ST-PINN: A Self-Training Physics-Informed Neural Network for Partial
  Differential Equations
Junjun Yan Xinhai Chen Zhichao Wang Enqiang Zhoui Jie Liu
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.