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