Mathematical Sciences

Below you will find Data-Centric Engineering projects offered by supervisors within the School of Mathematical Sciences

This is not an exhaustive list. If you have your own research idea, or if you are a prospective PDS candidate, please return to the main DCE Research page for further guidance, or contact us at dce-cdt@qmul.ac.uk  

Data-driven analysis and stochastic modelling of power-grid frequency dynamics

A fundamental understanding of the current power grid system with its production and demand fluctuations is necessary to develop potential pathways towards a future 100% sustainable system.

The project will be investigating specific questions within this complex topic of energy research, using stochastic analysis and data-driven approaches to work towards a quantitative understanding of fluctuating aspects of the energy system. This includes a detailed analysis of fluctuations in the power production itself, analysis of power production time series of renewable generators (wind and solar), demand trends and fluctuations, interaction with the energy market and more. To achieve a better understanding, we will perform a statistical analysis of measured frequency fluctuations around the nominal frequency of 50Hz, which mirrors demand and production fluctuations in a very efficient way. Based on previous work (B. Schäfer, C. Beck, et al, 2018; Gorjão et al, 2020) in this project we will use new mathematical models based on generalized stochastic differential equations to realistically model and predict frequency fluctuations, and compare with data measured in the UK and in various other European power grids. A recent development is also the usage of machine learning techniques as forecasting tools in this context.

Supervisors: Prof Christian Beck & Dr Benjamin Schaefer

Emulators for the analysis of computer experiments

A common feature of industrial experimentation is the use of simulation and computer experiments to at least partially replace complicated and expensive physical experiments. The analysis of computer experiments often builds a surrogate model termed an emulator. The emulator has a variety of uses including sensitivity analysis, forecasting, history matching and design of experiments, among other uses.

This project is concerned with practical aspects of construction and use of emulators, with special focus on a type of emulator called supersaturated models. During the project we aim to survey the methodology and apply it to some case studies, developing emulators and using them for subsequent analysis. Along the project we expect to also compare with other techniques although this comparison is not meant to be exhaustive but just indicative of practice.

Supervisor: Dr Hugo Maruri-Aguilar

Discovering Bayesian network structure through time

Network analysis has been recently used for studying economic crises and has shown to contribute to a better understanding of complex systems of interconnected institutions. Moreover, modeling high-dimensional time series with network dependence is a frequent yet challenging problem in real-world applications but recently has been accounted for by incorporating the overlapping community structure in a network. In this project, we will study the Bayesian approach to a novel strand of literature based on Network Autoregressive model.

This class of models accounts for the community and cross-sectional dependence structures in time series and the idea behind this project is to implement machine learning techniques to study the dynamic and panel structure of networks. Hence, this can be done through a multilayer representation of the networks characterizing the dependence processes.

To gain flexibility, we will employ Bayesian techniques; their nonparametric extension, and the connection to machine learning techniques.

Keywords: Bayesian inference; time series; network modeling; autoregressive; econometrics

Supervisors: Dr Alex Shestopaloff & Dr Luca Rossini

Gravitational wave data science with the Laser Interferometer Space Antenna (LISA)

The principal goal of the space-based LISA gravitational wave detector is to observe the extreme mass ratio inspiral (EMRI) of stellar-size black holes orbiting supermassive black holes. Detection and parameter estimation require accurate gravitational waveforms associated with generic orbits, that are most efficiently computed within a perturbative expansion. We will combine novel numerical methods with time-domain numerical computation to construct high-precision waveforms. The prospective student will have the opportunity to join the QMUL LISA group and/or the newly established QMUL LIGO group, and to be trained on gravitational-wave source modelling using novel numerical and AI data analysis schemes. Theoretical high-precision waveform templates are necessary for extracting the extremely weak waveform signals from noisy detector data. Thus, part of the focus will be on the development of novel collocation methods and time-symmetric integration methods for numerically evolving PDEs with time-domain gravitational self-force computation in a radiation gauge to construct high-precision gravitational waveforms. 

The student will use our templates to perform gravitational-wave data analysis for the LISA and/or LIGO detectors via novel deep learning techniques and traditional match filtering techniques. Match filtering relies on computationally intensive MCMC methods that take weeks and need to be repeated for each detection. In contrast, our template database will be used to train a deep neural network for detecting gravitational wave signals (via classification) and estimating astrophysical source parameters (via regression). Deep neural networks for gravitational wave data analysis only need to be pre-trained once, and then enable detection and parameter estimation in milliseconds. This will allow real-time detection of gravitational signals, enabling astronomers to point telescopes to the source and observe electromagnetic counterparts. 
 
The proposed research is aimed at computationally exploring the theory of black holes, in order to improve our understanding of fundamental physical laws and reveal how nature operates on scales where our current understanding breaks down. As detectors improve their sensitivity and range, the rate of events inside their observable volume will increase cubically. Keeping up with this increase in signals necessitates the use of AI in space data science, which is expected to form a new paradigm in multi-messenger astronomy. 
 
Candidates with experience in deep neural networks, numerical analysis, signal analysis, data science, Bayesian inference, scientific computing or artificial intelligence are encouraged to apply. 

Keywords: space data science, deep neural networks

Supervisor: Dr Charalampos Markakis