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.