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

arXiv: https://arxiv.org/abs/2507.01714 · HTML: https://mlsanity.com/paper/2507.01714/

## 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.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [Challenges in Training PINNs: A Loss Landscape Perspective](https://mlsanity.com/paper/2402.01868/) (2024)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks](https://mlsanity.com/paper/2007.07442/) (2020)
- [Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling](https://mlsanity.com/paper/2207.02338/) (2022)
- [Learning in Sinusoidal Spaces with Physics-Informed Neural Networks](https://mlsanity.com/paper/2109.09338/) (2021)
- [Data vs. Physics: The Apparent Pareto Front of Physics-Informed Neural Networks](https://mlsanity.com/paper/2105.00862/) (2021)
- [On Last-Layer Algorithms for Classification: Decoupling Representation from Uncertainty Estimation](https://mlsanity.com/paper/2001.08049/) (2020)
- [On the Role of Fixed Points of Dynamical Systems in Training Physics-Informed Neural Networks](https://mlsanity.com/paper/2203.13648/) (2022)
- [Improved Training of Physics-Informed Neural Networks with Model Ensembles](https://mlsanity.com/paper/2204.05108/) (2022)
- [How to Avoid Trivial Solutions in Physics-Informed Neural Networks](https://mlsanity.com/paper/2112.05620/) (2021)
- [The Relevance of Bayesian Layer Positioning to Model Uncertainty in Deep Bayesian Active Learning](https://mlsanity.com/paper/1811.12535/) (2018)
- [Prior choice affects ability of Bayesian neural networks to identify unknowns](https://mlsanity.com/paper/2005.04987/) (2020)
- [PSO-PINN: Physics-Informed Neural Networks Trained with Particle Swarm Optimization](https://mlsanity.com/paper/2202.01943/) (2022)

## 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.