The Augmented Jump Chain
- Modern methods of simulating molecular systems are based on the mathematical theory of Markov operators with a focus on autonomous equilibrated systems. However, non-autonomous physical systems or non-autonomous simulation processes are becoming more and more important. A representation of non-autonomous Markov jump processes is presented as autonomous Markov chains on space-time. Augmenting the spatial information of the embedded Markov chain by the temporal information of the associated jump times, the so-called augmented jump chain is derived. The augmented jump chain inherits the sparseness of the infinitesimal generator of the original process and therefore provides a useful tool for studying time-dependent dynamics even in high dimensions. Furthermore, possible generalizations and applications to the computation of committor functions and coherent sets in the non-autonomous setting are discussed. After deriving the theoretical foundations, the concepts with a proof-of-concept Galerkin discretization of the transfer operator of the augmented jump chain applied to simple examples are illustrated.
Author: | Alexander SikorskiORCiD, Marcus Weber, Christof Schütte |
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Document Type: | Article |
Parent Title (English): | Advanced Theory and Simulations |
Volume: | 4 |
Issue: | 4 |
Publisher: | Wiley-VCH |
Year of first publication: | 2021 |
ArXiv Id: | http://arxiv.org/abs/2008.04624 |
DOI: | https://doi.org/10.1002/adts.202000274 |