  Multiscale problems are challenging for neural network-based discretizations
of differential equations, such as physics-informed neural networks (PINNs).
This can be (partly) attributed to the so-called spectral bias of neural
networks. To improve the performance of PINNs for time-dependent problems, a
combination of multifidelity stacking PINNs and domain decomposition-based
finite basis PINNs is employed. In particular, to learn the high-fidelity part
of the multifidelity model, a domain decomposition in time is employed. The
performance is investigated for a pendulum and a two-frequency problem as well
as the Allen-Cahn equation. It can be observed that the domain decomposition
approach clearly improves the PINN and stacking PINN approaches. Finally, it is
demonstrated that the FBPINN approach can be extended to multifidelity
physics-informed deep operator networks.
