Advanced Scientific Machine Learning

This book is a collection of notes on advanced scientific machine learning. I develop it as part of the course ME 697 (with a similar name) at Purdue University. The book is intended for graduates students in engineering and science who want to learn about machine learning in the context of scientific applications.

Prerequisites

This book is not an introduction to machine learning. You cannot start this book without a good basic understanding of the topic. Also, you can probably not follow the book unless you are familiar with the basics of scientific computing and numerical methods. You need a fairly strong understanding of linear algebra, calculus, differential equations, probability, and standard machine learning. To build this understanding, my suggestion is to take the following courses (or similar) first:

• ME 581 (Numerical Methods in Mechanical Engineering), and

• ME 539 (Introduction to Scientific Machine Learning).

• Functional Programming
• Typing Systems, Pytrees, and Models
• Differentiable Programming
• Local Sensitivity Analysis of ODEs and PDEs
• Uncertainty Propagation using Polynomial Chaos
• Optimization for Scientific Machine Learning
• Physics Informed Neural Networks (PINNs)
• Proper Orthogonal Decomposition
• Learning non-linear dynamics from data
• Homework Problems