Group Members

I am usually on the lookout for new PhD students, Postdocs, Masters and Bachelors students to join the team
Please visit:

BSc and MMath students normally get involved via final year projects; scroll down for examples of recent projects.

Staff and PhD Students

Benedict Leimkuhler FIMA FRSE

Professor of Applied Mathematics

  • BSc, Purdue University, 1983
  • MSc (Computer Science), University of Illinois,1986
  • PhD, University of Illinois, 1988
  • Academy of Finland Postoctoral Fellow, Helsinki University of Technology 1988-90
  • University of Kansas (Assistant/Assoc. Prof.), 1990-99
  • University of Leicester, Professor of Applied Mathematics, 2000-2006
  • University of Edinburgh, Professor of Applied Mathematics, 2006-present

Rene Lohmann

PhD Student, MAC-MIGS programme, started 2019. Studying distributed algorithms for deep learning and constraint-based neural network training. Co-supervised by Michele Ottobre (HWU) and Amos Storkey (Informatics).

  • BSc Physics, Heinrich Heine University, Düsseldorf, 2015
  • MSc Physics, Heinrich Heine University, Düsseldorf, 2019

Katerina Karoni

PhD Student, MAC-MIGS programme, started 2020. Research topic - machine learning for molecular dynamics. Currently studying symmetry preservation in machine-learned force fields. Co-supervised by Ben Goddard (Mathematics), Antonia Mey (Chemistry), James McDonagh (IBM Research)

  • BSc Mechanical Engineering, National Technical University of Athens, 2015
  • MSc Computational Fluid Mechanics, National Technical University of Athens, 2018

Peter Whalley

PhD Student, MAC-MIGS programme, started 2020. Research topic- scalable Bayesian inference methods for high dimensional stochastic models. Currently studying sampling methods on manifolds. Co-supervised by Daniel Paulin (Statistics).

  • BSc Mathematics, Imperial College London, 2019
  • MSc Mathematics, University of Oxford, 2020

Donald Hobson

PhD Student, MAC-MIGS programme, started 2020. Research topic- simplification of causal graphs and analysis of neural computational models. Co-supervised by Michal Branicki (Mathematics).

  • Mathematics Part III, Cambridge, 2020

Dominic Phillips

PhD student, Biomedical AI CDT programme, started 2021. Research topic -incorporating machine learning into molecular dynamics for accelerated drug discovery; Brownian dynamics algorithms. Co-supervised by Antonia Mey (Chemistry) and Flaviu Cipcigan (IBM Research).

  • BSc Natural Sciences, University of Cambridge, 2015
  • MSc Physics, University of Cambridge, 2018
  • MSc Artificial Intelligence, University of Edinburgh, 2020

Alix Leroy

PhD Student, MAC-MIGS programme, started 2021. Studying variable step size numerical methods for SDEs. Co-supervised by Jonas Latz (HWU) and Des Higham (UoE).

  • BSc in business engineering, Universit&eacute Libre de Bruxelles, 2015
  • BSc in engineering and physics, Universit&eacute Libre de Bruxelles, 2017
  • Msc in environment and development, London School of economics and political sciences, 2018
  • MSc in applied computational mathematics, University of Edinburgh, 2021

Recent Alumni

Tiffany Vlaar

PhD Student, MIGSAA CDT programme, started 2017. Research interests- Developing new optimization schemes for the training of deep neural networks, numerical methods for stochastic differential equations, deep learning theory, molecular dynamics, sampling methods.

  • BSc in Physics, Leiden University, 2013
  • MSc in Applied geophysics, joint degree from Delft University of Technology, RWTH Aachen, and ETH Zurich, 2015
  • MSc in Theoretical Physics, Perimeter Institute for Theoretical Physics (joint degree with University of Waterloo), 2016
  • PhD, MIGSAA Centre for Doctoral Training, 2022
  • Postdoc, MILA Montreal, 2022

Timothee Pouchon

postdoc visiting the group from 2019-2021 studied constrained algorithms for neural network training

  • BSc and Masters's, EPFL, 2012
  • PhD, EPFL, 2017
  • Postdoc, University of Edinburgh, 2019-2021

Matthias Sachs

Worked on generalized Langevin equation, nonequilibrium models, and numerical methods. Moved on to postdocs first at SAMSI and Duke University, then to UBC where he is now working with Christoph Ortner.

