Research Overview

My primary research interests lie in machine learning, particularly at the intersection of applied probability, dynamical systems, and modern neural networks. While my work focuses on leveraging foundational questions to advance the science and engineering of learning systems, the theory is closely connected to implementation challenges and a broad spectrum of practical applications across the sciences.

Some topics of interest include:

• Generative modeling: how to understand and improve generative modeling methods that are based on dynamical measure transport, particularly for sequential data
• Sequence modeling: how to use ML and ideas from dynamical systems to model and learn sequential data, particularly those with underlying non-trivial dynamics, and study the mathematical foundations behind them
• Optimization and sampling: how to understand and improve optimization and sampling algorithms in ML meaningfully
• Robustness and reliability: how to leverage randomness to make ML safer and more reliable

I also have a long-standing interest in multiscale stochastic dynamics, especially homogenization and related applications in statistical mechanics, including both classical mathematical approaches and emerging data-driven methods.