Hi! I am a postdoctoral researcher in the group headed by Prof. Beatrice Riviere at the department of Computational and Applied Mathematics, Rice University. My research involves the study of numerical techniques for partial differential equations. A few key topics are listed below.
My primary objective is to develop numerical methods for conservation laws, which satisfy important physical model properties, such as entropy stabilty and kineteic 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.
I am interested in using machine learning techniques to replace and resolve bottlenecks in several existing numerical methods. This becomes particularly relevant for techniques that require the specification of problem-dependent parameters.
I am interested in quantifying the uncertainty in hyperbolic models (and their extensions), using various Monte-Carlo techniques.