TY - GEN
T1 - Mitigating Coordinate Transformation for Solving Partial Differential Equations with Physic-Informed Neural Networks
AU - Hwang, Hyo Seok
AU - Son, Suhan
AU - Kim, Yoojoong
AU - Seok, Junhee
N1 - Funding Information:
ACKNOWLED*MENT This work was supported by a grant from the National Research Foundation of Korea (NRF-2022R1A2C200400 )
Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
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.
KW - deep learning
KW - Partial differential equation
KW - physics-informed neural network
UR - http://www.scopus.com/inward/record.url?scp=85135229648&partnerID=8YFLogxK
U2 - 10.1109/ICUFN55119.2022.9829676
DO - 10.1109/ICUFN55119.2022.9829676
M3 - Conference contribution
AN - SCOPUS:85135229648
T3 - International Conference on Ubiquitous and Future Networks, ICUFN
SP - 382
EP - 385
BT - ICUFN 2022 - 13th International Conference on Ubiquitous and Future Networks
PB - IEEE Computer Society
T2 - 13th International Conference on Ubiquitous and Future Networks, ICUFN 2022
Y2 - 5 July 2022 through 8 July 2022
ER -