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.

翻译：物理信息神经网络（PINNs）已成为求解偏微分方程（PDEs）的有前途的替代模型。其有效性在于能够通过神经网络捕获与解相关的特征。然而，原始PINNs常面临低精度和不收敛等瓶颈，限制了其在复杂物理场景中的适用性。为解决这些问题，我们提出了基于辅助任务学习的物理信息神经网络（ATL-PINNs），该网络提供了四种不同的辅助任务学习模式，并研究了其与原始PINNs相比的性能表现。我们还采用梯度余弦相似度算法将辅助问题损失与主问题损失在ATL-PINNs中进行整合，旨在增强辅助任务学习模式的有效性。据我们所知，这是首次在物理信息学习背景下引入辅助任务学习模式的研究。我们在不同领域和场景的三个PDE问题上进行了实验。实验结果表明，所提出的辅助任务学习模式能显著提高解精度，与原始单任务PINNs相比，性能提升最高达96.62%（平均提升28.23%）。代码和数据集已在https://github.com/junjun-yan/ATL-PINN开源。