Optimizing Free Energy Estimation with Machine Learning

Free energy perturbation [1] is a bedrock technique for estimation of free energy differences. Fast, reliable convergence of the free energy difference, however, demands that the respective distributions share a large overlap in configuration space. One strategy to address this requirement is Targeted Free Energy Perturbation (TFEP) [2], whereby a bijective mapping on configuration space is used to increase an effective overlap. Despite its appeal, TFEP has seen little use in practice since it relies on handcrafting effective mappings. Here we turn TFEP into a machine learning problem whereby the mapping is represented by a deep neural network whose parameters are optimized so as to maximize overlap. We test the approach on a prototypical solvation system, employing a novel normalizing flow architecture that respects periodic boundary conditions and permutational symmetry of identical particles. Our technique leads to significant error reduction in free energy estimates compared to baselines, without requiring additional data.

[1] R. W. Zwanzig, J. Chem. Phys. 22, 1420 (1954)
[2] C. Jarzynski, Phys. Rev. E 65, 046122 (2002)

*PW and AJB contributed equally to this work.

This research has been first published in J. Chem. Phys. 153, 144112 (2020), with the permission of AIP Publishing.