Publications

Recent Highlights

(For a full list see below or go to Google Scholar, ResearcherID)

Multirate training of neural networks

...dramatically improve neural network training by making use of latent multiscale structure...


T. Vlaar and B. Leimkuhler, 2021 arxiv

Two-dimensional mobile breather scattering in a hexagonal crystal lattice

...two-dimensional scattering of long-lived breathers in a model hexagonal lattice of atoms...


J. Bajars. C. Eilbeck and B. Leimkuhler, Physical Review E 103,9354, 2020 journal

Efficient Numerical Algorithms for the Generalized Langevin Equation

...fast numerical methods for quasi-Markovian GLEs (Langevin dynamics with memory) and applications to sampling...


B. Leimkuhler and M. Sachs, 2021 arxiv

Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions

A simple-to-implement weak-sense numerical method to approximate reflected stochastic differential equations (RSDEs) is proposed and analysed, with discussion of ergodic limits.


B Leimkuhler, A Sharma, MV Tretyakov, 2020 arxiv

Constraint-Based Regularization of Neural Networks

We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks, enabling direct control of the parameter space of the model.


B Leimkuhler, T Pouchon, T Vlaar, A Storkey, 12th Annual Workshop on Optimization for Machine Learning (NEURIPS OPT2020) ,, 2020 workshop

Posterior sampling strategies based on discretized stochastic differential equations for machine learning applications

We discuss Bayesian parametrization in machine learning based on Markov Chain Monte Carlo, e.g. Langevin dynamics and extended system methods based on an ensemble of walkers. We also describe a new software package, TATI, for tensorflow-based sampling of neural network posteriors.


F. Heber, Z. Trstanova, and B. Leimkuhler, Journal of Machine Learning Research 21,1-33, 2020 journal

Hypocoercivity properties of adaptive Langevin dynamics

Adaptive Langevin dynamics is a method for sampling the Boltzmann--Gibbs distribution at prescribed temperature in cases where the potential gradient is subject to stochastic perturbation of unknown magnitude. It replaces the friction in underdamped Langevin dynamics with a dynamical variable, updated according to a negative feedback loop control law. This paper shows hypocoercivity imply geometric convergence to equilibrium and an asymptotic central limit theorem.


Benedict Leimkuhler, Matthias Sachs, and Gabriel Stoltz, SIAM Journal on Applied Mathematics 80,1197-1222, 2020 journal

 

Publication List

Multirate training of neural networks, T. Vlaar and B. Leimkuhler, 2021 arxiv

Two-dimensional mobile breather scattering in a hexagonal crystal lattice J. Bajars. C. Eilbeck and B. Leimkuhler, Physical Review E 103,9354, 2020 journal

Efficient Numerical Algorithms for the Generalized Langevin Equation, B. Leimkuhler and M. Sachs, 2021 arxiv

Simplest random walk for approximating Robin boundary value problems and ergodic limits of reflected diffusions, B Leimkuhler, A Sharma, MV Tretyakov, 2020 arxiv

Constraint-Based Regularization of Neural Networks B Leimkuhler, T Pouchon, T Vlaar, A Storkey, 12th Annual Workshop on Optimization for Machine Learning (NEURIPS OPT2020) ,, 2020 workshop

Posterior sampling strategies based on discretized stochastic differential equations for machine learning applications F. Heber, Z. Trstanova, and B. Leimkuhler, Journal of Machine Learning Research 21,1-33, 2020 journal

Partitioned integrators for thermodynamic parameterization of neural networks Benedict Leimkuhler, Charles Matthews, Tiffany Vlaar, Foundations of Data Science 1,457-489, 2019 journal

Hypocoercivity properties of adaptive Langevin dynamics Benedict Leimkuhler, Matthias Sachs, and Gabriel Stoltz, SIAM Journal on Applied Mathematics 80,1197-1222, 2020 journal

Transferability of Operational Status Classification Models Among Different Wind Turbine Types Z. Trstanova, A. Martinsson, C. Matthews, S. Jimenez, B. Leimkuhler, T. Van Delft, and M. Wilkinson, Journal of Physics-Conference Series 1222,12041, 2019

