How can mathematics deepen our understanding of machine learning, and how can
machine learning algorithms discover mathematical structure in data and physical systems?

My research establishes mathematical principles that explain learning, computation, and intelligent systems. By combining approximation theory, optimization, numerical analysis, and machine learning, I develop rigorous foundations for modern AI together with algorithms for scientific computing, differential equations, and data-driven discovery.

Research Areas

Mathematical Machine Learning
My research develops mathematical foundations for modern machine learning and AI, with a focus on approximation theory, generalization, optimization, stability and representation learning. This research direction develops rigorous principles that explain, characterize, and guide the design of intelligent learning systems.

Scientific Machine Learning and Operator Learning
My research develops mathematical theory and machine learning methods for approximating operators and  AI systems for scientific computing. My current research interests include neural operators, multi-operator learning, transferable operator representations, multimodal scientific learning, and foundation models for differential equations, forecasting, data assimilation, simulation, and scientific discovery.

Optimization
Optimization provides the computational foundation underlying modern machine learning and AI. I study the analysis and design of optimization algorithms for large-scale learning, scientific computing, and inverse problems, with interests in sparse optimization, stochastic optimization, and structure-exploiting algorithms with rigorous theoretical guarantees.