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Functional Networks: A New Network-Based Methodology.

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Title: Functional Networks: A New Network-Based Methodology.
Authors: Castillo>, Enrique, Cobo, Angel, Gutiérrez, José Manuel, Pruneda, Eva
Source: Computer-Aided Civil & Infrastructure Engineering. Mar2000, Vol. 15 Issue 2, p90. 17p.
Subjects: Computer-aided engineering, Artificial neural networks
Abstract: In this article we give a general methodology to build and work with functional networks, a network-based alternative to the neural networks paradigm. In functional networks, neural functions are allowed to be not only multivariate but also truly multiargument and different for all neurons. Thus neural functions instead of weights are learned. In addition, outputs coming from different neurons can be connected, that is, forced to output the same values. The topology and neuron functions of functional networks can be selected based on data, domain knowledge, or a combination of the two. Functional equations play an important role in functional networks, since the preceding types of connections lead to functional equations that impose a substantial reduction in the degrees of freedom of the initial neural functions. Some methods are given to obtain equivalent functional and differential equations, and they are applied to approximating the solutions of differential equations problems. The examples of an associative operator, a cantilever beam, and a mass supported by two springs and a viscous damper are given to illustrate the methods and show their power. [ABSTRACT FROM AUTHOR]
Copyright of Computer-Aided Civil & Infrastructure Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: In this article we give a general methodology to build and work with functional networks, a network-based alternative to the neural networks paradigm. In functional networks, neural functions are allowed to be not only multivariate but also truly multiargument and different for all neurons. Thus neural functions instead of weights are learned. In addition, outputs coming from different neurons can be connected, that is, forced to output the same values. The topology and neuron functions of functional networks can be selected based on data, domain knowledge, or a combination of the two. Functional equations play an important role in functional networks, since the preceding types of connections lead to functional equations that impose a substantial reduction in the degrees of freedom of the initial neural functions. Some methods are given to obtain equivalent functional and differential equations, and they are applied to approximating the solutions of differential equations problems. The examples of an associative operator, a cantilever beam, and a mass supported by two springs and a viscous damper are given to illustrate the methods and show their power. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computer-Aided Civil & Infrastructure Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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