Local and Global Perspectives on Diffusion Maps in the Analysis of Molecular Systems Z. Trstanova, B. Leimkuhler and T. Lelievre, Proceedings of the Royal Society A 476,20190036, 2019 journal

MIST - A Simple and Efficient Molecular Dynamics Abstraction Library for Integrator Development I. Bethune et al, Computer Physics Communications 236,224-236, 2019 journal

Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise M. Sachs and B. Leimkuhler, Stochastic Dynamics Out of Equilibrium (IHPStochDyn 2017), Springer 282,282-330, 2019 journal

Quantifying configuration-sampling error in Langevin simulations of complex molecular systems J Fass, D Sivak, GE Crooks, KA Beauchamp, B Leimkuhler, and J Chodera, Entropy 20,318, 2018 journal

Simulated Tempering Method in the Infinite Switch Limit with Adaptive Weight Learning A. Martinsson, J. Lu, B. Leimkuhler and E. Vanden-Eijnden, Journal of Statistical Mechanics-Theory and Experiment 2019,13207, 2019 journal

Assessing numerical methods for molecular and particle simulation X. Shang, M. Kroger and B. Leimkuhler, Soft Matter 13,8565-8578, 2017 journal

Langevin Dynamics with Variable Coefficients and Nonconservative Forces-From Stationary States to Numerical Methods M. Sachs, B. Leimkuhler, and V. Danos, Entropy 19,647-667, 2017 journal

Ensemble preconditioning for Markov chain Monte Carlo simulation C. Matthews, J. Weare, B. Leimkuhler, Statistics and Computing 28,277-290, 2018 journal

Observation-based correction of dynamical models using thermostats K. Myerscough, J. Frank, and B. Leimkuhler, Proceedings of the Royal Society A 473,20160730, 2017 journal

Pairwise adaptive thermostats for improved accuracy and stability in dissipative particle dynamics B. Leimkuhler and X. Shang, Journal of Computational Physics 324,174-193, 2016 journal

Efficient molecular dynamics using geodesic integration and solvent-solute splitting B. Leimkuhler and C. Matthews, Proceedings of the Royal Society A 472,20160138, 2016 journal

A stochastic algorithm for the isobaric-isothermal ensemble with Ewald summations for all long range forces M. Di Pierro, R. Elber,and B. Leimkuhler, Journal of Chemical Theory and Computation ,5624-5637, 2015 journal

Covariance-controlled adaptive Langevin thermostat for large-scale Bayesian sampling X. Shang, Z. Zhu, B. Leimkuhler and A. Storkey, Advances in Neural Information Processing Systems (NIPS 2015) 28,, 2015 proceedings

Extended Hamiltonian approach to continuous tempering G. Gobbo and B. Leimkuhler, Phys Rev E 91,61301, 2015 journal

Adaptive Thermostats for Noisy Gradient Systems B. Leimkuhler and X. Shang, SIAM Journal on Scientific Computing 38,A712-A736, 2015 journal

Direct control of the small-scale energy balance in 2D fluid dynamics J. Frank, B. Leimkuhler and K. Myerscough, Journal of Fluid Mechanics 782,11, 2015 journal

The Adaptive Buffered Force QM/MM method in the CP2K and Amber software packages L. Mones, A. Jones, A. Götz, T. Laino, R. Walker, B. Leimkuhler, G. Csànyi, and N. Bernstein, Journal of Computational Chemistry 36,633-648, 2015 journal

Numerical simulations of nonlinear modes in mica - past, present and future J. Bajars, C. Eilbeck and B. Leimkuhler, in Quodons in Mica-Nonlinear Localized Travelling Excitations in Crystals; Springer Series in Materials Science Vol 221 ,35-67, 2015 journal

Nonlinear propagating localized modes in a 2D hexagonal crystal lattice J. Bajars, C. Eilbeck and B. Leimkuhler, Physica D 301-302,8-20, 2015 journal

