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 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).

• Modern Machine Learning Software
• Uncertainty Propagation through Scientific Models
• High-dimensional Uncertainty Propagation
• Inverse Problems in Deterministic Scientific Models
• Physics-informed Neural Networks (PINNs)
• Inverse Problems in Stochastic Scientific Models
• Homework Problems