Nonequilibrium force matching for alchemical free energy estimation

As alchemical free energy calculations come to occupy central roles throughout chemistry, physics and biology, it is timely to address cost-efficiency challenges in high-throughput applications such as computational drug discovery. Jarzynski's nonequilibrium work theorem, a foundational result in stochastic thermodynamics, relates free energy differences to the cumulative statistics of a trajectory-wise notion of dissipated work and suggests ways to accelerate alchemical free energy calculations by reweighing trajectory data from nonadiabatic alchemical transformations. However, free-energy estimation methods based on the nonequilibrium work theorem have long faced convergence challenges due to the rarity of the low-dissipation pathways that contribute most toward the relevant averages. Here, we leverage formal connections between time-reversed driven trajectory ensembles and statistically optimal nonequilibrium work averaging to characterize switching protocols that render rare, time-reversed trajectories typical through stochastically controlled Langevin dynamics. We arrive at a simple method to substantially enhance the accuracy of cumulant-based approximations to the nonequilibrium work theorem, by training a force (or "score") that matches the forward time-evolution of the nonadiabatically switched system and using that force to guide its time-reversed evolution back to equilibrium. Applying the method to estimate the absolute free energy of molecular solids and the solvation free energy of an isomerizing molecule shows accurate results compared to ground-truth values from thermodynamic integration, along with a marked computational walltime reduction where our approach is deployed using fast alchemical transitions.