  Physics-informed neural networks (PINNs) provide a deep learning framework
for numerically solving partial differential equations (PDEs), and have been
widely used in a variety of PDE problems. However, there still remain some
challenges in the application of PINNs: 1) the mechanism of PINNs is unsuitable
(at least cannot be directly applied) to exploiting a small size of (usually
very few) extra informative samples to refine the networks; and 2) the
efficiency of training PINNs often becomes low for some complicated PDEs. In
this paper, we propose the generative adversarial physics-informed neural
network (GA-PINN), which integrates the generative adversarial (GA) mechanism
with the structure of PINNs, to improve the performance of PINNs by exploiting
only a small size of exact solutions to the PDEs. Inspired from the weighting
strategy of the Adaboost method, we then introduce a point-weighting (PW)
method to improve the training efficiency of PINNs, where the weight of each
sample point is adaptively updated at each training iteration. The numerical
experiments show that GA-PINNs outperform PINNs in many well-known PDEs and the
PW method also improves the efficiency of training PINNs and GA-PINNs.
