Self-tuning Hamiltonian Monte Carlo for accelerated sampling.

Area of Science:

• Computational Physics
• Statistical Mechanics
• Molecular Dynamics

Background:

• Hamiltonian Monte Carlo (HMC) simulations are powerful for exploring complex systems but sensitive to parameter choices.
• Optimizing integration timestep and steps is crucial for efficient phase space exploration.
• Current methods often involve time-consuming parameter searches.

Purpose of the Study:

• To develop an adaptive, general-purpose framework for automatic parameter tuning in HMC simulations.
• To establish a link between a local loss function and autocorrelation time for efficient optimization.
• To enable gradient-driven learning for simulation parameter optimization.

Main Methods:

• Introduced a novel adaptive framework with a local loss function to promote rapid phase space exploration.
• Developed a fully differentiable setup enabling gradient-based optimization of HMC parameters.
• Designed the loss function to facilitate gradient-driven learning of the distribution for integration steps.
• Applied and validated the approach on the one-dimensional harmonic oscillator and alanine dipeptide systems.

Main Results:

• Demonstrated a strong correlation between the proposed loss function and autocorrelation time.
• Achieved over a 100-fold speedup in parameter optimization for alanine dipeptide compared to grid search.
• Highlighted the importance of adaptive timesteps, showing a further 25% reduction in autocorrelation times for alanine dipeptide.
• Identified that fixed timesteps can lead to rugged loss surfaces and optimization trapping.

Conclusions:

• The adaptive framework effectively optimizes HMC simulation parameters, significantly enhancing efficiency.
• The differentiable loss function provides a robust and scalable method for tuning simulation settings.
• Atom-dependent timesteps offer further improvements in simulation performance for complex molecular systems.