  • Exchange Student, Tsinghua University, 2010
  • Diploma, Technical University of Munich, 2012
  • PhD, University of Edinburgh, 2017 (sup. B. Leimkuhler and V. Danos)
  • Postdoc, SAMSI and Duke University, 2017-2020 (w. J. Lu and J. Mattingly)
  • Postdoc, University of British Columbia 2020- (w. C. Ortner)
  • Lecturer in Mathematics and Statistics, University of Birmingham 2021-

Xiaocheng Shang

numerical methods for dissipative particle dynamics, adaptive (noisy gradient) sampling algorithms, machine learning training algorithms

  • BSc in Mathematics, Zhejiang University of Technology, China 2011
  • MSc in Mathematical Biology, University of Dundee, United Kingdom 2012
  • PhD, University of Edinburgh, 2016 (sup. B. Leimkuhler)
  • Postdoc, Brown University, 2016-2017 (w. G. Karniadakis)
  • Postdoc, ETH, 2017-2019 (H.C. Öttinger)
  • Lecturer in Mathematics and Statistics, 2019-, University of Birmingham

Frederik Heber

algorithms and software design for ensemble study of neural networks and complex models; the force behind TATi the Thermodynamic Analytics Toolkit.

  • Diploma in Physics, Bonn, 2006
  • Doctoral thesis in Applied Mathematics, Bonn, 2014
  • Postdoc U. Bonn, Institute of Numerical Simulation, 2014-2017
  • Postdoc U. Edinburgh and Alan Turing Institute, 2017-19
  • Rutherford-Turing Fellow, Alan Turing Institute, 2018-19
  •, 2019-

Zofia Trstanova

studied algorithms based on diffusion maps for accelerating the sampling of molecular models; she also set up a collaboration with DNV GL to study classification methods for wind form SCADA data and worked with Anton Martinsson to create the acwind python package for this purpose; currently working in Paris as a machine learning developer.

  • BSc, Vienna University of Technology, 2010
  • Masters, Vienna University of Technology, 2013
  • Doctorate in Mathematics, Grenoble, 2016
  • Postdoc, U. Edinburgh, 2017-2019
  • Criteo, Paris, 2019-
  • Spotify, Paris, 2021-

Anton Martinsson

worked on sampling algorithms including an infinite swap simulated tempering algorithm; these methods were implemented in MIST by Iain Bethune. Also developed the acwind python software for wind turbine farm data analysis, with Zofia Trstanova.

  • BSc, U. Manchester, 2015
  • PhD, U. Edinburgh, 2019
  • Senior Data Scientist, Threatlabs, JAMF, Czech Republic

Iain Bethune

high performance computing genius and chief architect of the MIST software suite for interfacing novel integration methods into existing molecular dynamics codes like LAMPPS and Gromacs. Studied a wide variety of algorithms using MIST. Defended his PhD in late 2020. Currently head of software development at a Perth startup.

  • BSc, U. Edinburgh, 2005
  • PhD Physics (with G. Ackland and B. Leimkuhler) , U. Edinburgh, 2020
  • WRLD3D, Ltd 2020-2022
  • HPC Project Manager, Atos 2022-

Charles Matthews

collaborated on a variety of projects, include Langevin integrators and their application/analysis in molecular dynamics applications, including constrained MD methods. Moved to a postdoc at U. Chicago after his PhD and worked with J. Weare (further collaboration on an ensemble sampling method). Returned for projects in 2018-19 on wind data analysis, among other things. Now working in machine learning for an Edinburgh startup.

  • BSc, U. Edinburgh, 2010
  • PhD, U. Edinburgh, 2014
  • Postdoc, U. Chicago, 2014-2017
  • Postdoc, U. Edinburgh 2018-2019

MSc Projects

I supervise projects in the Computational Applied Mathematics (CAM) MSc Programme .

Xuexun Lu (now - PhD Student, Warwick University) , 2022 : Bayesian Uncertainty Reduction Analysis by Langevin Dynamics, Sampling

Alix Leroy (now - PhD Student, Edinburgh University) , 2021 : Numerical methods for weak approximation of stochastic differential equations and their applications to urban modelling

Kermani Nejad Mohammadreza (now - PhD Student, Bristol University) , 2020 : Acceleration of Statistical Sampling with Application to Machine Learning

Kevin Cheok Kim Tsang (now - PhD Student, Edinburgh University) , 2019 : Efficient Learning Algorithms with Incomplete Gradients

BSc Projects

I supervise a limited number of BSc projects.

Gabrijel Boduljak , 2022 : On Universality of Fully-Connected Neural Networks

Manuel Brea Carreras , 2022 : Feedforward Neural Networks - Approximation Properties and Robustness as Classifiers

Neil Macintyre, Sam Kelso, Ruairidh McVean , 2022 : Deep Neural Networks - Analytical and Numerical Studies

Guiomar Pescador Barrios, Jay Holley, Leah Seah , 2021 : Adaptive Single Hidden Layer Perceptrons

Ben Honey, Charlotte Tyndale-Hardy and Sam Weston , 2020 : Evaluating the Fairness of Political Constituencies Using Monte Carlo Sampling II

Luke Donnely, Kate Hassell, Stephen Cameron , 2019 : Evaluating the Fairness of Political Constituencies Using Monte Carlo Sampling I