Research

My work centers on formulating and studying mechanistic models that describe nonlinear interactions between populations to discover how they shape the structure, stability, and functions of the system.  

• In my PhD research, I derived and analyzed reaction-diffusion models to study the spatio-temporal dynamics of mosquito populations interacting with their biological control agents. My work investigated how mosquito dispersal and environmental heterogeneity affect the efficacy of biological control techniques [1], [2], [3], [5]. 

• In my postdoc research, I used dynamical systems to design a neural circuit model of excitatory and inhibitory neuron populations across different cortical layers. I studied how these two populations interact to produce complex patterns of activity and identified the neural mechanisms underlying the brain's response to different stimuli. 

During my research, I work closely with biologists to analyze and model biological datasets. I am interested in estimating the parameters of the mechanistic models with statistical inference, featuring advances in deep neural networks

• To address an extremely sparse dataset of captured mosquitoes, we developed a hybrid model that combines a stochastic individual-based model with its deterministic population limit, yielding a likelihood for a given observation [4]. 

• However, for more complex datasets, the probability density (or likelihood) is typically intractable. When dealing with high-dimensional neural recordings, we apply simulation-based inference in which the likelihood function is defined implicitly, and we use deep neural networks trained on simulated data to learn the posterior distribution of the parameters. 

When tackling more complex and realistic systems, such as those found in neuroscience, epidemiology, and ecology, there is a basic lack of known physical laws that provide first principles to derive equations. As data becomes increasingly abundant, we can identify governing dynamical systems directly from data using regression and machine learning techniques.

In my postdoc research, I work with the so-called Koopman operator theory, which provides a path to identifying intrinsic coordinate systems that represent nonlinear dynamics within a linear framework. Koopman-based methods aim to learn finite-dimensional approximations of the Koopman operator from data. We aim to develop data-driven Koopman-based methods to provide a phase-amplitude reduction to study and control neural oscillations [6].