Physics-informed neural networks (PINNs) have been proven to be a useful tool for solving general partial differential equations (PDEs), which is meshless and dimensionally free compared with traditional numerical solvers. Based on PINNs, gradient-enhanced physics-informed neural networks (gPINNs) add the partial derivative loss term of the independent variable and the physical constraint term, which improves the accuracy of network training. In this paper, the gPINNs method is proposed to solve the wave problem. The equation boundary value of the wave problem is added in the network construction, thus the network is forced to satisfy the equation boundary value during each training process. Two examples of wave equations are given in our paper, which are solved numerically by PINNs and gPINNs, respectively. It is found that using fewer data sets, gPINNs can learn data features more fully than PINNs and better results of gPINNs can be obtained.

中文翻译：

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波动方程的梯度增强物理通知神经网络方法


物理信息神经网络 (PINN) 已被证明是求解一般偏微分方程 (PDE) 的有用工具，与传统数值求解器相比，它是无网格且无量纲的。梯度增强物理信息神经网络（gPINNs）在PINN的基础上增加了自变量的偏导数损失项和物理约束项，提高了网络训练的准确性。本文提出gPINNs方法来解决波浪问题。在网络构建中加入了波动问题的方程边值，使得网络在每次训练过程中都被迫满足方程边值。我们的论文给出了波动方程的两个例子，分别用 PINN 和 gPINN 进行数值求解。研究发现，使用更少的数据集，gPINNs 可以比 PINNs 更全面地学习数据特征，并且可以获得更好的 gPINNs 结果。