Overcoming the timescale barrier in molecular dynamics: Transfer operators, variational principles and machine learning

Christof Schütte, Stefan Klus, Carsten Hartmann

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
27 Downloads (Pure)

Abstract

One of the main challenges in molecular dynamics is overcoming the 'timescale barrier': in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, even on the largest or specifically dedicated supercomputers. This article discusses how to circumvent the timescale barrier by a collection of transfer operator-based techniques that have emerged from dynamical systems theory, numerical mathematics and machine learning over the last two decades. We will focus on how transfer operators can be used to approximate the dynamical behaviour on long timescales, review the introduction of this approach into molecular dynamics, and outline the respective theory, as well as the algorithmic development, from the early numerics-based methods, via variational reformulations, to modern data-based techniques utilizing and improving concepts from machine learning. Furthermore, its relation to rare event simulation techniques will be explained, revealing a broad equivalence of variational principles for long-time quantities in molecular dynamics. The article will mainly take a mathematical perspective and will leave the application to real-world molecular systems to the more than 1000 research articles already written on this subject.

Original languageEnglish
Pages (from-to)517-673
Number of pages157
JournalActa Numerica
Volume32
Early online date11 May 2023
DOIs
Publication statusPublished - May 2023

ASJC Scopus subject areas

  • Numerical Analysis
  • Mathematics(all)

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