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Applied Mathematician specialising in Machine Learning and Numerical Analysis
Applied Mathematician specialising in Machine Learning and Numerical Analysis
Department of Mathematics
King's College London
UK
I am an applied mathematician with a particular interest in Machine Learning, Numerical Analysis and Computational Mathematics in general. My research focusses on:
Understanding the role and potential of Machine Learning techniques in modern applied mathematics.
Investigating the stability of Machine Learning methods, such as their susceptibility to adversarial or stealth attacks.
Developing and analysing numerical algorithms for simulating phenomena observed in Biology and Physics described by systems of partial differential equations.
Exploring the potential of flexible new numerical algorithms based on meshes containing general polygonal or polyhedral elements or exotic discrete function spaces. Amongst these are adaptive techniques, which automatically modify their fundamental components in response to local indicators of the quality of the simulation.
For a more detailed description of my research, see my Research Highlights and List of Publications.
An adaptive polygonal mesh tracking a time-dependent layer
A key aim of adaptive meshing is to tracking time-dependent features of the solution which are not known beforehand. In this experiment, a mesh consisting of arbitrary polygonal elements is used to focus the mesh resolution around the layers, where it is needed. See my Research Highlights page for further details.
A new pattern-forming mechanism we recently discovered in a biological competition system
A new pattern-forming mechanism we recently discovered in a biological competition system
A snapshot of a similar simulation from this research project was featured on the front cover of the May 2018 issue of Proceedings of the Royal Society A. See my Research Highlights page for further details.
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