title: Projected metastable Markov processes and their estimation with observable operator models.
abstract: The determination of kinetics of high-dimensional dynamical systems, such as macromolecules, polymers, or spin systems, is a difficult and generally unsolved problem - both in simulation, where the optimal reaction coordinate(s) are generally unknown and are difficult to compute, and in experimental measurements, where only specific coordinates are observable. Markov models, or Markov state models, are widely used but suffer from the fact that the dynamics on a coarsely discretized state spaced are no longer Markovian, even if the dynamics in the full phase space are. The recently proposed projected Markov models (PMMs) are a formulation that provides a description of the kinetics on a low-dimensional projection without making the Markovianity assumption. However, as yet no general way of estimating PMMs from data has been available. Here, we show that the observed dynamics of a PMM can be exactly described by an observable operator model (OOM) and derive a PMM estimator based on the OOM learning.
authors.affiliation: DFG Research Center Matheon, Free University Berlin, Arnimallee 6, 14195 Berlin, Germany.
authors.forename: Hao
authors.initials: H
authors.lastname: Wu
authors.affiliation: DFG Research Center Matheon, Free University Berlin, Arnimallee 6, 14195 Berlin, Germany.
authors.forename: Jan-Hendrik
authors.initials: JH
authors.lastname: Prinz
authors.affiliation: DFG Research Center Matheon, Free University Berlin, Arnimallee 6, 14195 Berlin, Germany.
authors.forename: Frank
authors.initials: F
authors.lastname: Noé