Data-driven methods for accelerating the simulation of rare transitions in molecular dynamics

Abstract

Molecular dynamics (MD) simulations provide a powerful framework for investigating molecular systems at atomic resolution.In MD simulations, we face two major challenges: high dimensionality and the limited time scales accessible to simulation. Many systems of interest in MD are characterized by a large number of degrees of freedom, and phenomena of interest—such as conformational changes—are typically described by transitions between metastable states separated by high-energy barriers. Observing these slow conformational changes, which are considered rare events, requires substantially extended timeframes that exceed those feasible in direct simulations. The goal of this dissertation is to accelerate the simulation of rare events in molecular systems using data-driven methods. The dissertation consists of three contributions that address different aspects of this challenge: sampling rare transition trajectories and estimating transition rates, developing algorithms for learning collective variables, and accelerating SDE simulations using foundation models. The first work develops a methodology for sampling transition trajectories between metastable states using optimal stochastic control and for estimating transition rates. We show that, for a broad class of Itō diffusion processes, the optimal control can be constructed from the committor function and generates transition trajectories exclusively. This result provides a theoretical foundation for efficient sampling of reactive trajectories. Using approximate committors, we estimate transition rates with high accuracy from the sampled transition trajectories, even when the committor itself is only approximated. The second work addresses the learning of collective variables (CVs) for systems with permutational symmetry. CVs provide low-dimensional representations that capture the slow dynamics of a system and are essential for enhanced sampling and rate estimation. This work focuses on systems lacking obvious physically motivated reaction coordinates, such as interacting particle systems with permutational symmetry. We propose an algorithmic framework for learning CVs that respect translational, rotational, and permutational symmetries. The approach combines sort-based featurization, residence-manifold learning in feature space, and autoencoder-based dimensionality reduction. Using the learned CVs, we estimate transition rates for the Lennard-Jones-7 system in two dimensions and the Lennard-Jones-8 system in three dimensions. The third work explores fast simulation of general SDEs. Classical numerical integrators face an inherent trade-off between accuracy and computational cost, particularly for long-time or large-scale simulations. Building on ideas from foundation models, we develop a pretrained simulation model that leverages coarse numerical trajectories and performs error correction to recover fine-scale behavior. This approach aims to bridge the gap between efficiency and accuracy, enabling fast and reliable simulations of SDEs across a wide range of systems.