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Optimal updating magnitude in adaptive flat-distribution sampling.

Cheng Zhang¹, Justin A Drake¹, Jianpeng Ma²

¹Sealy Center for Structural Biology and Molecular Biophysics, The University of Texas Medical Branch, Galveston, Texas 77555-0304, USA.

The Journal of Chemical Physics

|November 10, 2017

Summary

Optimizing bias potential updates in free energy methods like Wang-Landau (WL) and metadynamics is key. This study reveals optimal schedules for faster convergence, particularly for bandpass updating schemes.

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Area of Science:

Computational Chemistry
Statistical Mechanics
Biophysics

Background:

Free energy methods, such as Wang-Landau (WL) and metadynamics, are crucial for simulating complex molecular systems.
These methods utilize adaptive bias potentials to overcome energy barriers and explore conformational landscapes.
Convergence of these simulations depends heavily on the schedule for updating the bias potential.

Purpose of the Study:

To optimize the updating magnitude schedule for free energy methods based on flat-distribution sampling.
To analyze the convergence properties of different updating schemes, including single-bin and Gaussian updates.
To introduce and evaluate generalized bandpass updating schemes.

Main Methods:

Analysis of bias potential convergence in free energy calculations.
Derivation of optimal updating schedules for single-bin and Gaussian schemes.
Development and application of bandpass updating schemes based on orthogonal polynomials.

Main Results:

The asymptotically optimal schedule for the single-bin updating scheme follows an inverse-time formula.
The Gaussian updating scheme often requires more complex optimal schedules.
Single-bin updating is optimal for long simulations and can be generalized to optimal bandpass schemes.

Conclusions:

Optimal updating schedules significantly improve the convergence of free energy calculations.
Bandpass updating schemes offer a generalized and efficient approach for parameter tuning in umbrella sampling.
The inverse-time formula provides an optimal schedule for single-bin and bandpass updating schemes.