On the numerical treatment of dissipative particle dynamics and related systems B. Leimkuhler and X. Shang, Journal of Computational Physics 280,72-95, 2015 journal

On the long-time integration of stochastic gradient systems B. Leimkuhler, C. Matthews and M. Tretyakov, Proceedings of the Royal Society A 470,20140120, 2014 journal

The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics B. Leimkuhler, C. Matthews and G. Stoltz, IMA Journal on Numerical Analysis ,, 2015 journal

Robust and efficient configurational molecular sampling via Langevin Dynamics B. Leimkuhler and C. Matthews, Journal of Chemical Physics 138,174102, 2013 journal

Stochastic resonance-free multiple time-step algorithm for molecular dynamics with very large time steps B. Leimkuhler, D. Margul and M. Tuckerman, Molecular Physics 111,3579-3594, 2013 journal

Weakly coupled heat bath models for Gibbs-like invariant states in nonlinear wave equations J. Bajars, J. Frank and B. Leimkuhler, Nonlinearity 26,1945-1973, 2013 journal

Rational construction of stochastic numerical methods for molecular sampling B. Leimkuhler and C. Matthews, Applied Mathematics Research Express 2013,34-56, 2013 journal

Comparing the efficiencies of stochastic isothermal molecular dynamics methods B. Leimkuhler, E. Noorizadeh and O. Penrose, Journal of Statistical Physics 143,921-942, 2011 journal

Adaptive stochastic methods for sampling driven molecular systems A. Jones and B. Leimkuhler, Journal of Chemical Physics 135,84125, 2011 journal

Dimensional reductions for the computation of time-dependent quantum expectations B. Leimkuhler and G. Mazzi, SIAM Journal on Scientific Computing 33,2024-2038, 2011 journal

Stochastic-dynamical thermostats for constraints and stiff restraints J. Bajars, J. Frank and B. Leimkuhler, The European Physical Journal 200,131-152, 2011 journal

Simplified modelling of a thermal bath, with application to a fluid vortex system S. Dubinkina, J. Frank, and B. Leimkuhler, SIAM Multiscale Modelling and Simulation 8,1882-1901, 2010 journal

Generalized Bulgac-Kusnezov methods for sampling of the Gibbs-Boltzmann measure B. Leimkuhler, Physical Review E 81,26703, 2010 journal

A gentle stochastic thermostat for molecular dynamics B. Leimkuhler, E. Noorizadeh and F. Theil, Journal of Statistical Physics 135,261-277, 2009 journal

A Metropolis-adjusted Nose-Hoover thermostat B. Leimkuhler and S. Reich, ESAIM Mathematical modelling and numerical analysis 43,743-755, 2009 journal

A temperature control technique for nonequilibrium molecular simulation B. Leimkuhler, F. Legoll and E. Noorizadeh, Journal of Chemical Physics 128,74105, 2008 journal

Molecular dynamics and the accuracy of numerically computed averages S. Bond and B. Leimkuhler, Acta Numerica 16,1-65, 2007 journal

Stabilized integration of Hamiltonian systems with hard-sphere inequality constraints S. Bond and B. Leimkuhler, SIAM Journal on Scientific Computing 30,134-147, 2007 journal

Molecular simulation in the canonical ensemble and beyond Z. Jia and B. Leimkuhler, ESAIM Mathematical modelling and numerical analysis 41,333-350, 2007 journal

Rapid thermal equilibration of coarse-grained molecular dynamics S. Gill, Z. Jia, B. Leimkuhler and A. Cocks, Physical Review B 73,184304, 2006 journal

Geometric integrators for multiple timescale simulation Z. Jia and B. Leimkuhler, Journal of Physics A 39,5379-5403, 2006 journal

Approach to thermal equilibrium in biomolecular simulation E. Barth, B. Leimkuhler, and C. Sweet, New Algorithms for Macromolecular Simulation (Springer Lecture Notes in Computational Science and Engineering) 49,125-140, 2006 journal

A projective thermostatting technique Z. Jia and B. Leimkuhler, SIAM Multiscale Modelling and Simulation 4,563-583, 2005 journal

