf pptx PS#06
Part 4: Limitations and Mitigation Strategies iHTML iColab pdf pptx PS#07
Part 5: Derivatives with AD and FDM iHTML iColab pdf pptx PS#08
Midterm
[Operator Learning]
[Equation Discovery]
Symbolic Regression iColab
Sparse Identification of Nonlinear Dynamics (SINDy) iColab
LLMs in Scientific Machine Learning iColab
Final Exam
Term Project