Simulated tempering with irreversible Gibbs sampling techniques

Area of Science:

• Computational Physics
• Statistical Mechanics
• Chemical Physics

Background:

• Simulated tempering (ST) is a powerful Monte Carlo method for exploring complex energy landscapes.
• Conventional ST methods often rely on detailed balance condition (DBC), which can limit efficiency.
• Breaking DBC while preserving target distribution invariance is a key challenge.

Purpose of the Study:

• To introduce two novel irreversible algorithms for simulated tempering.
• To demonstrate improved sampling efficiency compared to conventional methods.
• To validate the algorithms on diverse systems including Ising models and molecular dynamics.

Main Methods:

• Developed irreversible algorithms based on Gibbs sampling, specifically targeting temperature swap updates.
• Broke the detailed balance condition (DBC) while ensuring skewed detailed balance for target distribution invariance.
• Tested algorithms on a 1D double-well potential, the Ising model, and alanine pentapeptide (ALA5) molecular dynamics simulations.

Main Results:

• Achieved significant gains in sampling efficiency for the Ising model, evidenced by faster relaxation times for inverse temperature, magnetic susceptibility, and energy density.
• Observed improved mixing times for inverse temperature and system energy in ALA5 simulations with numerous temperature replicas compared to standard Metropolis-Hastings (MH).
• Demonstrated favorable constant scaling in Ising spin systems for large numbers of temperature ladders, outperforming both reversible and irreversible MH algorithms.

Conclusions:

• The novel irreversible algorithms offer a more efficient alternative to conventional simulated tempering methods with DBC, without additional computational overhead.
• These algorithms show particular promise for large-scale simulations with extensive temperature ranges.
• Future applications include tailoring these irreversible methods to other dynamical variables for flattening rugged free energy landscapes.