Free energy computations by minimization of Kullback-Leibler divergence: an efficient adaptive biasing potential method for sparse representations

TL;DR

This paper introduces an adaptive biasing potential method for free energy calculations that leverages Kullback-Leibler divergence minimization, offering efficient, sparse, and parallelizable solutions suitable for complex molecular systems.

Contribution

It unifies biasing and free energy estimation using a statistical learning framework with convergence diagnostics and sparse representations, enhancing efficiency in multidimensional free energy computations.

Findings

Demonstrated in three numerical examples.

Provides rigorous convergence diagnostics.

Employs parallelizable sampling schemes.

Abstract

The present paper proposes an adaptive biasing potential for the computation of free energy landscapes. It is motivated by statistical learning arguments and unifies the tasks of biasing the molecular dynamics to escape free energy wells and estimating the free energy function, under the same objective. It offers rigorous convergence diagnostics even though history dependent, non-Markovian dynamics are employed. It makes use of a greedy optimization scheme in order to obtain sparse representations of the free energy function which can be particularly useful in multidimensional cases. It employs embarrassingly parallelizable sampling schemes that are based on adaptive Sequential Monte Carlo and can be readily coupled with legacy molecular dynamics simulators. The sequential nature of the learning and sampling scheme enables the efficient calculation of free energy functions parametrized by the temperature. The characteristics and capabilities of the proposed method are demonstrated in three numerical examples.