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

Fuente: arXiv
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Autor principal: Melnik, Roderick V. N.
Formato: Preprint
Publicado: 2007
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author Melnik, Roderick V. N.
author_facet Melnik, Roderick V. N.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_cs_0702148
institution arXiv
publishDate 2007
record_format arxiv
spellingShingle Linking Microscopic and Macroscopic Models for Evolution: Markov Chain Network Training and Conservation Law Approximations
Melnik, Roderick V. N.
Computational Engineering, Finance, and Science
Information Theory
Numerical Analysis
Neural and Evolutionary Computing
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.
title Linking Microscopic and Macroscopic Models for Evolution: Markov Chain Network Training and Conservation Law Approximations
topic Computational Engineering, Finance, and Science
Information Theory
Numerical Analysis
Neural and Evolutionary Computing
url https://arxiv.org/abs/cs/0702148