Arbitrarily accurate representation of atomistic dynamics via Markov Renewal Processes

TL;DR

This paper introduces a discretization scheme for atomistic simulation trajectories that achieves arbitrarily accurate modeling using Markov Renewal Processes, with exponential convergence based on a local correlation time.

Contribution

It presents a novel discretization method enabling highly accurate Markov Renewal Process representations of atomistic dynamics.

Findings

Model accuracy converges exponentially with the local correlation time.

The scheme provides a flexible, low-dimensional representation of complex trajectories.

Enables better analysis and interpretation of nanoscale dynamical behavior.

Abstract

Atomistic simulations with methods such as molecular dynamics are extremely powerful tools to understand nanoscale dynamical behavior. The resulting trajectories, by the virtue of being embedded in a high-dimensional configuration space, can however be difficult to analyze and interpret. This makes low-dimensional representations, especially in terms of discrete jump processes, extremely valuable. This simplicity however usually comes at the cost of accuracy, as tractable representations often entail simplifying assumptions that are not guaranteed to be realized in practice. In this paper, we describe a discretization scheme for continuous trajectories that enables an arbitrarily accurate representation in terms of a Markov Renewal Process over a discrete state space. The accuracy of the model converges exponentially fast as a function of a continuous parameter that has the interpretation of a local correlation time of the dynamics.