Hi! I am a postdoctoral researcher in the group headed by Assad A. Oberai at the Viterbi School of Engineering, University of Southern California. My research involves the study of numerical techniques for partial differential equations. A few key topics are listed below.

• Data-driven computational physics:

  I use deep learning tools to replace and resolve bottlenecks in existing numerical methods. This is particularly relevant for techniques that require the specification of problem-dependent parameters, or contain computationally expensive sub-algorithms. Some areas of application I work on include

  • Shock-capturing algorithms for conservation laws.
  • Reduced order modelling for flow problems.
  • Acceleration of Monte-Carlo algorithms using deep surrogates.
  • PDE constrained optimization.
  • Physics-based deep Bayesian inference.
  
  
• Hyperbolic conservation laws:

  I develop numerical methods for conservation laws, which satisfy important physical model properties, such as entropy stabilty and kinetic energy preservation. In particular, I have developed high-order entropy-stable finite volume schemes for the compressible Euler equations, and extensions accomodate the viscous terms of the Navier-Stokes model.

• Pore-scale dynamics:

  I develop high-order numerical solvers to simulate multi-phase flows through real rock structures. Furthermore, I study the effects of introducing surfactants into the flow dynamics. This is a part of ongoing work with the Computational Modeling of Porous Media group at Rice University.