TY - JOUR A1 - Sarich, Marco A1 - Schütte, Christof A1 - Vanden-Eijnden, E. T1 - Optimal Fuzzy Aggregation of Networks JF - Multiscale Modeling and Simulation Y1 - 2010 U6 - https://doi.org/10.1137/090758519 VL - 8 IS - 4 SP - 1535 EP - 1561 ER - TY - JOUR A1 - Sarich, Marco A1 - Schütte, Christof T1 - Approximating Selected Non-dominant Timescales by Markov State Models JF - Comm. Math. Sci. Y1 - 2012 U6 - https://doi.org/10.4310/CMS.2012.v10.n3.a14 VL - 10 IS - 3 SP - 1001 EP - 1013 ER - TY - GEN A1 - Sarich, Marco A1 - Schütte, Christof T1 - Utilizing hitting times for finding metastable sets in non-reversible Markov chains N2 - Techniques for finding metastable or almost invariant sets have been investigated, e.g., for deterministic dynamical systems in set-oriented numerics, for stochastic processes in molecular dynamics, and for random walks on complex networks. Most prominent algorithms are based on spectral apporaches and identify metastable sets via the doimant eigenvalues of the transfer operator associated with the dynamical system under consideration. These algorithms require the dominant eigenvalues to be real-valued. However, for many types of dynamics, e.g. for non-reversible Markov chains, this condition is not met. In this paper we utilize the hitting time apporach to metastable sets and demonstrate how the wellknown statements about optimal metastable decompositions of reversible chains can be reformulated for non-reversible chains if one switches from a spectral approach to an exit time approach. The performance of the resulting algorithm is illustrated by numerical experiments on random walks on complex networks. T3 - ZIB-Report - 14-32 KW - metastability KW - hitting times KW - non-reversible Markov chain KW - directed networks KW - random walk Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-51209 SN - 1438-0064 ER - TY - GEN A1 - Schütte, Christof A1 - Sarich, Marco T1 - A Critical Appraisal of Markov State Models N2 - Markov State Modelling as a concept for a coarse grained description of the essential kinetics of a molecular system in equilibrium has gained a lot of atten- tion recently. The last 10 years have seen an ever increasing publication activity on how to construct Markov State Models (MSMs) for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecu- lar sensors to molecular aggregation. Simultaneously the accompanying theory behind MSM building and approximation quality has been developed well be- yond the concepts and ideas used in practical applications. This article reviews the main theoretical results, provides links to crucial new developments, outlines the full power of MSM building today, and discusses the essential limitations still to overcome. T3 - ZIB-Report - 15-18 Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-54218 SN - 1438-0064 ER - TY - BOOK A1 - Schütte, Christof A1 - Sarich, Marco T1 - Metastability and Markov State Models in Molecular Dynamics: Modeling, Analysis, Algorithmic Approaches Y1 - 2013 N1 - Courant Lecture Notes No. 32, American Mathematical Society PB - American Mathematical Society ER - TY - JOUR A1 - Rüdrich, S. A1 - Sarich, Marco A1 - Schütte, Christof T1 - Utilizing hitting times for finding metastable sets in non-reversible Markov chains JF - Journal of Comp. Dynamics Y1 - 2017 ER - TY - JOUR A1 - Schütte, Christof A1 - Sarich, Marco T1 - A Critical Appraisal of Markov State Models JF - The European Physical Journal Special Topics N2 - Markov State Modelling as a concept for a coarse grained description of the essential kinetics of a molecular system in equilibrium has gained a lot of atten- tion recently. The last 10 years have seen an ever increasing publication activity on how to construct Markov State Models (MSMs) for very different molecular systems ranging from peptides to proteins, from RNA to DNA, and via molecu- lar sensors to molecular aggregation. Simultaneously the accompanying theory behind MSM building and approximation quality has been developed well be- yond the concepts and ideas used in practical applications. This article reviews the main theoretical results, provides links to crucial new developments, outlines the full power of MSM building today, and discusses the essential limitations still to overcome. Y1 - 2015 U6 - https://doi.org/10.1140/epjst/e2015-02421-0 VL - 224 IS - 12 SP - 2445 EP - 2462 ER - TY - GEN A1 - Sarich, Marco A1 - Schütte, Christof ED - Bowman, Gregory R. ED - Pande, Vijay S. ED - Noé, Frank T1 - Markov Model Theory T2 - An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation N2 - This section reviews the relation between the continuous dynamics of a molecular system in thermal equilibrium and the kinetics given by a Markov State Model (MSM). We will introduce the dynamical propagator, an error-less, alternative description of the continuous dynamics, and show how MSMs result from its discretization. This allows for an precise understanding of the approximation quality of MSMs in comparison to the continuous dynamics. The results on the approximation quality are key for the design of good MSMs. While this section is important for understanding the theory of discretization and related systematic errors, practitioners wishing only to learn how to construct MSMs may skip directly