Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linking Microscopic and Macroscopic Models for Evolution: Markov Chain
  Network Training and Conservation Law Approximations   In this paper, a general framework for the analysis of a connection between
the training of artificial neural networks via the dynamics of Markov chains
and the approximation of conservation law equations is proposed. This framework
allows us to demonstrate an intrinsic link between microscopic and macroscopic
models for evolution via the concept of perturbed generalized dynamic systems.
The main result is exemplified with a number of illustrative examples where
efficient numerical approximations follow directly from network-based
computational models, viewed here as Markov chain approximations. Finally,
stability and consistency conditions of such computational models are
discussed.

18
The categories of this paper are: econ
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn