School of Mathematical Sciences
Faculty of Sciences, Engineering and Technology
Eligible to supervise Masters and PhD - email supervisor to discuss availability.
I am a Lecturer in Data Science and Statistics, with chief interests in Data Assimilation and numerical multiscale methods. For access to preprints, please follow the arXiv link below `External Profiles', at the bottom of the page.
Prospective students are encouraged to contact me directly, but may find some inspiration in the following:
Data Assimilation (DA) - the mathematical and statistical question of how to combine an uncertain model forecast with data. I am interested in:
- Coherent structure DA, that is, employing low-dimensional structures in the DA update in place of the original data. Research questions here may tend towards statistics (how do measurement errors in data create measurement errors in coherent structures?) or applied maths (from the oceanographic/atmospheric sciences literature; how should we employ coherent structures, and on what scales?).
- Projected DA, that is, employing projections to split one DA problem into several. The advantage is that one can use a DA method with high accuracy on key parts of the DA problem, and use a DA method suited to high-dimensional inference on the remainder of the DA problem. Some overlap with coherent structures; the key in projected DA is translating dynamical information to statistical information.
- Non-Gaussian problems; DA algorithms are often founded on the assumption that measurement errors are distributed normally. However there are counter-examples, and work has shown that DA methods constructed for non-Gaussian measurement errors are promising. (This would be a new research area for me - based on work by Craig Bishop.)
- Surrogate DA, the design of DA methods where a statistical surrogate is trained to empower a large ensemble of forecasts to be approximated from a small number of computationally intensive runs of the physical model. Many open questions - see my preprint with A/Prof. Elaine Spiller.
Numerical Multiscale Methods - key focus is on Projective Integration, that accelerates simulation of stiff systems, and patch dynamics, that accelerates simulation of systems with fine and coarse spatial components.
- Projective Integration for stochastic systems; there is a wealth of literature on this topic, but to my view two questions remain. First is how to implement an accurate, fast PI solver for stochastic systems with unknown slow and fast variables. Second is how to modify such methods to nonstandard slow-fast systems of the sort discussed in http://dx.doi.org/10.1137/19M1242677
- Patch dynamics; recent work has developed an adaptive moving patch scheme. The scheme can simulate moving fine-scale meshes that come together to form shocks at unknown locations in the spatial domain. A project here might focus on extending and applying the moving patch dynamics to travelling wave problems.
Thanks for coming this far! Please accept a beautiful picture of adaptive moving patches simulating a problem with heterogeneous advection and diffusion terms; the inset shows details of the little black box.
Year Citation 2019 Budhiraja, A., Friedlander, E., Guider, C., Jones, C. K., & Maclean, J. (2019). Assimilating Data into Models. In A. E. Gelfand, M. Fuentes, J. A. Hoeting, & R. L. Smith (Eds.), Handbook of Environmental and Ecological Statistics (1 ed., pp. 687-708). Florida; USA: CRC Press.
Report for External Bodies
Year Citation 2022 Loch, A., Sexton, S., Scholz, G., Maclean, J., & O'Connor, P. (2022). Willingness to Pay and Avoided Health Costs associated with Metropolitan Parks. Adelaide, SA: South Australian Department for Environment and Water.
Current Higher Degree by Research Supervision (University of Adelaide)
Date Role Research Topic Program Degree Type Student Load Student Name 2022 Co-Supervisor Employing stochastic sensitivity to quantify trajectory uncertainty in Lagrangian data assimilation Master of Philosophy Master Full Time Mr Liam Andrew Alex Blake 2022 Co-Supervisor Analysis of the trends, topics and sentiments of Australian television captions. Master of Philosophy Master Full Time Miss Irulan Claire Prowse Murphy 2022 Co-Supervisor Fast likelihood-free inference for epidemic models using neural density estimation techniques. Master of Philosophy Master Full Time Mr Luke Phillip O'Loughlin 2022 Co-Supervisor More than just a result: using cycle threshold values in household epidemic modelling Doctor of Philosophy Doctorate Full Time Mr Dylan John Morris 2021 Co-Supervisor A modelling framework for estimating the risk of importation of a novel disease Master of Philosophy Master Full Time Mr Antonio Max Parrella 2021 Principal Supervisor Predicting Clinical Need During Dispatch to Guide Ambulance Response Master of Philosophy Master Part Time Mr Trevor Paul Matthews 2021 Co-Supervisor Modelling and Quantification of Food Deserts Doctor of Philosophy under a Jointly-awarded Degree Agreement with Doctorate Full Time Miss Tayla Paige Broadbridge
Past Higher Degree by Research Supervision (University of Adelaide)
Date Role Research Topic Program Degree Type Student Load Student Name 2019 - 2021 Co-Supervisor Lagrangian Coherent Data Assimilation for Chaotic Geophysical Systems Master of Philosophy Master Full Time Ms Rose Joy Crocker
Date Title Engagement Type Institution Country 2021 - 2021 Colloquium Organiser Scientific Community Engagement University of Adelaide 2021 - ongoing Outreach Committee Scientific Community Engagement University of Adelaide
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