Dr Matthias Sachs PhD

Dr Matthias Sachs

School of Mathematics
Assistant Professor in Applied Mathematics and Statistics

Contact details

School of Mathematics
Watson Building
University of Birmingham
B15 2TT

Matthias Sachs is an applied mathematician working at the interface of numerical analysis, probability theory and statistical modelling. As part of his research, he tries to produce sound and rigorously derived mathematical theory while at the same time provide practically relevant algorithmic solutions and results. His approach to bridging this gap is to work in close collaborations with researchers in other areas of science (e.g., material science, applied statistics) and industry as well as spending a significant amount of his time with software development to provide computationally efficient implementations of his and his collaborators' work to other researchers.

Personal webpage.


  • PhD in Applied and Computational Mathematics, University of Edinburgh, 2017


  • Since Dec 2021 Assistant Professor, University of Birmingham, UK.
  • 2020-2021 Postdoctoral Fellow, University of British Columbia, Vancouver, Canada.
  • 2017-2020 SAMSI-postdoctoral associate, Duke University, NC, USA.


Semester 2

LC Data, Probability and Statistics (Jinan)


Research themes

  • Numerical analysis of stochastic differential equations;
  • Computational statistics: design and analysis of Markov Chain Monte Carlo methods;
  • Machine learning methods for molecular systems/dynamics: learnable equivariant representations of scalar/vector/tensor valued quantities, active learning.

Research activity

Machine learning for molecular systems/dynamics

I work on the development and implementation of machine learning methods in the context of molecular modelling. This includes in particular:

  • equivariant representations of physical quantities such as inter-molecular forcefields and friction tensors that allow for data-efficient learning of such quantities;
  • Bayesian inference methods based on the above-mentioned equivariant representations;
  • Active learning approaches for automatic data-generation of atomic configurations.

Design and analysis of sampling algorithms

I am interested in the design and analysis of sampling algorithms. Besides classical Markov chain Monte Carlo algorithms this includes approximate Monte Carlo algorithms that are obtained as a discretisation of stochastic differential equation. Among others I have been and am working on are

  • non-reversible Markov Chain Monte Carlo method for sampling of discrete probability measures (e.g., graph partitions),
  • stochastic thermostat methods (e.g., generalised/adaptive Langevin dynamics) and piecewise deterministic Markov processes for efficient sampling of Bayesian posterior distributions in the presence of big data.


Recent publications


Witt, WC, Oord, CVD, Gelžinytė, E, Järvinen, T, Ross, A, Darby, JP, Ho, CH, Baldwin, WJ, Sachs, M, Kermode, J, Bernstein, N, Csányi, G & Ortner, C 2023, 'ACEpotentials.jl: A Julia implementation of the atomic cluster expansion', The Journal of Chemical Physics, vol. 159, no. 16, 164101. https://doi.org/10.1063/5.0158783

van der Oord, C, Sachs, M, Kovács, DP, Ortner, C & Csányi, G 2023, 'Hyperactive learning for data-driven interatomic potentials', npj Computational Materials, vol. 9, no. 1, 168. https://doi.org/10.1038/s41524-023-01104-6

Sachs, M, Sen, D, Lu, J & Dunson, D 2023, 'Posterior computation with the Gibbs zig-zag sampler', Bayesian Analysis, vol. 18, no. 3, pp. 909-927. https://doi.org/10.1214/22-BA1319

Leimkuhler, B & Sachs, M 2022, 'Efficient numerical algorithms for the generalized Langevin equation', SIAM Journal on Scientific Computing, vol. 44, no. 1, pp. A364-A388. https://doi.org/10.1137/20M138497X

Sen, D, Sachs, M, Lu, J & Dunson, DB 2020, 'Efficient posterior sampling for high-dimensional imbalanced logistic regression', Biometrika, vol. 107, no. 4, pp. 1005-1012. https://doi.org/10.1093/biomet/asaa035

Leimkuhler, B, Sachs, M & Stoltz, G 2020, 'Hypocoercivity Properties of Adaptive Langevin Dynamics', SIAM Journal on Applied Mathematics, vol. 80, no. 3, pp. 1197-1222. https://doi.org/10.1137/19M1291649

Lu, J, Sachs, M & Steinerberger, S 2020, 'Quadrature Points via Heat Kernel Repulsion', Constructive Approximation, vol. 51, no. 1, pp. 27-48. https://doi.org/10.1007/s00365-019-09471-4

Sachs, M, Leimkuhler, B & Danos, V 2017, 'Langevin dynamics with variable coefficients and nonconservative forces: From stationary states to numerical methods', Entropy, vol. 19, no. 12, 647. https://doi.org/10.3390/e19120647

Conference contribution

Leimkuhler, B & Sachs, M 2019, Ergodic Properties of Quasi-Markovian Generalized Langevin Equations with Configuration Dependent Noise and Non-conservative Force. in G Giacomin, S Olla, E Saada, H Spohn, G Stoltz & G Stoltz (eds), Stochastic Dynamics Out of Equilibrium - Institut Henri Poincaré, 2017. Springer Proceedings in Mathematics and Statistics, vol. 282, Springer, pp. 282-330, International workshop on Stochastic Dynamics out of Equilibrium, IHPStochDyn 2017, Paris, France, 12/06/17. https://doi.org/10.1007/978-3-030-15096-9_8


Witt, WC, Oord, CVD, Gelžinytė, E, Järvinen, T, Ross, A, Darby, JP, Ho, CH, Baldwin, WJ, Sachs, M, Kermode, J, Bernstein, N, Csányi, G & Ortner, C 2023 'ACEpotentials.jl: A Julia Implementation of the Atomic Cluster Expansion' arXiv. https://doi.org/10.48550/arXiv.2309.03161

Oord, CVD, Sachs, M, Kovács, DP, Ortner, C & Csányi, G 2022 'Hyperactive Learning (HAL) for Data-Driven Interatomic Potentials'. https://doi.org/10.48550/arXiv.2210.04225

Herschlag, G, Mattingly, JC, Sachs, M & Wyse, E 2020 'Non-reversible Markov chain Monte Carlo for sampling of districting maps' arXiv. https://doi.org/10.48550/arXiv.2008.07843

View all publications in research portal