A Hamiltonian formulation for recursive multiple thermostats in a common timescale B. Leimkuhler and C. Sweet, SIAM Journal on Applied Dynamical Systems 4,187-216, 2005 journal

An efficient geometric integrator for thermostatted anti-/ferromagnetic Models T. Arponen and B. Leimkuhler, BIT Numerical Mathematics 44,403-424, 2004 journal

The canonical ensemble via symplectic integration using Nose and Nose-Poincare chains B. Leimkuhler and C. Sweet, Journal of Chemical Physics 121,108-117, 2004 journal

A parallel multiple time-scale reversible integrator for dynamics simulation Z. Jia and B. Leimkuhler, Future Generation Computer Systems 19,415-424, 2003 journal

Generating generalized distributions from dynamical simulation E. Barth, B. Laird and B. Leimkuhler, Journal of Chemical Physics 118,5759-5769, 2003 journal

Generalized dynamical thermostatting technique B. Laird and B. Leimkuhler, Physical Review E 68, 016704 (2003) 68,16704, 2003 journal

On the approximation of Feynman-Kac path integrals S. Bond, B. Laird, and B. Leimkuhler, Journal of Computational Physics 185,472-483, 2003 journal

An efficient multiple time-scale reversible integrator for the gravitational N-body problem B. Leimkuhler, Applied Numerical Mathematics 43,175-190, 2002 journal

A separated form of Nosé dynamics for constant temperature and pressure simulation B. Leimkuhler, Computer Physics Communications 148,206-213, 2002 journal

A test set for molecular dynamics E. Barth, B. Leimkuhler, and S. Reich, Lecture Notes in Computational Science and Engineering 24,73-103, 2002 journal

A reversible averaging integrator for multiple timescale dynamics B. Leimkuhler and S. Reich, Journal of Computational Physics 171,95-114, 2001 journal

Explicit, time-reversible and variable stepsize integration T. Holder, B. Leimkuhler, and S. Reich, Applied Numerical Mathematics 39,367-377, 2001 journal

Scaling invariance and adaptivity C. Budd, B. Leimkuhler and M. Piggott, Applied Numerical Mathematics 39,261-288, 2001 journal

Molecular dynamics algorithms for mixed hard-core/continuous potentials Y. Houndonougbo, B. Laird, and B. Leimkuhler, Journal of Molecular Physics 98,309-316, 2000 journal

A time-reversible, regularized, switching integrator for the N-body problem A. Kvaerno and B. Leimkuhler, SIAM Journal on Scientific Computing 22,1016-1035, 2000 journal

Geometric integrators based on scaling and switching B. Leimkuhler, Proceedings of the Equadiff Conference (Berlin, 1999), World Scientific ,988-993, 2000 journal

A Semi-explicit, variable-stepsize integrator for constrained dynamics E. Barth, B. Leimkuhler, and S. Reich, SIAM Journal on Scientific Computing 21,1027-1044, 1999 journal

Reversible adaptive regularization- perturbed Kepler motion and classical atomic trajectories B. Leimkuhler, Philosophical Transactions of the Royal Society of London A 357,1101-1134, 1999 journal

Reversible adaptive regularization methods for atomic N-body problems in applied fields B. Leimkuhler, Applied Numerical Mathematics 29,31-43, 1999 journal

Asymptotic error analysis of the Adaptive Verlet method S. Cirilli, E. Hairer and B. Leimkuhler, BIT Numerical Mathematics 39,25-33, 1999 journal

The Nose-Poincare method for constant temperature molecular dynamics S. Bond, B. Leimkuhler and B. Laird, Journal of Computational Physics 151,114-134, 1999 journal

Timestep acceleration of waveform relaxation B. Leimkuhler, SIAM Journal on Numerical Analysis 35,31-50, 1998 journal

Symplectic methods for rigid body dynamics B. Leimkuhler, in Computational Molecular Dynamics - Challenges, Methods, Ideas, Springer Lecture Notes in Computational Science and Engineering 4,, 1998 journal

Time transformations for reversible variable stepsize integration S. Bond and B. Leimkuhler, Numerical Algorithms 19,55-71, 1998 journal

