Repository: Freie Universität Berlin, Math Department

Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning

Schütte, Christof and Klus, Stefan and Hartmann, Carsten (2022) Overcoming the Timescale Barrier in Molecular Dynamics: Transfer Operators, Variational Principles, and Machine Learning. ZIB . (Submitted)

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Official URL: https://opus4.kobv.de/opus4-zib/frontdoor/index/in...

Abstract

One of the main challenges in molecular dynamics is overcoming the “timescale barrier”, a phrase used to describe that in many realistic molecular systems, biologically important rare transitions occur on timescales that are not accessible to direct numerical simulation, not 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 behavior 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 MD. 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

Item Type:Article
Additional Information:Accepted for Acta Numerica (2023)
Subjects:Mathematical and Computer Sciences
Mathematical and Computer Sciences > Mathematics
Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2960
Deposited By: Monika Drueck
Deposited On:20 Apr 2023 10:37
Last Modified:02 May 2023 08:42

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