Research

My research connects partial differential equations and machine learning. In particular, my research develops along two complementary directions: using PDE analysis to understand and justify machine-learning algorithms, and developing machine-learning strategies for physical problems governed by PDEs.

PDE Analysis for Machine Learning

Using PDE analysis to understand and justify machine-learning algorithms.

Schematic mean-field limit: a discrete particle system and its continuum probability-density description.

Mean-field analysis & learning dynamics
Optimization over probability measures

Machine Learning for PDE-Based Physical Problems

Developing learning strategies for physical problems governed by PDEs.

Schematic high-frequency limit: an oscillatory wave beam is connected to a family of ray trajectories.

Numerical homogenization & feature learning
Inverse problems through scaling limits

For papers, preprints, and related work, see Publications. Research code is available on GitHub ↗.