On-the-Fly Lifting of Coarse Reaction-Coordinate Paths to Full-Dimensional Transition Path Ensembles

TL;DR

This paper introduces a local, on-the-fly method to lift low-dimensional coarse reaction paths to full-dimensional transition ensembles using guided trajectories and importance sampling, enabling efficient and accurate simulation of rare events.

Contribution

It presents a novel, real-time lifting strategy combining coarse modeling, guided full-system trajectories, and Girsanov reweighting to generate realistic transition pathways without extensive global sampling.

Findings

Successfully converts coarse paths into full-dimensional trajectories.

Accelerates transition pathway estimation with minimal bias.

Demonstrates effectiveness on numerical experiments involving barrier crossings.

Abstract

Effective dynamics on a low-dimensional collective-variable (CV) or latent space can be simulated far more cheaply than the underlying high-dimensional stochastic system, but exploiting such coarse predictions requires lifting: turning a coarse CV trajectory into dynamically consistent full-dimensional states and path ensembles, without relying on global sampling of invariant or conditional fiber measures. We present a local, on-the-fly lifting strategy based on guided full-system trajectories. First an effective model in CV space is used to obtain a coarse reference trajectory. Then, an ensemble of full-dimensional trajectories is generated from a guided version of the original dynamics, where the guidance steers the trajectory to track the CV reference path. Because guidance biases the path distribution, we correct it via pathwise Girsanov reweighting, yielding a correct-by-construction importance-sampling approximation of the conditional law of the uncontrolled dynamics. We further connect the approach to stochastic optimal control, clarifying how coarse models can inform variance-reducing guidance for rare-event quantities. Numerical experiments demonstrate that inexpensive coarse transition paths can be converted into realistic full-system transition pathways (including barrier crossings and detours) and can accelerate estimation of transition pathways and statistics while providing minimal bias through weighted ensembles.