Optimal prediction in molecular dynamics

TL;DR

This paper applies optimal prediction to molecular dynamics to reduce computational complexity by approximating high-dimensional systems with smaller models, validated through simulations.

Contribution

It demonstrates how asymptotic methods can be used within optimal prediction to effectively reduce the number of particles in molecular dynamics simulations.

Findings

Optimal prediction provides accurate approximations under certain conditions.

Asymptotic methods help approximate high-dimensional expectations.

Smaller systems replicate key statistical properties of original systems.

Abstract

Optimal prediction approximates the average solution of a large system of ordinary differential equations by a smaller system. We present how optimal prediction can be applied to a typical problem in the field of molecular dynamics, in order to reduce the number of particles to be tracked in the computations. We consider a model problem, which describes a surface coating process, and show how asymptotic methods can be employed to approximate the high dimensional conditional expectations, which arise in optimal prediction. The thus derived smaller system is compared to the original system in terms of statistical quantities, such as diffusion constants. The comparison is carried out by Monte-Carlo simulations, and it is shown under which conditions optimal prediction yields a valid approximation to the original system.