arXiv:2610.34345v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising mesh-free framework for solving partial differential equations (PDEs), with broad applications in physics, engineering, and medicine. However, their performance is highly sensitive to the sampling strategy for training points. Conventional uniform sampling often fails to adequately resolve regions with complex solution features, leading to low efficiency and limited accuracy. To address these challenges, we propose a Lie symmetry-driven adaptive sampling framework for PINNs, termed Lie-AS-ISC. For PDEs admitting Lie symmetry groups, symmetry transformations are exploited to derive intrinsic functional relationships between the solution and its variables, enabling the construction of basis points with exact solutions that span the solution domain. Building on this, an adaptive sampling strategy is developed by jointly considering absolute error and invariant surface conditions, while a dual-index loss is introduced to enhance training constraints. The proposed method significantly improves prediction accuracy. The experimental results show that this method consistently outperforms existing methods in accuracy.