to the discussion of Markov model estimation. Y1 - 2014 U6 - https://doi.org/10.1007/978-94-007-7606-7 VL - 797 SP - 23 EP - 44 PB - Springer ER - TY - JOUR A1 - Djurdjevac Conrad, Natasa A1 - Sarich, Marco A1 - Schütte, Christof T1 - Estimating the eigenvalue error of Markov State Models JF - Multiscale Modeling & Simulation Y1 - 2012 UR - http://publications.imp.fu-berlin.de/914/ U6 - https://doi.org/10.1137/100798910 VL - 10 IS - 1 SP - 61 EP - 81 ER - TY - CHAP A1 - Djurdjevac Conrad, Natasa A1 - Sarich, Marco A1 - Schütte, Christof T1 - On Markov State Models for Metastable Processes T2 - Proceedings of the International Congress of Mathematics, Hyderabad, India, Section Invited Talks. (ICM) 2010 Y1 - 2010 UR - http://publications.imp.fu-berlin.de/991/ ER - TY - JOUR A1 - Sarich, Marco A1 - Noé, Frank A1 - Schütte, Christof T1 - On the Approximation Quality of Markov State Models JF - Multiscale Model. Simul. Y1 - 2010 UR - http://publications.imp.fu-berlin.de/771/ U6 - https://doi.org/10.1137/090764049 VL - 8 IS - 4 SP - 1154 EP - 1177 ER - TY - JOUR A1 - Prinz, J.-H. A1 - Wu, Hao A1 - Sarich, Marco A1 - Keller, B. A1 - Fischbach, M. A1 - Held, M. A1 - Chodera, J. A1 - Schütte, Christof A1 - Noé, Frank T1 - Markov models of molecular kinetics JF - J. Chem. Phys. Y1 - 2011 UR - http://publications.imp.fu-berlin.de/944/ U6 - https://doi.org/10.1063/1.3565032 VL - 134 SP - 174105 ER - TY - JOUR A1 - Schütte, Christof A1 - Noé, Frank A1 - Lu, Jianfeng A1 - Sarich, Marco A1 - Vanden-Eijnden, E. T1 - Markov State Models Based on Milestoning JF - J. Chem. Phys. Y1 - 2011 UR - http://publications.imp.fu-berlin.de/1022/ U6 - https://doi.org/10.1063/1.3590108 VL - 134 IS - 20 SP - 204105 ER - TY - GEN A1 - Hartmann, Carsten A1 - Banisch, Ralf A1 - Sarich, Marco A1 - Badowski, Thomas A1 - Schütte, Christof T1 - Characterization of Rare Events in Molecular Dynamics N2 - A good deal of molecular dynamics simulations aims at predicting and quantifying rare events, such as the folding of a protein or a phase transition. Simulating rare events is often prohibitive, especially if the equations of motion are high-dimensional, as is the case in molecular dynamics. Various algorithms have been proposed for efficiently computing mean first passage times, transition rates or reaction pathways. This article surveys and discusses recent developments in the field of rare event simulation and outlines a new approach that combines ideas from optimal control and statistical mechanics. The optimal control approach described in detail resembles the use of Jarzynski's equality for free energy calculations, but with an optimized protocol that speeds up the sampling, while (theoretically) giving variance-free estimators of the rare events statistics. We illustrate the new approach with two numerical examples and discuss its relation to existing methods. T3 - ZIB-Report - 13-51 KW - rare events KW - moleculare dynamics KW - optimal pathways KW - stochastic control KW - dynamic programming KW - change of measure KW - cumulant generating function Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42410 SN - 1438-0064 ER - TY - GEN A1 - Sarich, Marco A1 - Banisch, Ralf A1 - Hartmann, Carsten A1 - Schütte, Christof T1 - Markov State Models for Rare Events in Molecular Dynamics N2 - Rare but important transition events between long lived states are a key feature of many molecular systems. In many cases the computation of rare event statistics by direct molecular dynamics (MD) simulations is infeasible even on the most powerful computers because of the immensely long simulation timescales needed. Recently a technique for spatial discretization of the molecular state space designed to help overcome such problems, so-called Markov State Models (MSMs), has attracted a lot of attention. We review the theoretical background and algorithmic realization of MSMs and illustrate their use by some numerical examples. Furthermore we introduce a novel approach to using MSMs for the efficient solution of optimal control problems that appear in applications where one desires to optimize molecular properties by means of external controls. T3 - ZIB-Report - 13-52 KW - rare events KW - Markov state models KW - long timescales KW - optimal control Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-42420 SN - 1438-0064 ER - TY - JOUR A1 - Hartmann, Carsten A1 - Banisch, Ralf A1 - Sarich, Marco A1 - Badowski, Thomas A1 - Schütte, Christof T1 - Characterization of Rare Events in Molecular Dynamics JF - Entropy (Special Issue) Y1 - 2013 U6 - https://doi.org/10.3390/e16010350 VL - 16 IS - 1 SP - 350 EP - 376 ER - TY - JOUR A1 - Sarich, Marco A1 - Banisch, Ralf A1 - Hartmann, Carsten A1 - Schütte, Christof T1 - Markov State Models for Rare Events in Molecular Dynamics JF - Entropy (Special Issue) Y1 - 2013 U6 - https://doi.org/10.3390/e16010258 VL - 16 IS - 1 SP - 258 EP - 286 ER - TY - JOUR A1 - Sarich, Marco A1 - Djurdjevac Conrad, Natasa A1 - Bruckner, Sharon A1 - Conrad, Tim A1 - Schütte, Christof T1 - Modularity revisited: A novel dynamics-based concept for decomposing complex networks JF - Journal of Computational Dynamics Y1 - 2014 UR - http://publications.mi.fu-berlin.de/1127/ U6 - https://doi.org/10.3934/jcd.2014.1.191 VL - 1 IS - 1 SP - 191 EP - 212 ER -