  Physics-informed neural networks (PINNs) have been widely used to solve
various scientific computing problems. However, large training costs limit
PINNs for some real-time applications. Although some works have been proposed
to improve the training efficiency of PINNs, few consider the influence of
initialization. To this end, we propose a New Reptile initialization based
Physics-Informed Neural Network (NRPINN). The original Reptile algorithm is a
meta-learning initialization method based on labeled data. PINNs can be trained
with less labeled data or even without any labeled data by adding partial
differential equations (PDEs) as a penalty term into the loss function.
Inspired by this idea, we propose the new Reptile initialization to sample more
tasks from the parameterized PDEs and adapt the penalty term of the loss. The
new Reptile initialization can acquire initialization parameters from related
tasks by supervised, unsupervised, and semi-supervised learning. Then, PINNs
with initialization parameters can efficiently solve PDEs. Besides, the new
Reptile initialization can also be used for the variants of PINNs. Finally, we
demonstrate and verify the NRPINN considering both forward problems, including
solving Poisson, Burgers, and Schr\"odinger equations, as well as inverse
problems, where unknown parameters in the PDEs are estimated. Experimental
results show that the NRPINN training is much faster and achieves higher
accuracy than PINNs with other initialization methods.
