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My 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, I explore 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, I have started working on the construction of structure-preserving integrators for dissipative systems.
My 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, I explore 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, I have started working on the construction of structure-preserving integrators for dissipative systems.
My 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.
My 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.
Research Interests:
Research Interests:
- Numerical Methods and Error Analysis for Stochastic Differential Equations
- Geometric Numerical Integration, Structure-Preserving Integrators, GENERIC
- 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
- R. McGuinness, D. Herring, X. Wu, M. Almandi, D. Bhangu, L. Collinson, X. Shang and and E. Černis: Identifying preliminary risk profiles for dissociation in 16- to 25-year-olds using machine learning. Early Intervention in Psychiatry, 19(2), e70015, (2025).
- S. L. Dance, A. Barber, C. Brierley, L. Chapman, M. Collins, J. A. Crook, S. Elvidge, N. R. Gawor, D. Giles, S. Guillas, J. F. Rodriguez Herrera, E. Highwood, A. Hogg, I. S. Jory, N. Konstantinidis, Y. Kovalchuk, A. S. Lawless, G. Leckebusch, J. H. Marsham, K. Maskell, M. Noguer, A. O'Keeffe, B. Percy, K. J. Pringle, M. R. D. Rodrigues, X. Shang, J. Styles, J. Thuburn, M. Tsamados, M. Weiland, H. T. P. Williams and C. C. Wood: Transatlantic Data Science Academy Project. Phase 1: Scoping and Shaping. (2024).
- M. H. Duong and X. Shang: Accurate and robust splitting methods for the generalized Langevin equation with a positive Prony series memory kernel. Journal of Computational Physics, 464, 111332, (2022).
- Y. Gou, J. Balling, V. De Sy, M. Herold, W. De Keersmaecker, B. Slagter, A. Mullissa, X. Shang and J. Reiche: Intra-annual relationship between precipitation and forest disturbance in the African rainforest. Environmental Research Letters, 17(4), 044044, (2022).
- A. Albano, E. le Guillou, A. Danzé, I. Moulitsas, I. H. Sahputra, A. Rahmat, C. A. Duque-Daza, X. Shang, K. C. Ng, M. Ariane and A. Alexiadis: How to modify LAMMPS: From the prospective of a particle method researcher. ChemEngineering, 5(2), 30, (2021).
- X. Shang: Accurate and efficient splitting methods for dissipative particle dynamics. SIAM Journal on Scientific Computing, 43(3), A1929-A1949, (2021).
- X. Shang and M. Kröger: Time correlation functions of equilibrium and nonequilibrium Langevin dynamics: Derivations and numerics using random numbers. SIAM Review, 62(4), 901-935 (2020).
- X. Shang and H. C. Öttinger: Structure-preserving integrators for dissipative systems based on reversible-irreversible splitting. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476(2234), 20190446, (2020).
- X. Shang, M. Kröger and B. Leimkuhler: Assessing numerical methods for molecular and particle simulation. Soft Matter, 13(45), 8565-8578, (2017).
- B. Leimkuhler and X. Shang: Pairwise adaptive thermostats for improved accuracy and stability in dissipative particle dynamics. Journal of Computational Physics, 324, 174-193, (2016).
- B. Leimkuhler and X. Shang: Adaptive thermostats for noisy gradient systems. SIAM Journal on Scientific Computing, 38(2), A712-A736, (2016).
- X. Shang, Z. Zhu, B. Leimkuhler and A. Storkey: Covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling. Advances in Neural Information Processing Systems (NeurIPS), 28, 37-45, (2015).
- B. Leimkuhler and X. Shang: On the numerical treatment of dissipative particle dynamics and related systems. Journal of Computational Physics, 280, 72-95, (2015).
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