A Variational Formulation for the Multilayer Perceptron

  • Roberto Lopez
  • Eugenio Oñate
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4131)


In this work we present a theory of the multilayer perceptron from the perspective of functional analysis and variational calculus. Within this formulation, the learning problem for the multilayer perceptron lies in terms of finding a function which is an extremal for some functional. As we will see, a variational formulation for the multilayer perceptron provides a direct method for the solution of general variational problems, in any dimension and up to any degree of accuracy. In order to validate this technique we use a multilayer perceptron to solve some classical problems in the calculus of variations.


Hide Layer Optimal Control Problem Variational Problem Variational Formulation Multilayer Perceptron 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Roberto Lopez
    • 1
  • Eugenio Oñate
    • 1
  1. 1.International Center for Numerical Methods in Engineering (CIMNE)Technical University of Catalonia (UPC)BarcelonaSpain

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