Dr Xiaocheng Shang BSc MSc PhD PGCHE

Dr Xiaocheng Shang

School of Mathematics
Lecturer in Mathematics and Statistics

Contact details

School of Mathematics
Watson Building
University of Birmingham
B15 2TT

Xiaocheng Shang is a Lecturer in Mathematics and Statistics. Xiaocheng’s primary research interests lie in the optimal design of numerical methods for stochastic differential equations with a strong emphasis on applications ranging from computational mathematics, statistics, physics, to data science. Xiaocheng is a member of the Numerical Analysis Group, the Applied and Computational Statistics Group, as well as the Institute for Interdisciplinary Data Science and AI. Xiaocheng is also a Fellow of The Alan Turing Institute, the UK's national institute for data science and artificial intelligence. Xiaocheng has received funding for his research from the Royal Society via an International Exchanges Award.

Personal webpage


  • Postgraduate Certificate in Higher Education (PGCHE) with Distinction, University of Birmingham, 2021
  • PhD in Applied and Computational Mathematics, University of Edinburgh, 2016
  • MSc in Mathematical Biology, University of Dundee, 2012
  • BSc in Mathematics and Applied Mathematics, Zhejiang University of Technology, 2011


Xiaocheng Shang obtained his PhD in Applied and Computational Mathematics under the supervision of Professor Ben Leimkuhler from the University of Edinburgh in 2016. After postdoctoral positions at the University of Edinburgh, Brown University in the United States, and ETH Zurich in Switzerland, he joined the School of Mathematics at the University of Birmingham as a Lecturer in 2019.


Semester 1

LH Statistical Methods in Economics (Jinan)

Semester 2

LH Statistical Methods in Economics (Jinan)

Postgraduate supervision

Xiaocheng is interested in working with highly motivated students who share any of his research interests. Please get in touch via email.


Research Themes

  • Numerical Methods and Error Analysis for Stochastic Differential Equations
  • Geometric Numerical Integration, Structure-Preserving Integrators
  • Molecular Dynamics, Statistical Mechanics, Multiscale Methods
  • Momentum-Conserving Thermostats, Dissipative Particle Dynamics
  • Nonequilibrium Modelling, Polymer Melts, Adaptive Thermostats
  • Bayesian Sampling, Data Science, Machine Learning of Potential Energy

Research Activities

Xiaocheng's research has been addressing the sampling problem in a high dimensional space, i.e., the computation of averages with respect to a defined probability density that is a function of many variables. Such sampling problems arise in many application areas, including molecular dynamics, multiscale models, and Bayesian sampling techniques used in emerging machine learning applications. In particular, Xiaocheng explores theory, algorithms, and numerous applications of thermostat techniques, in the setting of a stochastic-dynamical system, that preserve the canonical Gibbs ensemble defined by an exponentiated energy function. More recently, Xiaocheng has started working on the construction of structure-preserving integrators for dissipative systems.

Xiaocheng's goal is to bring together the tools of numerical analysis and probability theory with the powerful principles underpinning multiscale modelling in materials science and engineering.

Other activities

Director of Quality Assurance, Jinan University-University of Birmingham Joint Institute


Recent publications


Duong, MH & Shang, X 2022, 'Accurate and robust splitting methods for the generalized Langevin equation with a positive Prony series memory kernel', Journal of Computational Physics.

Gou, Y, Balling, J, De Sy, V, Herold, M, De Keersmaecker, W, Slagter, B, Mullissa, A, Shang, X & Reiche, J 2022, 'Intra-annual relationship between precipitation and forest disturbance in the African rainforest', Environmental Research Letters, vol. 17, no. 4, 044044. https://doi.org/10.1088/1748-9326/ac5ca0

Shang, X 2021, 'Accurate and efficient splitting methods for dissipative particle dynamics', SIAM Journal on Scientific Computing, vol. 43, no. 3, A1929–A1949. https://doi.org/10.1137/20M1336230

Albano, A, le Guillou, E, Danzé, A, Moulitsas, I, Sahputra, IH, Rahmat, A, Duque-Daza, CA, Shang, X, Ng, KC, Ariane, M & Alexiadis, A 2021, 'How to modify LAMMPS: from the prospective of a particle method researcher', ChemEngineering, vol. 5, no. 2, 30. https://doi.org/10.3390/chemengineering5020030

Shang, X & Öttinger, HC 2020, 'Structure-preserving integrators for dissipative systems based on reversible-irreversible splitting', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 476, no. 2234, 20190446. https://doi.org/10.1098/rspa.2019.0446

Shang, X & Kröger, M 2020, 'Time correlation functions of equilibrium and nonequilibrium Langevin dynamics: derivations and numerics using random numbers', SIAM Review, vol. 62, no. 4, pp. 901-935. https://doi.org/10.1137/19M1255471

Shang, X, Kröger, M & Leimkuhler, B 2017, 'Assessing numerical methods for molecular and particle simulation', Soft Matter, vol. 13, no. 45, pp. 8565-8578. https://doi.org/10.1039/C7SM01526G

Leimkuhler, B & Shang, X 2016, 'Adaptive thermostats for noisy gradient systems', SIAM Journal on Scientific Computing, vol. 38, no. 2, pp. A712-A736. https://doi.org/10.1137/15m102318x

Leimkuhler, B & Shang, X 2016, 'Pairwise adaptive thermostats for improved accuracy and stability in dissipative particle dynamics', Journal of Computational Physics, vol. 324, pp. 174-193. https://doi.org/10.1016/j.jcp.2016.07.034

Leimkuhler, B & Shang, X 2015, 'On the numerical treatment of dissipative particle dynamics and related systems', Journal of Computational Physics, vol. 280, pp. 72-95. https://doi.org/10.1016/j.jcp.2014.09.008

Conference contribution

Shang, X, Zhu, Z, Leimkuhler, B & Storkey, AJ 2015, Covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling. in Advances in Neural Information Processing Systems 28 . pp. 37-45. <https://papers.nips.cc/paper/5978-covariance-controlled-adaptive-langevin-thermostat-for-large-scale-bayesian-sampling.pdf>

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