Higher-order hybrid Monte Carlo algorithms.

By M. Creutz, A. Gocksch. 1989

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Generalizing Hamiltonian Monte Carlo with Neural Networks (2017, methodology): “…dynamics (Tripuraneni et al., 2016); with variants of AIS adapted to HMC proposals (Sohl-Dickstein & Culpepper, 2012); with the extension of HMC to discrete state spaces (Zhang et al., 2012); and with the use of alternative Hamiltonian integrators (Creutz & Gocksch, 1989; Chao et al., 2015).”
Handbook of Markov Chain Monte Carlo (2011, neutral): “…of the real Hamiltonian (Izagguirre and Hampton, 2004), and the use of symplectic integration methods more sophisticated than the leapfrog method (eg, Creutz and Gocksch, 1989), including a recent proposal by Girolami et al. (2009) of a symplectic integrator for a non-separable Hamiltonian in…”
Shadow hybrid Monte Carlo: an efficient propagator in phase space of macromolecules (2004, result): “This was attempted for latticegauge simulations in [7], but with disappointing results.”
MCMC Using Hamiltonian Dynamics (2011, methodology): “t is exactly conserved by the inexact simulation of the real Hamiltonian (Izagguirre and Hampton, 2004), and the use of symplectic integration methods more sophisticated than the leapfrog method (eg, Creutz and Gocksch, 1989), including a recent proposal by Girolami et al. (2009) of a symplectic int”