English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

This paper is concerned with the approximation of the solution of partialdifferential equations by means of artificial neural networks. Here afeedforward neural network is used to approximate the solution of the partialdifferential equation. The learning problem is formulated as a least squaresproblem, choosing the residual of the partial differential equation as a lossfunction, whereas a multilevel Levenberg-Marquardt method is employed as atraining method. This setting allows us to get further insight into thepotential of multilevel methods. Indeed, when the least squares problem arisesfrom the training of artificial neural networks, the variables subject tooptimization are not related by any geometrical constraints and the standardinterpolation and restriction operators cannot be employed any longer. Aheuristic, inspired by algebraic multigrid methods, is then proposed toconstruct the multilevel transfer operators. Numerical experiments showencouraging results related to the efficiency of the new multileveloptimization method for the training of artificial neural networks, compared tothe standard corresponding one-level procedure.

On the approximation of the solution of partial differential equations  by artificial neural networks trained by a multilevel Levenberg-Marquardt  method