Ben Burns
My research interests
What I’m currently thinking about, and what I was thinking about in the past
I am broadly interested in scientific machine learning and uncertainty quantification. My current research focuses on using reduced-order modeling and neural operator surrogates to perform large-scale PDE parameter inference.
I am interested in principled ways of using generative models as effective priors for scientific problems, where learning a high-quality data-driven prior is difficult as we typically have relatively little training data for such a high-dimensional space. In addition, I’m interested in investigating how to find data-driven priors that are robust to distribution shift.
prior research experience
In my undergrad, I bounced around between strategic algorithms, algebraic topology, and robotics before figuring out I liked mathematical ML.
In my last year at UMass, I completed a mathematics REU and an honor thesis supervised by Professor Markos Katsoulakis and Dr. Benjamin Zhang. The project focused on the mathematics of diffusion-based generative models, and how formulating them as mean-field games can be utilized to obtain both better understanding of diffusion models and better score functions for sampling through the game’s Hamilton-Jacobi-Bellman equation. My thesis was titled A mean-field games approach to score-based generative modeling.
In my junior and senior year at UMass, I studied how matrix Lie groups could be used to solve the SLAM problem while an undergraduate research assistant in the DARoS Laboratory, supervised by Professor Donghyun Kim and PhD candidate Shifan Zhu. The project focused on applying recent work on right-invariant extended Kalman filters to quadruped robots with optical sensors.
In the summer after my sophomore year, I completed a mathematics REU supervised by Professor R. İnanç Baykur. The project studied Stein fillings and mapping class groups, specifically relations of Dehn twists on genus 0 surfaces. The project concluded with an expository paper on fundamental group presentations under local curve conjugation.
Before getting involved in academic research, I interned for two summers under Dr. Scott James in the Air Traffic Systems group at Noblis. A summary of my work at Noblis is available upon request.