Score dynamics: scaling molecular dynamics with picoseconds timestep via conditional diffusion model

TL;DR

Score dynamics (SD) introduces a score-based, conditional diffusion framework to scale molecular dynamics in time by learning transitions across large timesteps from MD data. It models a high‑level stochastic evolution as a conditional diffusion process whose score function drives sampling of next configurations in a graph‑based representation. The approach reproduces equilibrium distributions and kinetics for alanine dipeptide and short alkanes and generalizes to unseen butane, achieving speedups of up to about $10^2$ on standard hardware. The authors discuss open challenges, including training cost, velocity effects, and extension to larger molecules, and propose directions for future improvements and integration with other sampling strategies.

Abstract

We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular-dynamics simulations. SD is centered around scores, or derivatives of the transition log-probability with respect to the dynamical degrees of freedom. The latter play the same role as force fields in MD but are used in denoising diffusion probability models to generate discrete transitions of the dynamical variables in an SD timestep, which can be orders of magnitude larger than a typical MD timestep. In this work, we construct graph neural network based score dynamics models of realistic molecular systems that are evolved with 10~ps timesteps. We demonstrate the efficacy of score dynamics with case studies of alanine dipeptide and short alkanes in aqueous solution. Both equilibrium predictions derived from the stationary distributions of the conditional probability and kinetic predictions for the transition rates and transition paths are in good agreement with MD. Our current SD implementation is about two orders of magnitude faster than the MD counterpart for the systems studied in this work. Open challenges and possible future remedies to improve score dynamics are also discussed.

Figures (12)

• Figure 1: (a) Schematic illustration of distribution of diverging simulation outcomes after finite time interval. (b) Workflow of score dynamics, which maps both the current conditioning structure and a randomly displaced candidate structure into a new one by probabilistic denoising.
• Figure 1: Ethane SD result compared to MD training data. Note that the dihedral angle distribution (and its corresponding first passage time) refers to only one of the H-C-C-H quadruplets.
• Figure 2: The alanine dipeptide SD trajectory is realistic relative to literature reference and in-house MD data. (a) The alanine dipeptide structure and the dihedral angles $(\phi, \psi)$ used for describing the instantaneous configurations. (b) Free energy profile reference, reprinted (adapted) with permission from vymetal2010metadynamics (copyright 2010 American Chemical Society). (c, d) SD trajectory (over 100ns with 1ps timesteps) visualized in Ramachandran plots, in both scatter and KDE (kernel density estimation) energy contour format. Two energy minima are annotated as $\alpha$ and $\beta$. (e, f) In-house MD trajectory reference based on the OPLS-aa potential visualized in Ramachandran plots. (g, h) First passage time ($\alpha \rightarrow \beta$ and $\beta \rightarrow \alpha$) distribution from the SD trajectory compared to the in-house MD reference. The energy levels in (b, d, f) are in the unit of kJ/mol.
• Figure 2: Propane SD result compared to MD training data.
• Figure 3: Ramachandran plots of conditional distributions $P(\mathbf{X}_t | \mathbf{X}_0)$ from SD trajectories and in-house MD data. In each plot, 1,000 scatter points (from 1,000 independent runs) and their KDE contours are plotted.