On the Approximation Quality of Markov State Models

By Marco Sarich, Frank No'e, Christof Schutte. 2010

178 citations recorded by the source corpus.

Subfields: Molecular Biology, Statistics and Probability

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Citations in the corpus

Deep Generative Markov State Models (2018, background): “In practice, the long-time behavior of dynamical systems can be accurately described in a Markovian model when suitable features or variables are used, and when the time resolution of the model is sufficiently coarse such that the time-evolution can be represented with a manageable number of dynamic”
VAMPnets for deep learning of molecular kinetics (2017, background): “However, since any Markovian model of MD can be only approximate [8, 64], Eq.”
Unsupervised Learning Methods for Molecular Simulation Data (2021, methodology): “327 Because the VAC de ﬁ nes a scoring function, it enables us to optimize the model ’ s description of the true system ’ s global kinetics by variationally maximizing eq 51.”
Data-Driven Model Reduction and Transfer Operator Approximation (2017, background): “Due to their simple basis functions, they conduct relatively rough approximations, but when only a few spectral components are required, the approximation error can be controlled by choosing sufficiently large lag times τ [52].”
Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification (2013, background): “Today it is often referred to as Markov state modelling (MSM), see Chodera et al. (2007), Bowman et al. (2009), Sarich et al. (2010), Prinz et al. (2011).”
Machine learning for molecular simulation (2019, background): “(10) We can express the transition density (10) as the action of the Markov propagator in continuous-space, and by its spectral decomposition [72, 73]:”
Kinetic distance and kinetic maps from molecular dynamics simulation. (2015, background): “The first question has been answered: building on conformation dynamics theory [29, 28, 24, 15] it has been shown that the eigenfunctions of the backward Markov propagator underlying the MD are the optimal reaction coordinates: Projecting the dynamics upon these eigenfunctions will give rise to a ma”