Research

I use mathematical and computational tools to understand a broad range of scientific phenomena that arise in social, physical, and biological systems. My research interests include network sciences, model reduction, and scientific computing .

Dynamics on networks

My work stands 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 dynamics. I seek methods that identify the intrinsic properties of the system from data or partially observed data. My work includes developing theoretical guarantees of the inference method and designing fast and scalable algorithms. Past and ongoing projects include:

• Inference of interaction kernels of a mean-field opinion model
• Non-parametric inference of dynamics of interconnected systems

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. I use multiscale and projection methods such as Mori–Zwanzig formalism, operator splitting, Petro–Galerkin projection, homogenization, and lubrication theory to reduce the dimension of problems that arise in various fields. Some applications include

• Heat and energy transfer in molecular dynamics and nano-scale materials
• Quantum and electron transport in quantum mechanics