Multifidelity domain decomposition-based physics-informed neural
  networks for time-dependent problems
Alexander Heinlein Amanda A. Howard Damien Beecroft Panos Stinis
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 are 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.