Nonadiabatic force matching for alchemical free-energy estimation

TL;DR

Applying the method to evaluate the alchemical free energy of atomistic models shows that it can substantially reduce the simulation cost of a free-energy estimate at a negligible loss of accuracy when compared with thermodynamic integration.

Abstract

We propose a method to compute free-energy differences from nonadiabatic alchemical transformations using flow-based generative models. The method, nonadiabatic force matching, hinges on estimating the dissipation along an alchemical switching process in terms of a nonadiabatic force field that can be learned through stochastic flow matching. The learned field can be used in conjunction with short-time trajectory data to evaluate upper and lower bounds on the alchemical free energy that variationally converge to the exact value if the field is optimal. Applying the method to evaluate the alchemical free energy of atomistic models shows that it can substantially reduce the simulation cost of a free-energy estimate at negligible loss of accuracy when compared with thermodynamic integration.

Figures (4)

• Figure 1: A flow matching model for nonadiabatic alchemical free-energy estimation (a) Sample realizations of the forward process that drives a system from state $\mathsf{A}$, a bimodal distribution, toward state $\mathsf{B}$, a Gaussian distribution, according to a switch $\lambda(t)$ of duration $\tau$. (b) The switching potential $\beta U \mathopen{}\boldsymbol{(}\bm{x}, \lambda(t)\mathclose{}\boldsymbol{)}$ drives the system away from a bimodal distribution and toward a Gaussian distribution. (c) The backward process, using the learned nonadiabatic potential $V_{\!\bm{\theta}^\star}(\bm{x}, t)$, stochastically reverses the transition driven by the switching potential. (d) The nonadiabatic switching potential $\beta U \mathopen{}\boldsymbol{(}\bm{x}, \lambda(\tau\mspace{-1mu}\mathord{ \mspace{2mu} \hbox{[}1.0]{$-$} \mspace{3mu} }\mspace{-1mu}t) \mathclose{}\boldsymbol{)} + 2V_{\!\bm{\theta}^\star}(\bm{x}, \tau\mspace{-1mu}\mathord{ \mspace{2mu} \hbox{[}1.0]{$-$} \mspace{3mu} }\mspace{-1mu}t)$ restores the system to a bimodal distribution.
• Figure 2: Alchemical solvation in a WCA liquid. (a) Configuration snapshots along the alchemical path of a growing solute (red) within a WCA solvent (gray). (b) Estimates of the cumulative work done on the system to grow the solute at various rates $\tau^{-1}$, compared to adiabatic growth at the quasistatic limit (black).
• Figure 3: WCA solvation free energies from nonadiabatic force matching. (a) Snapshots from a realization of the backward process, where the solute growth is reversed by the nonadiabatic switching potential. (b) The cumulative free-energy differences estimated from the denoised solute growth (colored) closely match the quasistatic limit (black). (c) Accuracy of solvation free-energy estimates as a function of solute growth rate $\tau^{-1}$.
• Figure 4: Estimates of the free energy to form an LJ solid. (a) Configuration snapshots along the Frenkel--Ladd alchemical path, wherein a harmonic FCC lattice is driven toward an LJ solid. (b) The cumulative work per site at lattice relaxation rates $\tau^{-1}$ spanning two orders of magnitude. (c) Backward estimates of the formation free-energy difference per site are accurate across a range of relaxation rates $\tau^{-1}$. (d) The bias in the formation free-energy difference per site at alchemical switching rates $\tau^{-1}$.