Deep Neural Networks and Adaptive Quadrature for Solving Variational Problems

Daria Fokina, Oleg Iliev, Ivan Oseledets

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The great success of deep neural networks (DNNs) in such areas as image processing, natural language processing has motivated also their usage in many other areas. It has been shown that in particular cases they provide very good approximation to different classes of functions. The aim of this work is to explore the usage of deep learning methods for approximation of functions, which are solutions of boundary value problems for particular differential equations. More specific, the class of methods known as physics-informed neural network will be explored. Components of the DNN algorithms, such as the definition of loss function and the choice of the minimization method will be discussed while presenting results from the computational experiments.

Original languageEnglish
Title of host publicationLarge-Scale Scientific Computing - 13th International Conference, LSSC 2021, Revised Selected Papers
EditorsIvan Lirkov, Svetozar Margenov
PublisherSpringer Science and Business Media Deutschland GmbH
Pages369-377
Number of pages9
ISBN (Print)9783030975487
DOIs
Publication statusPublished - 2022
Event13th International Conference on Large-Scale Scientific Computations, LSSC 2021 - Sozopol, Bulgaria
Duration: 7 Jun 202111 Jun 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13127 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Conference on Large-Scale Scientific Computations, LSSC 2021
Country/TerritoryBulgaria
CitySozopol
Period7/06/2111/06/21

Keywords

  • Adaptive quadrature
  • Physics-informed neural networks
  • Variational problem

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