Iterative trajectory reweighting for estimation of equilibrium and non-equilibrium observables

TL;DR

This paper introduces two iterative reweighting algorithms for short unbiased trajectories to estimate steady state distributions and committors in both equilibrium and non-equilibrium systems, without Markov assumptions.

Contribution

The paper presents novel algorithms that reweight trajectories to estimate observables without relying on transition matrices or Markov models.

Findings

Algorithms accurately estimate steady state distributions.

Methods work for both equilibrium and non-equilibrium systems.

Validated on double-well potential and atomistic folding trajectory.

Abstract

We present two algorithms by which a set of short, unbiased trajectories can be iteratively reweighted to obtain various observables. The first algorithm estimates the stationary (steady state) distribution of a system by iteratively reweighting the trajectories based on the average probability in each state. The algorithm applies to equilibrium or non-equilibrium steady states, exploiting the `left' stationarity of the distribution under dynamics -- i.e., in a discrete setting, when the column vector of probabilities is multiplied by the transition matrix expressed as a left stochastic matrix. The second procedure relies on the `right' stationarity of the committor (splitting probability) expressed as a row vector. The algorithms are unbiased, do not rely on computing transition matrices, and make no Markov assumption about discretized states. Here, we apply the procedures to a one-dimensional double-well potential, and to a 208$\mu$s atomistic Trp-cage folding trajectory from D.E. Shaw Research.