A Fourier-based machine learning technique with application in engineering
PEIGNEY
Type de document
ARTICLE A COMITE DE LECTURE REPERTORIE DANS BDI (ACL)
Langue
anglais
Auteur
PEIGNEY
Résumé / Abstract
The generic problem in supervised machine learning is to learn a function f from a collection of samples, with the objective of predicting the value taken by f for any given input. In e?ect, the learning procedure consists in constructing an explicit function that approximates f in some sense. In this paper is introduced a Fourier-based machine learning method which could be an alternative or a complement to neural networks for applications in engineering. The basic idea is to extend f into a periodic function so as to use partial sums of the Fourier series as approximations. For this approach to be e?ective in high dimension, it proved necessary to use several ideas and concepts such as regularization, Sobol sequences and hyperbolic crosses. An attractive feature of the proposed method is that the training stage reduces to a quadratic programming problem. The presented method is ?rst applied to some examples of high-dimensional analytical functions, which allows some comparisons with neural networks to be made. An application to a homogenization problem in nonlinear conduction is discussed in detail. Various examples related to global sensi-tivity analysis, assessing e?ective energies of microstructures, and solving boundary value problems are presented.
Source
International Journal for Numerical Methods in Engineering, 58 p p.
Editeur
Wiley
