Deep Learning and Computational Physics (Lecture Notes)

TL;DR

This lecture note compendium introduces the connections between deep learning and computational physics, aiming to enhance understanding and develop novel algorithms for physics problems using deep learning techniques.

Contribution

It bridges deep learning and computational physics, providing insights and new algorithms to solve complex physical problems with deep learning methods.

Findings

Deep learning concepts can be understood through computational physics principles.

Novel deep learning algorithms are proposed for solving physics problems.

The notes facilitate interdisciplinary understanding between physics and machine learning.

Abstract

These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics. The main objective of these notes is to introduce a student who is familiar with concepts in linear algebra and partial differential equations to select topics in deep learning. These lecture notes exploit the strong connections between deep learning algorithms and the more conventional techniques of computational physics to achieve two goals. First, they use concepts from computational physics to develop an understanding of deep learning algorithms. Not surprisingly, many concepts in deep learning can be connected to similar concepts in computational physics, and one can utilize this connection to better understand these algorithms. Second, several novel deep learning algorithms can be used to solve challenging problems in computational physics. Thus, they offer someone who is interested in modeling a physical phenomena with a complementary set of tools.