Arbitrarily accurate, nonparametric coarse graining with Markov renewal processes and the Mori–Zwanzig formulation

Aristoff, David; Johnson, Mats; Perez, Danny

doi:10.1063/5.0162440

Arbitrarily accurate, nonparametric coarse graining with Markov renewal processes and the Mori–Zwanzig formulation

Journal Article · Fri Sep 29 00:00:00 EDT 2023 · AIP Advances

DOI:https://doi.org/10.1063/5.0162440· OSTI ID:2439465

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Colorado State Univ., Fort Collins, CO (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Stochastic dynamics, such as molecular dynamics, are important in many scientific applications. However, summarizing and analyzing the results of such simulations is often challenging due to the high dimension in which simulations are carried out and, consequently, due to the very large amount of data that are typically generated. Coarse graining is a popular technique for addressing this problem by providing compact and expressive representations. Coarse graining, however, potentially comes at the cost of accuracy, as dynamical information is, in general, lost when projecting the problem in a lower-dimensional space. This article shows how to eliminate coarse-graining error using two key ideas. First, we represent coarse-grained dynamics as a Markov renewal process. Second, we outline a data-driven, non-parametric Mori–Zwanzig approach for computing jump times of the renewal process. Numerical tests on a small protein illustrate the method.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2439465

Report Number(s):: LA-UR--23-25692

Journal Information:: AIP Advances, Journal Name: AIP Advances Journal Issue: 9 Vol. 13; ISSN 2158-3226

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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