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B-PL-PINN: Stabilizing PINN Training with Bayesian Pseudo Labeling

arXiv 2507.01714 ↗First posted 2 Jul 2025cs.LGcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 19 of its 34 references that are in the map. First posted on arXiv 2 Jul 2025.

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19 of 34 references.

References · 19

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,305
  3. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,501
  4. 2021Characterizing possible failure modes in physics-informed neural networkscited by 643
  5. 2020B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Datacited by 335
  6. 2021Physics-informed neural networks with hard constraints for inverse designcited by 280
  7. 2024Challenges in Training PINNs: A Loss Landscape Perspectivecited by 113
  8. 2017TensorFlow Distributionscited by 106
  9. 2020A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networkscited by 87
  10. 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 73
  11. 2021Learning in Sinusoidal Spaces with Physics-Informed Neural Networkscited by 62
  12. 2021Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networkscited by 27
7 more
  1. 2020On Last-Layer Algorithms for Classification: Decoupling Representation from Uncertainty Estimationcited by 23
  2. 2022On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networkscited by 23
  3. 2022Improved Training of Physics-Informed Neural Networks with Model Ensemblescited by 19
  4. 2021How to Avoid Trivial Solutions in Physics-Informed Neural Networkscited by 15
  5. 2018The Relevance of Bayesian Layer Positioning to Model Uncertainty in Deep Bayesian Active Learningcited by 13
  6. 2020Prior choice affects ability of Bayesian neural networks to identify unknownscited by 12
  7. 2022PSO-PINN: Physics-Informed Neural Networks Trained with Particle Swarm Optimizationcited by 11

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