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This research introduces label propagation techniques to enhance physics-informed neural networks and Gaussian processes, specifically addressing the challenge of propagating boundary information into stiff time-dependent partial differential equations. By combining self-training and co-training approaches, the study establishes a hybrid framework that mitigates common failure modes in solving complex physical systems.
Label Propagation for Physics-Informed Neural Networks and Physics-Informed Gaussian Processes
arXiv:2404.05817v2 Announce Type: replace Abstract: We present a series of empirical results of the application of semi-supervised label propagation techniques in training physics-informed machine learning methods. This includes self-training of physics-informed neural networks and physics-informed Gaussian processes in isolation, and the integration of the two via co-training, therefore establishing a hybrid between these two main classes of physics-informed machine learning. We demonstrate via extensive numerical experiments how these methods can ameliorate the issue of propagating information from boundaries into the physical domain, including information from initial conditions in the case of solving stiff time-dependent partial differential equations, which is known to be a common failure mode of physics-informed machine learning.
Abstract:We present a series of empirical results of the application of semi-supervised label propagation techniques in training physics-informed machine learning methods. This includes self-training of physics-informed neural networks and physics-informed Gaussian processes in isolation, and the integration of the two via co-training, therefore establishing a hybrid between these two main classes of physics-informed machine learning. We demonstrate via extensive numerical experiments how these methods can ameliorate the issue of propagating information from boundaries into the physical domain, including information from initial conditions in the case of solving stiff time-dependent partial differential equations, which is known to be a common failure mode of physics-informed machine learning.
Machine Learning (cs.LG)
arXiv:2404.05817 [cs.LG]
(or arXiv:2404.05817v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2404.05817 Focus to learn more arXiv-issued DOI via DataCite
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