Overview of Methods in Course

(Left to Right): Avalanche activity cascades in a sandpile automaton; a vortex street formed by flow past a cylinder; and Turing patterns in a reaction-diffusion model. All simulations from the course homeworks; a higher-resolution video may be viewed here

Computational Physics

Summary

Materials for computational physics course, taught by William Gilpin.

This course aims to provide a very broad survey of computational methods that are particularly relevant to modern physics research. We will aim to cover efficient algorithm design and performance analysis, traditional numerical recipes such as integration and matrix manipulation, and emerging methods in data analysis and machine learning. Our goal by the end of the class will be to feel comfortable approaching diverse, open-ended computational problems that arise during research, and to be ready to design and share new algorithms with the broader research community.

The class website is located here.

If you are enrolled in 329 at UT, the syllabus and calendar are here.
If you are enrolled in 381C at UT, the syllabus and calendar are here.
For both UT courses, the Discussions page may be found here.

Many links below direct to Google Colab, and can be run-in-browser without installation as long as you are signed into a Google account. To download the raw source files, please refer to the GitHub repository. Some lecture videos are linked below, and the remaining lecture videos are linked in the Syllabus (above).

Homework Assignments

HW1: The sandpile cellular automaton and directed percolation. [ipynb] Covers recursion, runtime scaling, vectorization
HW2: Linear dynamical systems and decomposing a chaotic flow. [ipynb] Covers numerical linear algebra, optimization, and unsupervised learning
HW3: Turing patterns and phase separation. [ipynb] Covers numerical integration; finite-differences and spectral methods
HW4: Predicting turbulence with operator methods. [ipynb] Covers Supervised learning, time series forecasting, ridge, kernel, and logistic regression

Lecture Slides

Notes

Laboratory Exercises

Example Final Projects

Usage and improvements

If you are teaching a similar course, please feel free to use any or all of these materials. If you have any suggestions for improvements or find any errors, I would very much appreciate any feedback. Consider submitting corrections as issues or pull requests on GitHub.

For students, logistics and project questions are best posted on the classroom forum (Ed Discussions); errors in the materials should be issues on the course repository; for other issues, I can be reached via email

Requirements

We will primarily use Python 3 with the following packages

numpy
matplotlib
scipy
scikit-learn
jupyter

For projects and other parts of the class, you might also need

ipykernel
scikit-image
umap-learn
statsmodels
pytorch
jax
numba

Attributions

Portions of the material in this course are adapted or inspired by other open-source classes, including: Pankaj Mehta’s Machine Learning for Physics Course, Chris Rycroft’s Numerical Recipe’s Course, Volodymyr Kuleshov’s Applied Machine Learning course, Fei-Fei Li’s Deep Learning for Computer Vision course, Lorena Barba’s CFD course and Jim Crutchfield’s Nonlinear Dynamics course