• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Learning stochastic eigenvalues

Thumbnail
View/Open
UQNN_HAL_20161212.pdf (848.7Kb)
Date
2016
Collection title
cahier de recherche CEREMADE- Paris-Dauphine
Dewey
Analyse
Sujet
finite elements; Smolyak; sparse grids; neural networks; stochastic eigenvalues; uncertainty quantification
URI
https://basepub.dauphine.fr/handle/123456789/17409
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Andreev, Roman
25 Laboratoire Jacques-Louis Lions [LJLL]
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Document de travail / Working paper
Item number of pages
5
Abstract (EN)
We train an artificial neural network with one hidden layer on realizations of the first few eigenvalues of a partial differential operator that is parameterized by a vector of independent random variables. The eigenvalues exhibit "crossings" in the high-dimensional parameter space. The training set is constructed by sampling the parameter either at random nodes or at the Smolyak collocation nodes. The performance of the neural network is evaluated empirically on a large random test set. We find that training on random or quasi-random nodes is preferable to the Smolyak nodes. The neural network outperforms the Smolyak interpolation in terms of error bias and variance on nonsimple eigenvalues but not on the simple ones.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.