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Neural networks for variational problems in engineering

AuthorsLópez, R.; Balsa-Canto, Eva ; Oñate, Eugenio
KeywordsNeural network
Multilayer perceptron
Functional analysis
Variational calculus
Shape design
Optimal control
Inverse problems
Issue Date2008
PublisherJohn Wiley & Sons
CitationInternational Journal for Numerical Methods in Engineering 75(11): 1341-1360 (2008)
AbstractIn this work a conceptual theory of neural networks (NNs) from the perspective of functional analysis and variational calculus is presented. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function, which is an extremal for some functional. Therefore, a variational formulation for NNs provides a direct method for the solution of variational problems. This proposed method is then applied to distinct types of engineering problems. In particular a shape design, an optimal control and an inverse problem are considered. The selected examples can be solved analytically, which enables a fair comparison with the NN results
Description20 páginas, 12 figuras, 3 tablas
Publisher version (URL)http://dx.doi.org/10.1002/nme.2304
Appears in Collections:(IIM) Artículos
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