Ceci n'est pas un committor, yet it samples like one: efficient sampling via approximated committor functions

TL;DR

This work proposes a simplified learning criterion formulated entirely in the descriptor space, which bypasses the need for explicit and costly coordinate gradients and provides a relaxed upper bound to the original variational principle.

Abstract

Atomistic simulations are widely used to investigate reactive processes but are often limited by the rare event problem due to kinetic bottlenecks. We recently introduced an enhanced sampling approach based on the committor function, machine-learned following a variational principle. This method combines a transition-state-oriented bias potential, expressed as a functional of the committor, with a metadynamics-like bias along a committor-based collective variable, enabling uniform exploration of reaction pathways. In its original formulation, the committor is represented by a neural network that takes physical descriptors as input and is trained by minimizing a functional involving gradients with respect to atomic coordinates, which can be computationally demanding in some cases. Here, we propose a simplified learning criterion formulated entirely in the descriptor space, which bypasses the need for explicit and costly coordinate gradients and provides a relaxed upper bound to the original variational principle. Although this approach does not formally target the exact committor, we show that it retains robust sampling performance while significantly reducing computational costs, thus enabling the study of processes that would be practically unfeasible using the original formulation.

Figures (11)

• Figure 1: Alanine dipeptide isomerization.A. Representative snapshots of the isomerization process. B. Sampling density distribution projected along the $\varphi$ torsional angle. C. Free energy surface (FES) plotted along the $\varphi$ torsional angle. In panels B and C, results obtained with a standard OPES run using $\varphi$ and $\psi$ torsional angles as CVs are reported in grey, those obtained with OPES+V$_K$ based on a committor model trained following the original variational approach (q$_{\boldsymbol{\theta}}$) are reported in purple, and those obtained with OPES+V$_K$ based on a committor model trained following the simplified variational approach ($\tilde{\text{q}}_{\boldsymbol{\theta}}$) are reported in pink.
• Figure 2: Proton transfer in tropolone.A. Representative snapshots of the reaction stages, with the transition state characterized by the shared proton between the two oxygens. B. Free energy surface (FES) plotted along the learned $z$ CV. C. Convergence with simulation time of the estimated free energy difference between the two main isomers. The dashed line shows the reference value, with the $\pm 0.5 \,$k$_B$T interval marked by the thin dotted lines. In panels B and C, average values obtained from 3 independent simulations are depicted as solid lines, whereas the corresponding standard deviations are shown as shaded areas.
• Figure 3: G2-OAMe binding.A. Representative snapshots of the binding stages, with the host molecule colored in pink and the guest in orange. Water molecules are represented as blue spheres in solid color when inside the pocket, and transparent otherwise. B. Free energy surface (FES) plotted along the learned $z$ CV. C. Convergence with simulation time of the estimated binding energy. The dashed line shows the reference value obtained with the same setup as Ref. rizzi2021role, with the $\pm 0.5 \,$k$_B$T interval marked by the thin dotted lines. In panels B and C, average values obtained from 3 independent simulations are depicted as solid lines, whereas the corresponding standard deviations are shown as shaded areas.
• Figure 4: Silicon crystallization.A. Representative top-view snapshots of the crystallization process from the disordered liquid phase to the ordered solid. Atoms are colored according to the degree of similarity of their local arrangement to the ideal diamond structure. The darker the color, the higher the similarity. B. Free energy surface (FES) plotted along the learned $z$ CV. C. Convergence with simulation time of the estimated free energy difference between the two states. The dashed line shows the reference value, with the $\pm\,$k$_B$T interval marked by the thin dotted lines. In panels B and C, average values obtained from 3 independent simulations are depicted as solid lines, whereas the corresponding standard deviations are shown as shaded areas.
• Figure S1: Iterative sampling on alanine. Top row: Scatter plot of the sampled points in the $\varphi\psi$ space at successive iterations. Points from trajectories initialized in state A are shown in purple, while those initialized in state B are shown in pink. Second row: Time series of the $\varphi$ dihedral angle for trajectories started from state A. Third row: Time series of the $\varphi$ dihedral angle for trajectories started from state B. Bottom row: Free energy surface (FES) plotted along $\varphi$, estimated from the sampled configurations at each iteration.