Fields of Interest

Applied Mathematics is an interdisciplinary field that represents the focus of my ongoing research. Researchers in this domain are primarily engaged in the mathematical investigation of various natural phenomena, encompassing mathematical modeling, analysis, and related pursuits. While I find all areas of Applied Mathematics captivating, I am particularly motivated to study:

• Biological Fluid Dynamics (biofluid)
  • Particularly, I am interested in enhancing Method of regularized Stokeslet based biofluid flow simulations utilizing numerical methods.
• Numerical methods for Partial Differential Equations(PDEs)
  • Especially, I am interested in time integration methods with enhanced stability properties and low cost (e.g.,Rosenbrock methods, Stabilized explicit RK methods, such as Runge-Kutta-Chebyshev).
• Scientific Machine Learning
  • Operator Learning (e.g., DeepONet),
  • Neural ODEs,
  • Physics-informed neural networks (PINNs),
  • Linear and nonlinear Model order reduction (MOR) for dynamical systems.