Auxiliary-Tasks Learning for Physics-Informed Neural Network-Based Partial Differential Equations Solving

• DOI: 10.48550/arxiv.2307.06167
• Publication Date: 2023-01-01
• Authors: Junjun Yan; Xinhai Chen; Zhichao Wang; Enqiang Zhou; Jie Liu
• Keywords: Code (set theory); Limiting

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 networks. However, original PINNs often suffer from bottlenecks, such low accuracy and non-convergence, limiting their applicability complex physical contexts. To alleviate these issues, we proposed auxiliary-task learning-based physics-informed (ATL-PINNs), which provide four different learning investigate performance compared with PINNs. We also employ gradient cosine similarity algorithm integrate auxiliary problem loss primary ATL-PINNs, aims enhance of modes. best our knowledge, this is first study introduce context learning. conduct experiments on three PDE problems across fields scenarios. Our findings demonstrate that can significantly improve solution accuracy, achieving a maximum boost 96.62% (averaging 28.23%) single-task The code dataset are open source at https://github.com/junjun-yan/ATL-PINN.