The main goal of this project is to develop the use of contemporary data science techniques in the context of applied mathematical modelling.
The project is divided into two strands:
Topological data analysis and quantum chaos
Topological data analysis (TDA) is increasingly being used to analyse large data sets, particularly for problems that involve high-dimensional, incomplete and/or noisy data. However, the use of TDA is sporadic through the physical sciences. This project aims to develop TDA in the context of physical systems that are strongly interacting, highly quantum and demonstrate chaotic behaviour. The dynamical evolution of such systems can be analysed numerically using holography (simulations of classical gravity systems in one dimension higher) and the numerics indeed give rise to high-dimensional data sets, which often have gaps due to the limitations of numerics.
The physical sciences community have to date inferred key characteristics of the underlying dynamics using conventional statistical physics techniques such as the computation of correlation functions. Here we will use TDA to map out features of the underlying phase spaces of such systems; this approach could well give profound insights into key conceptual questions such as when a system becomes maximally chaotic. This strand interfaces closely with the PhD work of Linus Too, who has just been offered an enhancement award at ATI, and Linus will collaborate with the PDRA.
Machine learning for occultation
Occultation is a phenomenon that arises when a heavy astrophysical body passes in front of a distant star. Relativistic gravitational lensing produces two images of the star, an outer image and a faint inner image. As the lens moves closer to the star, the outer image can become extinguished (occulted). Until recently such occultation phenomena were considered unlikely to be detected. The chance of detection has radically increased following major improvements in instrument sensitivity and the discovery that systems with the required mass/separation arise much more frequently than previously expected.
Here we will analyse occultation taking into account for the first time spin effects for the star and lens. While the defining equations for light rays are known, their analysis requires complex numerical techniques when the bodies have significant spin. We aim to produce a bank of template signals and then set up machine learning to scan observational data from collaborations such as SMARTnet for fits to these templates.
Both strands require a PDRA with a background in applied mathematical modelling; proficiency in Python and ability to work in interdisciplinary teams.
Principal Investigator: Professor Marika Taylor