Label Propagation for Physics-Informed Neural Networks and Physics-Informed Gaussian Processes
cs.LG
Submitted: 2024-04-08
Updated: 2026-09-19
License: http://creativecommons.org/licenses/by/4.0/
The gist: We present a series of empirical results of the application of semi-supervised label propagation techniques in training physics-informed machine learning methods.
Terminology
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.
Sources
- Improved Training of Physics-Informed Neural Networks with Model Ensembles
- Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism
- On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs
- Respecting causality is all you need for training physics-informed neural networks
- Understanding and mitigating gradient pathologies in physics-informed neural networks
- When and why PINNs fail to train: A neural tangent kernel perspective
- Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural Networks
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