# Data-augmented Learning of Geodesic Distances in Irregular Domains through Soner Boundary Conditions

arXiv: https://arxiv.org/abs/2503.04579 · HTML: https://mlsanity.com/paper/2503.04579/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 21 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 12 of 12)

- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Motion Policy Networks](https://mlsanity.com/paper/2210.12209/) (2022)
- [EikoNet: Solving the Eikonal equation with Deep Neural Networks](https://mlsanity.com/paper/2004.00361/) (2020)
- [NTFields: Neural Time Fields for Physics-Informed Robot Motion Planning](https://mlsanity.com/paper/2210.00120/) (2022)
- [Configuration Space Distance Fields for Manipulation Planning](https://mlsanity.com/paper/2406.01137/) (2024)
- [A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systems](https://mlsanity.com/paper/2502.11057/) (2025)
- [Progressive Learning for Physics-informed Neural Motion Planning](https://mlsanity.com/paper/2306.00616/) (2023)
- [Physics-informed Neural Mapping and Motion Planning in Unknown Environments](https://mlsanity.com/paper/2410.09883/) (2024)
- [A fast marching algorithm for the factored eikonal equation](https://mlsanity.com/paper/1607.00973/) (2016)
- [Computing distances and means on manifolds with a metric-constrained Eikonal approach](https://mlsanity.com/paper/2404.08754/) (2024)
- [A Riemannian Take on Distance Fields and Geodesic Flows in Robotics](https://mlsanity.com/paper/2412.05197/) (2024)

## Abstract (arXiv)

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.