Variational Inference

Scaling Gaussian Processes with Derivatives

Augmenting Gaussian Processes (GP) with derivative information can significantly enhance their predicitive capacity. However, there are serious scalability issues associated with training and inference when using GPs with derivatives, particularly in high dimensions. We are developing a Variational Inference technique for training GPs with derivatives that learns a reduced GP model, allowing for scalable training and inference at a minimal loss in accuracy.

Bayesian Optimization

Black-Box Risk-Averse Optimization with Gaussian Processes

Computing measures of risk from a black-box objective function can be hard. We have developed efficient methods for doing exactly this using Gaussian Processes. When used in a Bayesian Optimization loop, we can efficiently find points that hedge against risk.

Fusion Energy

Designing Stellarators with Bayesian Optimization

The Stellarator is a state-of-the-art nuclear fusion device designed to generate sustainable energy. Due to the sheer complexity of fusion reactor design, numerical optimization has come forth as a promising method for conceiving Stellarators. We are building new optimization models of Stellarator design as well as implementing scalable surrogate optimizers in STELLOPT, a Stellarator optimization toolbox, to revolutionize the design paradigm behind Stellarators.

Particle Accelerators

Parallel Design of Particle Accelerators

Fermilab houses a proton accelerator to be used as a part of Deep Underground Neutrino Experiment (DUNE), an international, multi-decadal physics program for leading-edge neutrino science and proton decay studies. However by the inception of DUNE in 2032, the FermiLab proton complex must undergo a substantial upgrade in order to meet the particle acclerator beam power requirements. My role in this project is to employ numerial optimization and machine learning techniques to find a high power accelerator within a large class of configurations. This is joint work with Stefan Wild and Jeff Larson from Argonne National Labs, and Eric Stern and Jeffrey Eldred from FermiLab.


Fluctuating Hydrodynamics Methods for the Drift-Diffusion Dynamics of Microstructures

The goal of this project was to study the Drift-Diffusion Dyanamics of Microstructures embedded in spherical fluid interfaces. In nature we find that this is a good model for the interaction of proteins in the lipid-bilayer membrane (cell membrane). Throughout the project we developed fluctuating hydrodynamics approaches for capturing the fluid and microstructure interactions. We then used our model to study how the drift-diffusion dynamics of microstructures compare with and without hydrodynamic coupling within the curved fluid interface.

Machine Learning

Using Gaussian Process Regression to Solve the Heat Equation

We use a novel machine learning method, Gaussian Process Regression, to solve a classic problem, the heat equation. We aim to find the relationship between temperature at a position on a rod and the location of a heat source under the rod. This equation-free method greatly simplifies solving the partial differential equation and proves to be accurate even with small data samples.