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Language: English

Conflict of Interest: In relation to this article, we declare that there is no conflict of interest.

Publication history: Received November 4, 2022
Revised March 3, 2023
Accepted March 11, 2023

Acknowledgements: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (Ministry of Science and ICT, MSIT) (No. NRF-2018R1A5A1024127, NRF2020R1A2C2008141, and NRF-2021M3H4A6A01041234

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/bync/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Physics-informed neural networks for learning fluid flows with symmetry

Younghyeon Kim^† Hyungyeol Kwak^† Jaewook Nam^†

School of Chemical and Biological Engineering, Institute of Chemical Processes, Seoul National University, Seoul 08826, Korea

jaewooknam@snu.ac.kr

Korean Journal of Chemical Engineering, September 2023, 40(9), 2119-2127(9), 10.1007/s11814-023-1420-4

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Abstract

We suggest symmetric variational physics-informed neural networks (symmetric VPINN) to learn the symmetric fluid flow and physical properties of fluids from a limited set of data. Symmetric VPINN is based on the VPINN framework and guarantees the symmetry of the solutions by modifying the network architecture. The effectiveness of the symmetric VPINN is demonstrated by predicting the velocity profiles and power-law fluid properties in the Poiseuille flow of a parallel channel. Symmetric VPINN models robustly and accurately learn power-law fluid flow in both forward and inverse problems. We demonstrate that the symmetric VPINN can be particularly useful when the power-law index is small and the data are extremely limited. The modified network architecture in the symmetric VPINN guides the neural network towards an exact solution by reinforcing symmetry. We show that symmetric VPINN is effective in obtaining unknown physical properties in practical experiments where data are scarce, suggesting the possibility of introducing known conditions of the system directly into the network structure to improve the accuracy of the network.

Keywords

Physics-informed Machine Learning Network Architecture Power-law Fluid Pressure-driven Flow Inverse Problem

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