I am working on developing efficient Wasserstein-distance-based machine-learning algorithms for uncertainty quantification tasks. My recent work lies in two directions: i) reconstructing certain types of stochastic differential equations (SDEs) from time-series data, with applications in understanding noisy cellular dynamics and analyzing stock price dynamics and ii) quantifying extrinsic noise, i.e., reconstructing the distribution of unknown model parameters from observed data. 

After extracting dynamics from time-series data, kinetic modeling, which links individuals' behavior with macroscopic quantities, is required to understand population-level dynamics. I work on applying kinetic theories to build rigorous mathematical models for describing population dynamics to study how individuals' behavior would influence population dynamics, with applications in biology, ecology, and economics. Also, I work on controlling structured population dynamics with applications in controlling disease spread in social networks.

Equations that describe population dynamics in biophysics are sometimes defined in unbounded domains to track quantities whose scales span across different magnitudes. Thus, those quantities sometimes require tracking in unbounded domains. We developed a novel adaptive spectral method to efficiently solve unbounded-domain spatiotemporal equations for simulating population dynamics. My adaptive spectral method finds wide applications in other fields such as quantum mechanics and material science.