Accéder directement au contenu Accéder directement à la navigation
Nouvelle interface
Article dans une revue

A Fourier-based machine learning technique with application in engineering

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 effect, the learning procedure consists in constructing an explicit function that approximates f in some sense. In this article 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 effective 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 first 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 sensitivity analysis, assessing effective energies of microstructures, and solving boundary value problems are presented.
Type de document :
Article dans une revue
Liste complète des métadonnées
Contributeur : Michael Peigney Connectez-vous pour contacter le contributeur
Soumis le : jeudi 3 décembre 2020 - 12:08:52
Dernière modification le : vendredi 1 juillet 2022 - 14:00:24
Archivage à long terme le : : jeudi 4 mars 2021 - 19:01:13


Fichiers produits par l'(les) auteur(s)



Michaël Peigney. A Fourier-based machine learning technique with application in engineering. International Journal for Numerical Methods in Engineering, In press, ⟨10.1002/nme.6565⟩. ⟨hal-03038092⟩



Consultations de la notice


Téléchargements de fichiers