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 developed 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.
Global optimization in high dimensions is hard. By leveraging Stochastic Variational Gaussian Processes that can scalably incorporate derivative information within a Bayesian optimization loop we can accelerate global optimization and efficiently find solutions.
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. I developed and solved a derivative-free optimization model which seeks these high power accelerator configurations.
Real world optimization problems often have unrelaxable constraints, constraints which must be satisfied in order to evaluate the objective function. Solving these problems is difficult, and traditionally requires specialized algorithmic solutions. We are developing modeling appraoches which open the doors to "off-the-shelf" optimization routines, such as BFGS, to solve optimization problems with unrelaxable constraints.
The Stellarator is a state-of-the-art nuclear fusion device designed to generate sustainable energy. We are developing a stochastic optimization framework within FOCUS, an optimization toolbox for designing the magnetic coils for Stellarators. Our accelerated stochastic optimization methods allow for rapid development of coils with low construction tolerances, with the goal of saving millions of dollars in engineering costs.
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.
The critical downfall of machine learning comes with the inefficiency of training on massive data sets. We know from self-observation, however, that only a few samples should be needed to train a brain to classify. We introduce novel machine learning methods that rely on the use of "small data" to perform high accuracy classification. Using inisights from Optimal Control Theory, our adaptive methods can be implemented alongside current techniques to improve algorithmic efficiency.
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.
The Golestanian Swimmer is a three bead simple swimmer that leverages non-reciprocal motion to move through viscous media. Our three bead swimmer is propelled by the two oscillating harmonic springs that hold it together. Using computational simulation of these swimmers, we are able to investigate the role of fluid viscosity on the speed of the swimmers when moving through a spherical fluid interface.
We implement spectral clustering and semi-supervised labeling techniques on a voting network created from the UCI Congressional Voting Records data set, with the goal of understanding the voting stance of Congressional Representatives. We find interestingly that many politicians vote more akin to their opposing party.
Motivated by recent experimental systems where particles are immersed within curved two-dimensional fluid interfaces, such as colloids in a GUV’s or proteins in a lipid vesicle membrane, we investigate how active kinetics can modulate the size of particle clusters that self-assemble within spherical fluid interfaces.
As a ubiquitous equation in physical theory, Poisson's equation serves as the perfect testing ground for Multi-Grid Iterative PDE solvers. Multigrid is a state-of-the-art method for increasing the convergence rates of Iterative methods for solving linear systems. These methods are particularly effective when dealing with systems with sparse matrix representations, like the Poisson equation.
While found in a variety of environments, the protein Spectrin is commonly found forming a scaffolding over the exterior of red blood cells. This scaffolding is called a Spectrin Network as the Spectrin proteins are connected by bonds forming a triangulated mesh. Motivated by the Spectrin Networks, we investigate the fluid interactions generated from generalized harmonic polymeric networks embedded in spherical fluid interfaces. We use CFD techniques to measure the significance effects of hydrodynamics.