Repository: Freie Universität Berlin, Math Department

The augmented jump chain – a sparse representationof time-dependent Markov jump processes

Sikorski, Alexander and Weber, Marcus and Schütte, Christof (2021) The augmented jump chain – a sparse representationof time-dependent Markov jump processes. Advanced Theory and Simulations, 4(4):2000274, 2021, 4 (4).

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Abstract 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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:2718
Deposited By: Monika Drueck
Deposited On:11 Feb 2022 14:35
Last Modified:18 Mar 2022 14:30

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