Version 1
: Received: 10 July 2024 / Approved: 11 July 2024 / Online: 11 July 2024 (04:52:07 CEST)
How to cite:
Decke, J.; Heinen, A.; Sick, B.; Gruhl, C. Active Learning with Physics-Informed Graph Neural Networks on Unstructured Meshes. Preprints2024, 2024070922. https://doi.org/10.20944/preprints202407.0922.v1
Decke, J.; Heinen, A.; Sick, B.; Gruhl, C. Active Learning with Physics-Informed Graph Neural Networks on Unstructured Meshes. Preprints 2024, 2024070922. https://doi.org/10.20944/preprints202407.0922.v1
Decke, J.; Heinen, A.; Sick, B.; Gruhl, C. Active Learning with Physics-Informed Graph Neural Networks on Unstructured Meshes. Preprints2024, 2024070922. https://doi.org/10.20944/preprints202407.0922.v1
APA Style
Decke, J., Heinen, A., Sick, B., & Gruhl, C. (2024). Active Learning with Physics-Informed Graph Neural Networks on Unstructured Meshes. Preprints. https://doi.org/10.20944/preprints202407.0922.v1
Chicago/Turabian Style
Decke, J., Bernhard Sick and Christian Gruhl. 2024 "Active Learning with Physics-Informed Graph Neural Networks on Unstructured Meshes" Preprints. https://doi.org/10.20944/preprints202407.0922.v1
Abstract
This paper investigates the use of Physics-Informed Neural Networks (PINNs) in active learning cycles. We defined two scenarios: one semi-supervised and the other fully supervised. PINNs emphasize the integration of physical laws into neural networks to improve the predictive performance of vanilla neural networks and to enhance the efficiency of traditional methods for solving partial differential equations (PDEs). Key contributions include adapting existing computational frameworks to enable the use of Graph Neural Networks for solving problems that require the calculation of gradients on unstructured triangle meshes, a query strategy focusing on the physical loss, and a comparative analysis of this strategy against random sampling across both defined scenarios. This work establishes a foundation for future research aimed at expanding the application of Physics-Informed Graph Neural Networks (PIGNN) using active learning and addressing real-world problems in fluid dynamics and electrodynamics.
Computer Science and Mathematics, Artificial Intelligence and Machine Learning
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
