# Research

As an applied mathematician, I use mathematical tools to understand a broad range of scientific phenomena that can be addressed both analytically and computationally. My research interests include model reduction, network science, inference from data, and scientific computing.

## Model-reduction methods and multiscale modeling

One of my longstanding interests is to develop scalable and systematic approaches to reduce the dimensionality of complex models. My works in this theme can be devided into three categories:

- Mori–Zwanzig theory
- Petro–Galerkin projection
- Lubrication theory

## Dynamics on networks

My works stand at the intersection of networks and dynamics. In particular, I am interested in opinion-dynamics models on complex networks and their mathematical properties and essence. I also strive to investigate how to relate and unite dynamics on networks using agent-based (microscopic) and density-based (macroscopic) descriptions. Past and ongoing projects include:

- A density-based opinion model on hypergraphs
- Non-Markovian opinion dynamics on temporal graphs
- Mean-field approximation of density-based opinion models

## Inference from (partially observed) data

The parameters of many models play an essential role in shaping the behaviors of dynamics. I seek methods that identify the intrinsic properties of the system from data or partially observed data. My works include developing theoretical guarantees of the inference method and designing fast and scalable algorithms.

- Inference of interaction kernels of a mean-field opinion model
- Non-parametric inference of dynamics of inter-connected systems