PhD

PhD involving numerical simulation, approximation, and inference

Overview

I do not have any open positions for a PhD at present but if you are interested in the general topics outlined below then please get in touch. Please also note the admission deadlines below for the PhD program at the ANU.

Numerical Simulation and High Performance Computing

For many years, various computationally expensive techniques have been used for the simulation of complex physical phenomena within the Earth. An example from seismic tomography is full waveform simulation for the simulation of the Earths response due to an Earthquake, which coupled with adjoint simulations, can subsequently be used to infer the structure of the Earth. These techniques are well established and have community open source codes that are generally well optimized for running on super computing resources.

I am generally interested in research around both different methods for the solution of wave propagation problems (e.g. FEM, SEM, DG etc) and their efficient implementation on high performance computing resources.

Useful Approximations

In addition to high fidelity numerical simulation and advances therein outlined in the previous section, there is a great deal of interest in the use for numerical approximation techniques for approximating these simulations at dramatically reduced costs. Applications for this include (near) real-time monitoring of physical phenomena, or evaluating large number of solutions for scenario evaluations.

There are two broad categories that I am interested in: model order reduction (or reduced basis) methods and machine learning approaches.

On the first hand, model order reduction generally seaks a reduced basis (subspace) on to which a high fidelity system can be projected that produces a much lower dimension simulation while maintaining numerical stability and a high degree of accuracy. The general idea is that simulations can then be computed with 2-4 orders of magnitude less expense which incurring moderate approximation errors, i.e. < 1%.

On the other hand, machine learning techniques such as Physically Informed Neural Networks have been shown to accurately reproduced the results of partial differential equations under various scenarios. Some recent work has also shown the use of Auto Encoders that can act as efficient numerical integrators through time, i.e. they can predict the state of a numerical system and the next or the previous time step.

Bayesian Inference

Much of my early research was in Bayesian inference and in the so-called Trans-dimensional sampling algorithms. These are based on McMC or HMC sampling methods that attempt to approximate a posterior probability distribution using a population of likely models. As problems get larger, McMC/HMC become progressively less tractable due to the curse of dimensionality.

Primarily for this reason, I am more interested now in optimization techniques such as Variational Bayes and Generative Models as methods of approximating the posterior distribution.

Applying

There are two rounds each year for applying for entry into the PhD Program at ANU:

  • April (Both Domestic and International Students)
  • October (Domestic Students), August (International Students)

Detailed information can be found here: