用深度学习和物理信息网络高效计算参数曲面上的测地线类曲线
A Neural Network Framework for Geodesic-Like Curve Computation on Parametric Surfaces
- 基于物理信息神经网络构建测地线类曲线计算框架
- 可处理单曲面及多曲面系统，支持C^0及以上连续性
- 兼顾效率与鲁棒性，适用于复杂几何结构建模
2010年陈提出测地线类曲线概念，用于估计参数曲面上的最短路径（测地线），并已建立理论收敛性。然而，高效的数值计算框架尚未实现。本文提出一种优雅且高效的方法，利用深度学习与物理信息神经网络（PINNs）计算测地线类曲线。该框架不仅能高效处理单个参数曲面，还可稳健应对具有C^0或更高连续性的复杂多曲面系统以及旋转曲面等广义参数曲面。
原文摘要 · Abstract (English)
The concept of geodesic-like curves was introduced by Chen in 2010 as a method for estimating shortest paths (geodesics) on parametric surfaces, with its convergence established theoretically. However, an efficient numerical computational framework has not yet been developed. In this paper, we propose an elegant and efficient approach for computing geodesic-like curves by leveraging deep learning and Physics-Informed Neural Networks (PINNs). Under the proposed framework, not only can single parametric surfaces be handled efficiently, but a broad class of complex parametric surfaces including multi-surface systems with $C^0$ or higher continuity and surfaces of revolution can also be robustly addressed.
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