(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
Materials for UT Austin’s graduate 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.
Many links below direct to Google Colaboratory, and can be run-in-browser without any installation as long as you are signed into a Google account. To download the raw source files, please refer to the GitHub repository
- HW1: The sandpile cellular automaton and directed percolation. Covers recursion, runtime scaling, vectorization
- HW2: Linear dynamical systems and decomposing a chaotic flow. Covers numerical linear algebra, optimization, and unsupervised learning
- HW3: Turing patterns and phase separation. Covers numerical integration; finite-differences and spectral methods
- HW4: Predicting turbulence with operator methods. Covers Supervised learning, time series forecasting, ridge, kernel, and logistic regression
- Lab 1: Getting started with Python
- Lab 2: git, GitHub, and GitHub Pages
- Lab 3: Documentation and Formatting
- Lab 4: Automatically creating online documentation with Sphinx
- Lab 5: Unit Testing
- Lab 6: Structuring an Open-Source Repository
Example Final Projects
- Quantum Reinforcement Learning with the Grover method
- Modelling the contractile dynamics of muscle
- Tight binding and Anderson localization on complex graphs
- Neural System Identification by Training Recurrent Neural Networks
- Assimilating a realistic neuron model onto a reduced-order model
- Testing particle phenomenology beyond the Standard Model with Bayesian classification
- Monte Carlo sampling for many-body systems
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.
For errors or typos, please consider opening an issue or submitting corrections as pull requests on GitHub.
We will primarily use Python 3 with the following packages
For projects and other parts of the class, you might also need
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