Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast PDE solving in various applications. To address the issue of low accuracy and convergence problems of existing PINNs, we propose a self-training physics-informed neural network, ST-PINN. Specifically, ST-PINN introduces a pseudo label based self-learning algorithm during training. It employs governing equation as the pseudo-labeled evaluation index and selects the highest confidence examples from the sample points to attach the pseudo labels. To our best knowledge, we are the first to incorporate a self-training mechanism into physics-informed learning. We conduct experiments on five PDE problems in different fields and scenarios. The results demonstrate that the proposed method allows the network to learn more physical information and benefit convergence. The ST-PINN outperforms existing physics-informed neural network methods and improves the accuracy by a factor of 1.33x-2.54x. The code of ST-PINN is available at GitHub: https://github.com/junjun-yan/ST-PINN.

本文提出了一种基于自我训练的物理学受控神经网络(ST-PINN)的方法, 通过选取具有高置信度的样本点作为伪标签进行训练, 从而提高神经网络学习物理信息的效果及其收敛性, 在五个不同场景下进行的实验表明该方法优于现有的物理受控神经网络方法, 并将精度提高了1.33x-2.54x。

ST-PINN: 基于自学习的物理知识神经网络用于偏微分方程