Department of Mathematics

University of Maryland, College Park

(301) 405-2054

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I am an Assistant Professor of Mathematics holding a joint position at the Department of Mathematics and the Institute for Physical Science and Technology. My research lies at the interface of conventional numerical analysis and machine learning. A few key topics of interest are listed below.

**Scientific machine learning:**I use deep learning tools to overcome computational bottlenecks in existing numerical methods. This is particularly relevant for techniques that require the specification of problem-dependent parameters, or ailed by 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.
- Operator learning for surrogate modelling.

**Hyperbolic conservation laws:**I develop numerical methods for conservation laws, which satisfy important physical model properties, such as entropy stability and kinetic energy preservation. In particular, I have developed high-order entropy-stable finite volume schemes for the compressible Euler equations, and extensions accommodate 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.