Research Interests:
My research lies at the intersection of mathematical neuroscience, nonlinear dynamics, and deep learning. I focus on applying dynamical systems theory, particularly geometric singular perturbation and bifurcation analysis, to study the complex dynamics of neural systems. This includes understanding multiscale behavior in differential equations and the synchronization of neural networks. In addition to theoretical approaches, I integrate machine learning methods, such as physics-informed neural networks (PINNs), to explore neural dynamics. I also use deep learning tools, including diffusion models, for tasks like image denoising and generation.
Main Research Topics:
Multiscale Neural Dynamics and Nonlinear Systems
Geometric Singular Perturbation Analysis
Bifurcation Theory
Mathematical Biology/Neuroscience
Deep Learning and Physics-Informed Neural Networks (PINNs) in Nonlinear Dynamics
Data-Driven Science for Inverse Problems
Diffusion Probabilistic Models and GANs for Denoising and Image Generation