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.
Additionally, I am interested in principled ways of using generative models to solve scientific problems. I wish to investigate how the comparatively-low inference cost provided by flow- and optimal-transport-based generative models can be leveraged to construct surrogates for solving inverse problems, performing state estimation and data assimilation online, and more.
To this end, I am especially interested in developing methods for detect overfitting in generative models for scientific applications, and how these insights can be used to train generative models which generalize well in high-risk scientific domains given relatively few data examples.
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.