Research

I am an applied and computational mathematician. My current research focuses on the mathematical underpinnings of machine learning (ML). One of my primary objectives is to address the critical challenge of quantifying and enhancing the robustness and statistical efficiency of ML models, especially for data-scarce and resource-constrained applications. I am interested in understanding and leveraging the inherent structures of the underlying systems, aiming to develop novel and efficient ML models and computational algorithms with provable guarantees.

My work draws from a range of mathematical disciplines, including applied harmonic analysis, differential geometry, applied probability, PDEs, and optimization. Some of my current research interests include:

• Structure-preserving ML: theory and applications

• Generative modeling

• Implicit bias and optimization

• Scientific ML (PDEs, dynamical systems, computational fluid dynamics, etc.)

• Data-driven structure discovery (conservation law, symmetry, etc.)

My research is generously supported by AFOSR, NIH, and NSF.