Research Interest

Numerical Partial Differential Equations

  • Data driven models
  • Solving PDEs with deep learning
  • Time-Space Fractional Partial Differential Systems
  • Discontinuous Galerkin Methods
  • Efficient Implicit-Explicit Time Stepping Methods
  • Adaptive methods
  • Mesh free approximation using Radial Bases Functions
  • Numerical methods for Stochastic Partial Differential Equations
  • Numerical methods for Stiff Stochastic Differential Equations

Current Application Areas of Research

  • Scientific Machine Learning
    • Solving PDEs with deep learning
    • Data driven models with Noisy data
    • Parameter estimation and inverse problems
    • Mathematical and scinetific machine learning
  • Computational Finance
    • Pricing complex financial derivatives in high dimensions
    • Models with Stochastic Volatility and Transaction Cost
    • Regime Switching with Jumps
    • High Performance Computing is Finance
    • Numerical Methods for Estimating Risk Measures
  • Computational Bio Chemical Systems
    • Large scale Reaction Diffusion systems, Complex Pattern Formation
  • Computational Stochastic Analysis
    • Numerical analysis of Stochastic Ordinary and Partial Differential Equations.
  • Computational Modeling in Optics
    • System of Non-linear Schrodinger Equations