Fokker-Planck Score Learning: Efficient Free-Energy Estimation under Periodic Boundary Conditions.

Area of Science:

• Computational Chemistry
• Molecular Dynamics
• Statistical Mechanics

Background:

• Accurate free-energy estimation is crucial for molecular simulations.
• Traditional methods like umbrella sampling and Jarzynski's equality have limitations, including extensive sampling requirements and poor convergence.
• Periodic boundary conditions (PBC) are common in simulations but underexploited for free-energy calculations.

Purpose of the Study:

• To develop a more efficient method for free-energy estimation in molecular simulations that explicitly leverages periodic boundary conditions (PBC).
• To introduce a physics-informed, score-based diffusion framework for reconstructing the potential of mean force.

Main Methods:

• Mapping PBC simulations to a Brownian particle in a periodic potential.
• Deriving the Fokker-Planck steady-state score encoding free-energy gradients.
• Training a neural network on nonequilibrium trajectories to learn the score for efficient potential of mean force reconstruction.

Main Results:

• The developed diffusion framework directly encodes free-energy gradients from PBC simulations.
• A neural network successfully learned the score from nonequilibrium trajectories.
• The method demonstrated up to 1 order of magnitude greater efficiency compared to umbrella sampling on benchmark potentials and small-molecule membrane permeation.

Conclusions:

• The physics-informed, score-based diffusion framework offers a principled and efficient approach to free-energy estimation in simulations with PBC.
• This method overcomes limitations of existing techniques, providing a significant advancement in computational molecular science.
• The framework shows promise for accelerating molecular simulations and enabling more complex studies.