Targeted free energy estimation via learned mappings

• Published in: The Journal of chemical physics Vol. 153; no. 14; pp. 144112 - 144122
• Main Authors: Wirnsberger, Peter, Ballard, Andrew J., Papamakarios, George, Abercrombie, Stuart, Racanière, Sébastien, Pritzel, Alexander, Jimenez Rezende, Danilo, Blundell, Charles
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 14.10.2020
• Subjects: Free energy; Importance sampling; Machine learning; Mapping; Neural networks; Perturbation; Physics; Solvation
• ISSN: 0021-9606; 1089-7690; 1089-7690
• DOI: 10.1063/5.0018903

Free energy perturbation (FEP) was proposed by Zwanzig [J. Chem. Phys. 22, 1420 (1954)] more than six decades ago as a method to estimate free energy differences and has since inspired a huge body of related methods that use it as an integral building block. Being an importance sampling based estimator, however, FEP suffers from a severe limitation: the requirement of sufficient overlap between distributions. One strategy to mitigate this problem, called Targeted FEP, uses a high-dimensional mapping in configuration space to increase the overlap of the underlying distributions. Despite its potential, this method has attracted only limited attention due to the formidable challenge of formulating a tractable mapping. Here, we cast Targeted FEP as a machine learning problem in which the mapping is parameterized as a neural network that is optimized so as to increase the overlap. We develop a new model architecture that respects permutational and periodic symmetries often encountered in atomistic simulations and test our method on a fully periodic solvation system. We demonstrate that our method leads to a substantial variance reduction in free energy estimates when compared against baselines, without requiring any additional data.