Mitigating Coordinate Transformation for Solving Partial Differential Equations with Physic-Informed Neural Networks

Hyo Seok Hwang, Suhan Son, Yoojoong Kim, Junhee Seok

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this work, we investigate some coordinate systems to solve partial differential equations (PDEs) using a neural network. We approximate the solution using physics-informed neural networks (PINNs) both before and after the coordinate transformation for two cases: a coordinate system with periodicity and without periodicity. We demonstrate that PINNs with Cartesian coordinate shows better approximation accuracy. This implies in PINNs training the Cartesian coordinate system is superior to the other coordinate systems derived by coordinate transformation. To the best of our knowledge, this is the first work to test training of PINNs by modifying PDEs according to the boundary shape.

Original languageEnglish
Title of host publicationICUFN 2022 - 13th International Conference on Ubiquitous and Future Networks
PublisherIEEE Computer Society
Pages382-385
Number of pages4
ISBN (Electronic)9781665485500
DOIs
Publication statusPublished - 2022
Event13th International Conference on Ubiquitous and Future Networks, ICUFN 2022 - Virtual, Barcelona, Spain
Duration: 2022 Jul 52022 Jul 8

Publication series

NameInternational Conference on Ubiquitous and Future Networks, ICUFN
Volume2022-July
ISSN (Print)2165-8528
ISSN (Electronic)2165-8536

Conference

Conference13th International Conference on Ubiquitous and Future Networks, ICUFN 2022
Country/TerritorySpain
CityVirtual, Barcelona
Period22/7/522/7/8

Keywords

  • deep learning
  • Partial differential equation
  • physics-informed neural network

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications
  • Hardware and Architecture

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