Linking Microscopic and Macroscopic Models for Evolution: Markov Chain Network Training and Conservation Law Approximations

Details Linking Microscopic and Macroscopic Models for Evolution: Markov Chain Network Training and Conservation Law Approximations Linking Microscopic and Macroscopic Models for Evolution: Markov Chain Network Training and Conservation Law Approximations

2007-02-25

arxiv.org/abs/cs/0702148v1

Markov Chain network training and conservation law approximations: Linking microscopic and macroscopic models for evolution, M

Computer Science

Computational Engineering, Finance, and Science

21 pages, 5 figures

Scientific paper

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.

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