Multiscale problems in population dynamics as well as in other disciplines require mathematical modeling to link individuals' behavior with macroscopic quantities. Specifically, I am interested in applying kinetic theories to build rigorous mathematical models for describing such multiscale phenomena and learn how individuals' behavior would influence the mean-field level dynamics.

Equations that describe multiscale models are sometimes defined in unbounded domains. Therefore, I am especially interested in applying spectral methods for unbounded domain PDEs. I developed a novel adaptive spectral method, and machine-learning-based spectral methods for solving both forward- and inverse-type PDE problems are of my current interest.

I am interested in developing control algorithms for equations that describe the dynamics of multiscale systems, especially in biology and medicine. Particularly, I am interested in applying reinforcement learning in developing control algorithms. Reinforcement learning techniques could be combined with traditional control approaches to develop efficient algorithms for certain biological models.