B-PL-PINN: Stabilizing PINN Training with Bayesian Pseudo Labeling
This work addresses stability problems in PINN training for computational physics, offering an incremental improvement over existing ensemble techniques.
The paper tackles the convergence issues in training physics-informed neural networks (PINNs) for forward problems by replacing an ensemble approach with a Bayesian PINN and using posterior variance evaluation, resulting in improved performance on benchmark problems and competitiveness with ensemble methods.
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.