论文标题
Phygnnet：使用物理信息图神经网络求解时空PDE
PhyGNNet: Solving spatiotemporal PDEs with Physics-informed Graph Neural Network
论文作者
论文摘要
解决部分微分方程（PDE）是物理，生物学和化学领域的重要研究手段。作为数值方法的近似替代方法，Pinn在许多领域都受到了广泛的关注，并在许多领域发挥了重要作用。但是，Pinn使用完全连接的网络作为其模型，该模型在时间和空间中具有有限的拟合能力和有限的外推能力。在本文中，我们提出了用于求解图形神经网络基础的部分微分方程的Phygnnet，该方程由编码器，处理器和解码器块组成。特别是，我们将计算区域分为常规网格，在网格上定义部分差分运算符，然后构建PDE损失以使网络优化以构建Phygnnet模型。更重要的是，我们对汉堡方程和热方程进行了比较实验来验证我们的方法，结果表明，与PINN相比，我们的方法在时间和空间区域具有更好的拟合能力和外推能力。
Solving partial differential equations (PDEs) is an important research means in the fields of physics, biology, and chemistry. As an approximate alternative to numerical methods, PINN has received extensive attention and played an important role in many fields. However, PINN uses a fully connected network as its model, which has limited fitting ability and limited extrapolation ability in both time and space. In this paper, we propose PhyGNNet for solving partial differential equations on the basics of a graph neural network which consists of encoder, processer, and decoder blocks. In particular, we divide the computing area into regular grids, define partial differential operators on the grids, then construct pde loss for the network to optimize to build PhyGNNet model. What's more, we conduct comparative experiments on Burgers equation and heat equation to validate our approach, the results show that our method has better fit ability and extrapolation ability both in time and spatial areas compared with PINN.
