用数据增强提升不规则区域测地距离学习的稳定性
Data-augmented Learning of Geodesic Distances in Irregular Domains through Soner Boundary Conditions
- 引入Soner边界条件结合数据损失，改进物理信息神经网络训练
- 数据损失使训练收敛更鲁棒，降低对初始值敏感性
- 适合在稀疏数据下需可靠测地距离的机器人应用
测地距离在机器人领域至关重要，能高效编码域的全局几何信息。近期方法通过物理信息神经网络求解Eikonal方程来近似测地距离，但在复杂环境中常出现训练不稳定问题。本文提出一种基于Soner边界条件的数据增强框架，系统评估了数据损失对训练稳定性和解精度的影响。实验表明，引入数据损失显著提升了收敛鲁棒性，减少了训练不稳定性与初始化敏感性。结果表明，混合数据-物理方法可在稀疏数据条件下有效增强学习型测地距离求解器的可靠性。
原文摘要 · Abstract (English)
Geodesic distances play a fundamental role in robotics, as they efficiently encode global geometric information of the domain. Recent methods use neural networks to approximate geodesic distances by solving the Eikonal equation through physics-informed approaches. While effective, these approaches often suffer from unstable convergence during training in complex environments. We propose a framework to learn geodesic distances in irregular domains by using the Soner boundary condition, and systematically evaluate the impact of data losses on training stability and solution accuracy. Our experiments demonstrate that incorporating data losses significantly improves convergence robustness, reducing training instabilities and sensitivity to initialization. These findings suggest that hybrid data-physics approaches can effectively enhance the reliability of learning-based geodesic distance solvers with sparse data.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。