Auxiliary-Tasks Learning for Physics-Informed Neural Network-Based
  Partial Differential Equations Solving
Junjun Yan Xinhai Chen Zhichao Wang Enqiang Zhou Jie Liu
Physics-informed neural networks (PINNs) have emerged as promising surrogate
modes for solving partial differential equations (PDEs). Their effectiveness
lies in the ability to capture solution-related features through neural
networks. However, original PINNs often suffer from bottlenecks, such as low
accuracy and non-convergence, limiting their applicability in complex physical
contexts. To alleviate these issues, we proposed auxiliary-task learning-based
physics-informed neural networks (ATL-PINNs), which provide four different
auxiliary-task learning modes and investigate their performance compared with
original PINNs. We also employ the gradient cosine similarity algorithm to
integrate auxiliary problem loss with the primary problem loss in ATL-PINNs,
which aims to enhance the effectiveness of the auxiliary-task learning modes.
To the best of our knowledge, this is the first study to introduce
auxiliary-task learning modes in the context of physics-informed learning. We
conduct experiments on three PDE problems across different fields and
scenarios. Our findings demonstrate that the proposed auxiliary-task learning
modes can significantly improve solution accuracy, achieving a maximum
performance boost of 96.62% (averaging 28.23%) compared to the original
single-task PINNs. The code and dataset are open source at
https://github.com/junjun-yan/ATL-PINN.