Monte Carlo methods are fundamental tools for many applications ranging from machine learning to molecular simulation. The key idea of Monte Carlo simulation is to use (computational) random number generation in order to approximate the statistical properties of a stochastic system; for instance, one may approximate averages and variances over atomic vibrations within a material to determine its state (e.g. stress, strain, polarization, etc.). While Monte Carlo methods have proven to be powerful, there are still instances where, due to the complexity of the underlying probability distribution, their performance is poor.

Here the student will develop new Monte Carlo methods that leverage symmetry, clustering methods, and other advanced sampling techniques (e.g. based on divide and conquer algorithms). The project will utilize high performance computing and research code to perform MCMC simulations of new and emerging materials. Simulation data will be analyzed (using data science techniques such as dimensional reduction) in order to probe these materials for interesting and novel physics.

Kaushik Dayal - Mechanical Engineering and Civil and Environmental Engineering