Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deep learning Markov and Koopman models with physical constraints   The long-timescale behavior of complex dynamical systems can be described by
linear Markov or Koopman models in a suitable latent space. Recent variational
approaches allow the latent space representation and the linear dynamical model
to be optimized via unsupervised machine learning methods. Incorporation of
physical constraints such as time-reversibility or stochasticity into the
dynamical model has been established for a linear, but not for arbitrarily
nonlinear (deep learning) representations of the latent space. Here we develop
theory and methods for deep learning Markov and Koopman models that can bear
such physical constraints. We prove that the model is an universal approximator
for reversible Markov processes and that it can be optimized with either
maximum likelihood or the variational approach of Markov processes (VAMP). We
demonstrate that the model performs equally well for equilibrium and
systematically better for biased data compared to existing approaches, thus
providing a tool to study the long-timescale processes of dynamical systems.

9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th