  Physics-informed neural networks (PINNs) [4, 10] are an approach for solving
boundary value problems based on differential equations (PDEs). The key idea of
PINNs is to use a neural network to approximate the solution to the PDE and to
incorporate the residual of the PDE as well as boundary conditions into its
loss function when training it. This provides a simple and mesh-free approach
for solving problems relating to PDEs. However, a key limitation of PINNs is
their lack of accuracy and efficiency when solving problems with larger domains
and more complex, multi-scale solutions. In a more recent approach, finite
basis physics-informed neural networks (FBPINNs) [8] use ideas from domain
decomposition to accelerate the learning process of PINNs and improve their
accuracy. In this work, we show how Schwarz-like additive, multiplicative, and
hybrid iteration methods for training FBPINNs can be developed. We present
numerical experiments on the influence of these different training strategies
on convergence and accuracy. Furthermore, we propose and evaluate a preliminary
implementation of coarse space correction for FBPINNs.
