Research

Research topics

Cardiovascular modelling by learning the incompressible Navier-Stokes equation with physics-informed neural networks (PINNs)

Physics-informed neural networks, or PINNs, are a specialised type of neural networks that can learn physics by fitting the network output to known physical models. These can be trained both with and without data, and present a fascinating method for high-performance modelling in challenging real-world scenarios, such as cardiovascular modelling for heart disease studies.

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

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).