Hybrid Monte Carlo with non-uniform step size

Area of Science:

• Computational Physics
• Molecular Dynamics
• Statistical Mechanics

Background:

• The Hybrid Monte Carlo (HMC) method combines numerical integration of equations of motion with a Metropolis accept-or-reject step.
• This method is used for simulating dense systems, correcting for discretization errors in molecular dynamics simulations.
• Typically, HMC simulations use a uniform step size throughout the integration trajectory.

Purpose of the Study:

• To investigate the impact of non-uniform step sizes in HMC simulations.
• To determine if smaller time steps in trajectory tails can improve simulation accuracy and efficiency.
• To assess the general applicability of this optimization across different model systems.

Main Methods:

• Simulations were performed using the Lennard-Jones system, a harmonic oscillator, and a coarse-grained peptide model.
• The Hybrid Monte Carlo method was employed, with variations in time step size during trajectory integration.
• Comparisons were made between simulations using uniform step sizes and those with smaller steps in the trajectory tails.

Main Results:

• Utilizing smaller time steps in the tails of integration trajectories significantly reduces energy errors in Lennard-Jones system simulations.
• Acceptance rates increased by 10-15 percentage points compared to simulations with uniform step sizes.
• Similar improvements in accuracy and acceptance rates were observed for the harmonic oscillator and peptide models, demonstrating the approach's generality.

Conclusions:

• Varying time step sizes within HMC trajectories, specifically reducing them in the tails, is an effective strategy for enhancing simulation accuracy.
• This optimization leads to improved acceptance rates, making simulations more efficient.
• The findings suggest a broadly applicable method for improving HMC simulations across various physical and chemical systems.