Exploration, Sampling, And Reconstruction of Free Energy Surfaces with Gaussian Process Regression

Practical free energy reconstruction algorithms involve three separate tasks: biasing, measuring some observable, and finally reconstructing the free energy surface from those measurements. In more than one dimension, adaptive schemes make it possible to explore only relatively low lying regions of the landscape by progressively building up the bias toward the negative of the free energy surface so that free energy barriers are eliminated. Most schemes use the final bias as their best estimate of the free energy surface. We show that large gains in computational efficiency, as measured by the reduction of time to solution, can be obtained by separating the bias used for dynamics from the final free energy reconstruction itself. We find that biasing with metadynamics, measuring a free energy gradient estimator, and reconstructing using Gaussian process regression can give an order of magnitude reduction in computational cost.