Computer simulation of liquids
Computer simulation of liquids
An improved acceptance procedure for the hybrid Monte Carlo algorithm
Journal of Computational Physics
A rapidly convergent simulation method: mixed Monte Carlo/stochastic dynamics
Journal of Computational Chemistry
Long-Time-Step Methods for Oscillatory Differential Equations
SIAM Journal on Scientific Computing
The Nosé-Poincaré method for constant temperature molecular dynamics
Journal of Computational Physics - Special issue on computational molecular biophysics
A direct approach to conformational dynamics based on hybrid Monte Carlo
Journal of Computational Physics - Special issue on computational molecular biophysics
Backward Error Analysis for Numerical Integrators
SIAM Journal on Numerical Analysis
Bayesian Learning for Neural Networks
Bayesian Learning for Neural Networks
Understanding Molecular Simulation
Understanding Molecular Simulation
Digital Principles and Applications
Digital Principles and Applications
Practical Construction of Modified Hamiltonians
SIAM Journal on Scientific Computing
Molecular Modeling and Simulation: An Interdisciplinary Guide
Molecular Modeling and Simulation: An Interdisciplinary Guide
ProtoMol, an object-oriented framework for prototyping novel algorithms for molecular dynamics
ACM Transactions on Mathematical Software (TOMS)
ProtoMol, an object-oriented framework for prototyping novel algorithms for molecular dynamics
ACM Transactions on Mathematical Software (TOMS)
GIPSE: Streamlining the Management of Simulation on the Grid
ANSS '05 Proceedings of the 38th annual Symposium on Simulation
A comparison of generalized hybrid Monte Carlo methods with and without momentum flip
Journal of Computational Physics
Coupling control variates for Markov chain Monte Carlo
Journal of Computational Physics
On the estimation and correction of discretization error in molecular dynamics averages
Applied Numerical Mathematics
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Shadow hybrid Monte Carlo (SHMC) is a new method for sampling the phase space of large molecules, particularly biological molecules. It improves sampling of hybrid Monte Carlo (HMC) by allowing larger time steps and system sizes in the molecular dynamics (MD) step. The acceptance rate of HMC decreases exponentially with increasing system size N or time step δt. This is due to discretization errors introduced by the numerical integrator. SHMC achieves an asymptotic O(N1/4) speedup over HMC by sampling from all of phase space using high order approximations to a shadow or modified Hamiltonian exactly integrated by a symplectic MD integrator. SHMC satisfies microscopic reversibility and is a rigorous sampling method. SHMC requires extra storage, modest computational overhead, and a reweighting step to obtain averages from the canonical ensemble. This is validated by numerical experiments that compute observables for different molecules, ranging from a small n-alkane butane with four united atoms to a larger solvated protein with 14,281 atoms. In these experiments, SHMC achieves an order magnitude speedup in sampling efficiency for medium sized proteins. Sampling efficiency is measured by monitoring the rate at which different conformations of the molecules' dihedral angles are visited, and by computing ergodic measures of some observables.