EEL 6935: Physics-Informed Machine Learning

Course Description

This course looks to integrates physical properties and laws of nature into state-of-the-art data analysis, machine learning, and signal processing techniques. We address three critical data science and machine learning challenges in analyzing and understanding complex, physical systems and materials:

1. collecting enough data is often impossible for practical and financial reasons
2. capturing the data diversity for informed decision-making can be impossible due to insufficient laboratory conditions or lack of observations (i.e., rare events)
3. data-driven analytics are not as explainable as physics-based techniques These challenges make sophisticated data analytics and machine learning inapplicable in many fields. We expand state-of-the-art analytics into these physics-driven applications, focusing on both theory and practical applications.

We begin the course by exploring the geometric (or linear algebra based) perspective of data and physical laws. We discuss this perspective because it forms the basis for much of modern machine learning. In the second half of the course, you will help direct the course. You will learn these subjects through hands-on projects and research and present them to your peers, utilizing the tools developed in the first half of the course. Students from various disciplines are encouraged to join the course to provide the class with both machine learning as well as a physics application perspective of the topics discussed. However, all students are expected to have a robust mathematical maturity and programming experience in MATLAB or Python.

Learning Objectives

At the completion of this course, you should be able to:

1. Describe data science concepts from a geometric perspective
2. Describe physical laws (e.g., partial differential equations) from a geometric perspective
3. Derive and create a state-of-the-art physics-informed machine learning framework
4. Apply cutting-edge physics-informed machine learning techniques to real world problems

Prerequisites

• Programming experience in MATLAB and / or Python required
• Fundamentals of Machine Learning (EEL 5840) or equivalent recommended
• Foundations of Digital Signal Processing (EEE 5502) or equivalent recommended

Grade Distribution (First Half of Course):

Grade Distribution (Second Half of Course):