The Adaptive Verlet method W. Huang and B. Leimkuhler, SIAM Journal on Scientific Computing 18,239-256, 1997 journal

Geometric integrators for classical spin systems J. Frank, W. Huang and B. Leimkuhler, Journal of Computational Physics 133,160-172, 1997 journal

Split-Hamiltonian methods for rigid body molecular dynamics A. Dullweber, B. Leimkuhler and R. McLachlan, Journal of Chemical Physics 107,5840-5851, 1997 journal

A symplectic method for rigid-body molecular simulation A. Kol, B. Laird and B. Leimkuhler, Journal of Chemical Physics 107,2580–2588, 1997 journal

Integration Methods for Molecular Dynamics B. Leimkuhler, S. Reich and R.D. Skeel, in IMA Volumes in Mathematics and Its Applications, Springer-Verlag 82,, 1997 journal

A symplectic integrator for Riemannian manifolds B. Leimkuhler and G. Patrick, Journal of Nonlinear Science 6,367-384, 1996 journal

Orthosymplectic integration of linear Hamiltonian systems B. Leimkuhler and E. Van Vleck, Numerische Mathematik 77,269-282, 1996 journal

Symplectic Methods for Conservative Multibody Systems E. Barth and B. Leimkuhler, Communications of the Fields Institute 10,25-43, 1996 journal

Algorithms for constrained molecular dynamics E. Barth, K. Kuczera, B. Leimkuhler and R. Skeel, Journal of Computational Chemistry 16,1192-1209, 1995 journal

Symplectic integration of constrained Hamiltonian systems B. Leimkuhler and S. Reich, Mathematics of Computation 63,589-605, 1994 journal

Symplectic numerical integrators in constrained Hamiltonian systems B. Leimkuhler and R. Skeel, Journal of Computational Physics 112,117-125, 1994 journal

Estimating waveform relaxation convergence B. Leimkuhler, SIAM Journal on Scientific Computing 14,872-889, 1993 journal

Relaxation Techniques in Multibody Dynamics B. Leimkuhler, Transactions of the Canadian Society of Mechanical Engineering 17,459-471, 1993 journal

Rapid Convergence of Waveform Relaxation B. Leimkuhler and A. Ruehli, Applied Numerical Mathematics 11,211-224, 1993 journal

Dynamic Iteration Schemes for Differential-Algebraic Equations in Large Scale Circuit Simulation B. Leimkuhler, Proceedings of the Conference on Computational Ordinary Differential Equations(London, 1990), IMA 39,, 1992 journal

Waveform Relaxation for Linear RC-Circuits B. Leimkuhler, U. Miekkala and O.Nevanlinna, IMPACT of Computing in Science and Engineering 3,123-145, 1991 journal

Differentiation of Constraints in Differential-Algebraic Equations S.L. Campbell and B. Leimkuhler, Mechanics of Structures and Machines 19,19-39, 1991 journal

Numerical solution of differential-algebraic equations for constrained mechanical motion C. Fuehrer and B. Leimkuhler, Numerische Mathematik 59,55-69, 1991 journal

Formulation and Numerical Solution of the Equations of Constrained Mechanical Motion C. Fuehrer and B. Leimkuhler, Proceedings of NUMDIFF-5 (Halle, 1989), Teubner- Texte in Mathematics 121,, 1991 journal

Approximation Methods for the Consistent Initialization of Differential Algebraic Equations B. Leimkuhler, L.R.Petzold and C.W. Gear,, SIAM Journal on Numerical Analysis 28,205-226, 1991 journal

A New Class of Generalized Inverses for Discretized Euler-Lagrange Equations C. Fuehrer and B. Leimkuhler, in NATO Advanced Research Workshop on Real-Time Integration Methods for Mechanical System Simulation, Springer 69,143-154, 1990 journal

Automatic integration of Euler-Lagrange equations with constraints C.W. Gear, B. Leimkuhler, G.K. Gupta, Journal of Computational and Applied Mathematics 12-13,77-90, 1985 journal