B-PL-PINN: Stabilizing PINN Training with Bayesian Pseudo Labeling
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916822452797440 |
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| author | Innerebner, Kevin Rohrhofer, Franz M. Geiger, Bernhard C. |
| author_facet | Innerebner, Kevin Rohrhofer, Franz M. Geiger, Bernhard C. |
| contents | Training physics-informed neural networks (PINNs) for forward problems often suffers from severe convergence issues, hindering the propagation of information from regions where the desired solution is well-defined. Haitsiukevich and Ilin (2023) proposed an ensemble approach that extends the active training domain of each PINN based on i) ensemble consensus and ii) vicinity to (pseudo-)labeled points, thus ensuring that the information from the initial condition successfully propagates to the interior of the computational domain.
In this work, we suggest replacing the ensemble by a Bayesian PINN, and consensus by an evaluation of the PINN's posterior variance. Our experiments show that this mathematically principled approach outperforms the ensemble on a set of benchmark problems and is competitive with PINN ensembles trained with combinations of Adam and LBFGS. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01714 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | B-PL-PINN: Stabilizing PINN Training with Bayesian Pseudo Labeling Innerebner, Kevin Rohrhofer, Franz M. Geiger, Bernhard C. Machine Learning Training physics-informed neural networks (PINNs) for forward problems often suffers from severe convergence issues, hindering the propagation of information from regions where the desired solution is well-defined. Haitsiukevich and Ilin (2023) proposed an ensemble approach that extends the active training domain of each PINN based on i) ensemble consensus and ii) vicinity to (pseudo-)labeled points, thus ensuring that the information from the initial condition successfully propagates to the interior of the computational domain. In this work, we suggest replacing the ensemble by a Bayesian PINN, and consensus by an evaluation of the PINN's posterior variance. Our experiments show that this mathematically principled approach outperforms the ensemble on a set of benchmark problems and is competitive with PINN ensembles trained with combinations of Adam and LBFGS. |
| title | B-PL-PINN: Stabilizing PINN Training with Bayesian Pseudo Labeling |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2507.01714 |