Understanding the training of PINNs for unsteady flow past a plunging
  foil through the lens of input subdomain level loss function gradients
Rahul Sundar Didier Lucor Sunetra Sarkar
Recently immersed boundary method-inspired physics-informed neural networks
(PINNs) including the moving boundary-enabled PINNs (MB-PINNs) have shown the
ability to accurately reconstruct velocity and recover pressure as a hidden
variable for unsteady flow past moving bodies. Considering flow past a plunging
foil, MB-PINNs were trained with global physics loss relaxation and also in
conjunction with a physics-based undersampling method, obtaining good accuracy.
The purpose of this study was to investigate which input spatial subdomain
contributes to the training under the effect of physics loss relaxation and
physics-based undersampling. In the context of MB-PINNs training, three spatial
zones: the moving body, wake, and outer zones were defined. To quantify which
spatial zone drives the training, two novel metrics are computed from the zonal
loss component gradient statistics and the proportion of sample points in each
zone. Results confirm that the learning indeed depends on the combined effect
of the zonal loss component gradients and the proportion of points in each
zone. Moreover, the dominant input zones are also the ones that have the
strongest solution gradients in some sense.