Linking Microscopic and Macroscopic Models for Evolution: Markov Chain Network Training and Conservation Law Approximations
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arXiv
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| Format: | Preprint |
| Publié: |
2007
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| _version_ | 1866914099127910400 |
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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 |
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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 |