  Physics-informed neural networks (PINN) have recently emerged as a promising
application of deep learning in a wide range of engineering and scientific
problems based on partial differential equation (PDE) models. However, evidence
shows that PINN training by gradient descent displays pathologies that often
prevent convergence when solving PDEs with irregular solutions. In this paper,
we propose the use of a particle swarm optimization (PSO) approach to train
PINNs. The resulting PSO-PINN algorithm not only mitigates the undesired
behaviors of PINNs trained with standard gradient descent but also presents an
ensemble approach to PINN that affords the possibility of robust predictions
with quantified uncertainty. We also propose PSO-BP-CD (PSO with
Back-Propagation and Coefficient Decay), a hybrid PSO variant that combines
swarm optimization with gradient descent, putting more weight on the latter as
training progresses and the swarm zeros in on a good local optimum.
Comprehensive experimental results show that PSO-PINN with the proposed
PSO-BP-CD algorithm outperforms PINN ensembles trained with other PSO variants
or with pure gradient descent.
