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
Numerical Analysis Fundamentals
Neural ODEs
PINN: Introduction
PINN: Limitations and Extensions
Operator Learning: DeepONet
Operator Learning: FNO
Midterm Exam
Introduction to Hybrid Workflows
Equation Discovery: Sparse Identification of Nonlinear Dynamics
Transfer Learning and Few-Shot Learning
Domain Adaptation and Contrastive Learning
Generative AI: Diffusion Models
Transformers in Scientific Machine Learning
Basics of Large Language Models
Term Project