Published in Int. Journal for Numerical Methods in Engineering Vol. 75 (11), pp. 1341-1360, 2008
doi: 10.1002/nme.2304

Abstract

In 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.

The PDF file did not load properly or your web browser does not support viewing PDF files. Download directly to your device: Download PDF document
Back to Top

Document information

Published on 17/12/18
Submitted on 17/12/18

DOI: 10.1002/nme.2304
Licence: CC BY-NC-SA license

Document Score

0

Times cited: 12
Views 11
Recommendations 0

Share this document

claim authorship

Are you one of the authors of this document?