I am the PI of National Science Foundation (NSF) awards DMS- 2532987. 

My research lies at the intersection of applied mathematics, physics, and computation. I am particularly interested in understanding complex nonlinear phenomena through both rigorous analysis and numerical experiments. The overarching goal is to develop models and tools that offer both theoretical insight and practical utility; from turbulent fluid flows to the mathematical structure of neural networks. The main themes of my research include (but are not limited to):

• Nonlinear models in turbulence
  Theoretical and computational studies of nonlinear partial differential equations used in turbulence modeling;  particularly the Navier–Stokes equations (NSE) and large eddy simulation (LES) models. I explore both the mathematical foundations and the behavior of numerical approximations under different physical regimes.

• Data assimilation in modeling
  I work on developing and analyzing data assimilation methods that fuse physical models with observational data. These techniques are crucial for real-time forecasting, uncertainty quantification, and stabilizing complex simulations, especially in fluid dynamics and climate modeling.

• Mathematical foundations of neural networks
  Beyond implementation and coding, I focus on the mathematical understanding of how and why deep neural networks work. This includes questions of expressivity, generalization, and stability. My goal is to inform the development of new architectures and algorithms grounded in mathematical theory.