  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.
