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Dr Michael Faulkner

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Dr Michael Faulkner

Assistant Professor in Predictive Modelling and Scientific Computing 

Michael.Faulkner [AT]

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I'm an Assistant Professor in the Warwick Centre for Predictive Modelling. My academic career started as a PhD student at University College London and Ecole normale supérieure de Lyon from 2011 to 2015, under the co-supervision of Steve Bramwell and Peter Holdsworth. After a short postdoc and teaching position at Bristol Mathematics, I then moved to Bristol Physics in August 2017 after winning an EPSRC postdoctoral research fellowship. I was also a visiting scientist at Ecole normale supérieure (Paris) from September 2017 to October 2018, and won a Max Planck Institute research fellowship to visit the Max Planck Institute for the Physics of Complex Systems in Dresden in April 2018.

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My broad research field is computational statistical physics, where I specialise in:

  • Emergent electrostatics, slow mixing (eg, broken symmetry) and correlated dynamics in systems that experience the Berezinskii-Kosterlitz-Thouless phase transition, eg, certain planar magnets, superfluids and superconductors.
  • Molecular simulation in soft-matter physics, with a focus on electrostatics, high precision and numerical stability.
  • Monte Carlo sampling algorithms in statistical physics and Bayesian computational statistics, with a particular interest in piecewise deterministic Markov processes such as event-chain Monte Carlo.

My key 🔑 scientific achievements split between these three interconnected specialisms:

Planar materials

Molecular simulation and event-chain Monte Carlo

  • Designed an event-chain algorithm for numerically stable all-atom molecular Coulomb simulations in soft matter (with Liang Qin, Tony Maggs and Werner Krauth). This is the only molecular simulation algorithm that mixes (equilibrates from a random initial configuration) Coulomb-based models in O(N log(N)) computations, where N is the number of particles. It also achieves machine precision and is the basis of…
  • …our mediator-based Python-C application JeLLyFysh, which we set out in detail here with Philipp Höllmer.
  • Event-chain Monte Carlo is a piecewise deterministic Markov process (PDMP). PDMPs mix at least as fast (typically much faster) than the diffusive dynamics of Metropolis Monte Carlo, and also guarantee numerical stability, unlike molecular-dynamics simulations. JeLLyFysh therefore holds much promise for the simulation of electrically charged Coulomb systems.

Sampling algorithms and interface with Bayesian computational statistics

  • Presented an in-depth paper on statistical physics and its sampling algorithms, but in the language of statistics and machine learning (with statistician Sam Livingstone). We took a particular interest in phase transitions and event-chain Monte Carlo, presenting the latter in the language of PDMPs in Bayesian computation. This project used super-aLby and xy-type-models to simulate the models presented. We are now using our framework to explore correlated dynamics at phase transitions across statistical science — as we identified analogies with the emergent planar Coulomb liquid described above.
  • Designed super-relativistic Monte Carlo for high-stability simulation of probability models in Bayesian computation (with statisticians Sam Livingstone and Gareth Roberts — see section 5.2 of the linked paper for details). By slowing down the Newtonian dynamics in high-gradient regions of probability space, this new simulation algorithm circumvents the numerical instabilities of Hamiltonian Monte Carlo when applied to light-tailed probability distributions. It also achieves machine precision and is the basis of our Python application super-aLby.


My teaching focuses on the new MSc course Predictive Modelling and Scientific Computing, where I supervise a group project and will also provide a guest lecture on advanced simulation algorithms in Spring 2024.

I also provide weekly maths support to my first-year tutees and am co-lecturer for the third-year module ES386 Dynamics of Vibrating Systems.

Selected publications

  1. M. F. Faulkner and S. Livingstone, Sampling algorithms in statistical physics: a guide for statistics and machine learning, Statist. Sci. 39, 137 (2024) arXiv:2208.04751
  2. M. F. Faulkner, Symmetry breaking at a topological phase transition, Phys. Rev. B 109, 085405 (2024) [arXiv:2209.03699]
  3. P. Hoellmer, L. Qin, M. F. Faulkner, A. C. Maggs and W. Krauth, JeLLyFysh-Version1.0 – a Python application for all-atom event-chain Monte Carlo, Comput. Phys. Commun. 253, 107168 (2020) [arXiv:1907.12502]
  4. S. Livingstone, M. F. Faulkner and G. O. Roberts, Kinetic-energy choice in hybrid/Hamiltonian Monte Carlo, Biometrika 106, 303 (2019) [arXiv:1706.02649]
  5. M. F. Faulkner, L. Qin, A. C. Maggs and W. Krauth, All-atom computations with irreversible Markov chains, J. Chem. Phys. 149, 064113 (2018) [arXiv:1804.05795]
  6. M. F. Faulkner, S. T. Bramwell and P. C. W. Holdsworth, An electric-field representation of the harmonic XY model, J. Phys.: Condens. Matter 29, 085402 (2017) [arXiv:1610.06692]
  7. T. Roscilde, M. F. Faulkner, S. T. Bramwell and P. C. W. Holdsworth, From quantum to thermal topological-sector fluctuations of strongly interacting bosons in a ring lattice, New J. Phys. 18, 075003 (2016) [arXiv:1602.06247]
  8. S. T. Bramwell, M. F. Faulkner, P. C. W. Holdsworth and A. Taroni, Phase order in superfluid helium films, EPL (Europhys. Lett.) 112, 56003 (2015) [arXiv:1508.07773]
  9. M. F. Faulkner, S. T. Bramwell and P. C. W. Holdsworth, Topological-sector fluctuations and ergodicity breaking at the Berezinskii–Kosterlitz–Thouless transition, Phys. Rev. B 91, 155412 (2015) [arXiv:1502.0081]

Projects and grants

  • EPSRC Postdoctoral Fellowship EP/P033830/1, August 2017 – October 2023. Research fellowship worth £293,118. Research fellow and principal investigator of project.
  • Visiting scientist, Ecole normale supérieure, September 2017 – October 2018. £21,500 in-kind contribution to my EPSRC fellowship.
  • Max Planck Institute Visiting Fellowship, April 2018. Visiting research fellowship worth ~€2,500.
  • Funded by ANR JCJC-2013 ArtiQ, December 2014 – February 2015. ~£5,000 to fund the final three months of my doctoral research.
  • Joint CNRS – UCL IMPACT PhD studentship, December 2011 – November 2014. Doctoral research studentship worth ~£100,000.

Software packages

  • JeLLyFysh – a mediator-based Python-C package for event-chain simulation of atomistic 3D Coulomb fluids.
  • super-aLby – a mediator-based Python package for super-relativistic (and other) Monte Carlo.
  • xy-type-models – a Fortran-Python package for Metropolis/event-chain simulation of XY spin models and lattice-field electrolytes.


I have an open PhD position in my group. The project will develop advanced simulation algorithms to characterise strongly correlated system dynamics in both condensed matter and agent-based epidemic modelling.

Informal enquiries to michael.faulkner [AT] are welcome.