Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal data-driven estimation of generalized Markov state models for
  non-equilibrium dynamics   There are multiple ways in which a stochastic system can be out of
statistical equilibrium. It might be subject to time-varying forcing; or be in
a transient phase on its way towards equilibrium; it might even be in
equilibrium without us noticing it, due to insufficient observations; and it
even might be a system failing to admit an equilibrium distribution at all. We
review some of the approaches that model the effective statistical behavior of
equilibrium and non-equilibrium dynamical systems, and show that both cases can
be considered under the unified framework of optimal low-rank approximation of
so-called transfer operators. Particular attention is given to the connection
between these methods, Markov state models, and the concept of metastability,
further to the estimation of such reduced order models from finite simulation
data. We illustrate our considerations by numerical examples.

8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess