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Physics-informed neural networks (PINNs) have been widely used to solvevarious scientific computing problems. However, large training costs limitPINNs for some real-time applications. Although some works have been proposedto improve the training efficiency of PINNs, few consider the influence ofinitialization. To this end, we propose a New Reptile initialization basedPhysics-Informed Neural Network (NRPINN). The original Reptile algorithm is ameta-learning initialization method based on labeled data. PINNs can be trainedwith less labeled data or even without any labeled data by adding partialdifferential equations (PDEs) as a penalty term into the loss function.Inspired by this idea, we propose the new Reptile initialization to sample moretasks from the parameterized PDEs and adapt the penalty term of the loss. Thenew Reptile initialization can acquire initialization parameters from relatedtasks by supervised, unsupervised, and semi-supervised learning. Then, PINNswith initialization parameters can efficiently solve PDEs. Besides, the newReptile initialization can also be used for the variants of PINNs. Finally, wedemonstrate and verify the NRPINN considering both forward problems, includingsolving Poisson, Burgers, and Schr\"odinger equations, as well as inverseproblems, where unknown parameters in the PDEs are estimated. Experimentalresults show that the NRPINN training is much faster and achieves higheraccuracy than PINNs with other initialization methods.

A novel meta-learning initialization method for physics-informed neural networks