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

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

doi:10.1109/ICUFN55119.2022.9829676

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

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

Korea University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

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 language	English
Title of host publication	ICUFN 2022 - 13th International Conference on Ubiquitous and Future Networks
Publisher	IEEE Computer Society
Pages	382-385
Number of pages	4
ISBN (Electronic)	9781665485500
DOIs	https://doi.org/10.1109/ICUFN55119.2022.9829676
State	Published - 2022
Event	13th International Conference on Ubiquitous and Future Networks, ICUFN 2022 - Virtual, Barcelona, Spain Duration: 5 Jul 2022 → 8 Jul 2022

Publication series

Name	International Conference on Ubiquitous and Future Networks, ICUFN
Volume	2022-July
ISSN (Print)	2165-8528
ISSN (Electronic)	2165-8536

Conference

Conference	13th International Conference on Ubiquitous and Future Networks, ICUFN 2022
Country/Territory	Spain
City	Virtual, Barcelona
Period	5/07/22 → 8/07/22

Bibliographical note

Publisher Copyright:
© 2022 IEEE.

Keywords

Partial differential equation
deep learning
physics-informed neural network

Access to Document

10.1109/ICUFN55119.2022.9829676

Cite this

Hwang, H. S., Son, S., Kim, Y., & Seok, J. (2022). Mitigating Coordinate Transformation for Solving Partial Differential Equations with Physic-Informed Neural Networks. In ICUFN 2022 - 13th International Conference on Ubiquitous and Future Networks (pp. 382-385). (International Conference on Ubiquitous and Future Networks, ICUFN; Vol. 2022-July). IEEE Computer Society. https://doi.org/10.1109/ICUFN55119.2022.9829676

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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.",

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doi = "10.1109/ICUFN55119.2022.9829676",

language = "English",

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Hwang, HS, Son, S, Kim, Y & Seok, J 2022, Mitigating Coordinate Transformation for Solving Partial Differential Equations with Physic-Informed Neural Networks. in ICUFN 2022 - 13th International Conference on Ubiquitous and Future Networks. International Conference on Ubiquitous and Future Networks, ICUFN, vol. 2022-July, IEEE Computer Society, pp. 382-385, 13th International Conference on Ubiquitous and Future Networks, ICUFN 2022, Virtual, Barcelona, Spain, 5/07/22. https://doi.org/10.1109/ICUFN55119.2022.9829676

Mitigating Coordinate Transformation for Solving Partial Differential Equations with Physic-Informed Neural Networks. / Hwang, Hyo Seok; Son, Suhan; Kim, Yoojoong et al.
ICUFN 2022 - 13th International Conference on Ubiquitous and Future Networks. IEEE Computer Society, 2022. p. 382-385 (International Conference on Ubiquitous and Future Networks, ICUFN; Vol. 2022-July).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - 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.

AB - 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.

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KW - physics-informed neural network

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Hwang HS, Son S, Kim Y, Seok J. Mitigating Coordinate Transformation for Solving Partial Differential Equations with Physic-Informed Neural Networks. In ICUFN 2022 - 13th International Conference on Ubiquitous and Future Networks. IEEE Computer Society. 2022. p. 382-385. (International Conference on Ubiquitous and Future Networks, ICUFN). doi: 10.1109/ICUFN55119.2022.9829676

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

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