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Research interests
Research interests
Optimal experimental design
Inverse problems, especially for partial differential equations (PDEs)
Disaggregation of energy signals into separate devices
Large-scale computation and high-performance coding
Bifurcation theory and numerical simulation of bifurcating dynamical systems
Research topics
Research topics
Optimal experimental design for aeroacoustics
Aeroacoustics concerns itself with the propagation of sound waves through fluid media such as air. An important question in aeroacoustic experiments is how placement of sensors affects your ability to solve the inverse source problem of identifying the sound source from boundary measurements. Optimal design aims to answer this question in precise terms, by quantifying how sensor placement affects posterior uncertainty of our knowledge of the source.
Figure. An aeroacoustic experimental setup. Image taken from Aeroacoustic beamforming of a model wind-turbine in anechoic and reverberant environments, Fischer et al.,
Proceedings of ACOUSTICS 2016
Convolutional sparse coding for smart meter energy disaggregation [2]
Household smart meters carry a wealth of information about the usage of household appliances and their energy consumption. However, extracting this information is challenging, due to the extremely ill-posed nature of summation, and due to wishing to avoid invasive monitoring or supervision of individual devices. The success of the CSC software, and the accompanying analysis, was in creating an unsupervised learning-based method for identifying the usage of certain classes of devices based on aggregated smart meter data, providing accurate and non-invasive information on activity and usage with low computational cost.
Bifurcations in integrodifference equations [3]
It is natural that living beings disperse throughout spatial habitats. However, classical population models from theoretical ecology typically focus solely on population numbers, while neglecting the effect of spatial dispersal. By incorporating these ideas into a rigorous mathematical framework via integrodifference equations, one is able to employ bifurcation analysis to demonstrate that the spatial model displays dynamical behaviour that cannot be found in the classical models.
Figure. Living beings cannot occupy the same area in space, but must disperse throughout their viable habitat (top). A Neimark-Sacker bifurcation arising in a predator-prey ecosystem as birth rates vary (bottom).
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