About
I am a postdoctoral research associate in the School of Data Science and Society at the University of North Carolina at Chapel Hill working with Amarjit Budhiraja. My research topics lie broadly in the intersections of mathematics of machine learning, mathematical control theory, and Bayesian computation.
I was previously a postdoctoral research associate between the Division of Applied Mathematics at Brown University and the Department of Mathematics and Statistics at UMass Amherst with Paul Dupuis, Markos Katsoulakis, Luc Rey-Bellet.
I earned my PhD in Computational Science and Engineering from MIT in 2022. My advisor was Youssef Marzouk who heads the Uncertainty Quantification group. I earned my Master’s degree in Aeronautics & Astronautics at MIT in 2017, and my Bachelor’s degrees in Engineering Physics and Applied Mathematics at UC Berkeley in 2015. I was a MIT School of Engineering 2019-2020 Mathworks Fellow. I spent the summer of 2017 as a research intern at United Technologies Research Center (now Raytheon), where I worked with Tuhin Sahai on novel queuing systems.
Recent News
August
I have moved to the School of Data Science and Society at the University of North Carolina at Chapel Hill as a postdoctoral research associate.
July
Our paper Nonlinear denoising score matching for enhanced learning of structured distributions has been accepted to Computer Methods in Applied Mechanics and Engineering in their special issues on Generative Artificial Intelligence for Predictive Simulations and Decision-Making in Science and Engineering.
May
Three new preprints!
In Particle exchange Monte Carlo methods for eigenfunction and related nonlinear problems, we introduce a novel particle exchange Monte Carlo method that provide stochastic representations of eigenvalue problems related to generators of diffusion processes. We also discuss applications for approximating quasistationary distributions and ergodic stochastic control. This is joint work with Paul Dupuis.
In Optimal control for Transformer architectures, we provide a framework for understanding transformer neural network architectures using tools from optimal control theory. We provide theoretical guarantees and numerical experiments showing how optimal control ideas can enhance generalization, robustness, and training efficiency of transformers. This is joint work with Kelvin Kan, Xingjian Li, Tuhin Sahai, Stan Osher, and Markos Katsoulakis.
In Proximal optimal transport divergences, we introduce a new class of probability divergences based on the infimal convolution of divergences and optimal transport distances, including Wasserstein distances. These distances inherits the desirable properties of information divergences and transport distances, and we discuss how they are frequently unknowingly employed in generative modeling. This is joint work with Panagiota Birmpa, Ricardo Baptista, Markos Katsoulakis, and Luc Rey-Bellet.