# Neural Navigation Functions for Zero-Shot Generalizable Motion Planning

arXiv: https://arxiv.org/abs/2606.03756 · HTML: https://mlsanity.com/paper/2606.03756/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 57 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 29 of 29)

- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [Value Iteration Networks](https://mlsanity.com/paper/1602.02867/) (2016)
- [Learning Sampling Distributions for Robot Motion Planning](https://mlsanity.com/paper/1709.05448/) (2017)
- [Motion Planning Networks](https://mlsanity.com/paper/1806.05767/) (2018)
- [HouseExpo: A Large-scale 2D Indoor Layout Dataset for Learning-based Algorithms on Mobile Robots](https://mlsanity.com/paper/1903.09845/) (2019)
- [NTFields: Neural Time Fields for Physics-Informed Robot Motion Planning](https://mlsanity.com/paper/2210.00120/) (2022)
- [Graph Neural Networks for Motion Planning](https://mlsanity.com/paper/2006.06248/) (2020)
- [Learning Continuous Environment Fields via Implicit Functions](https://mlsanity.com/paper/2111.13997/) (2021)
- [Progressive Learning for Physics-informed Neural Motion Planning](https://mlsanity.com/paper/2306.00616/) (2023)
- [Structure-Preserving Digital Twins via Conditional Neural Whitney Forms](https://mlsanity.com/paper/2508.06981/) (2025)
- [Structure-Preserving Learning Improves Geometry Generalization in Neural PDEs](https://mlsanity.com/paper/2602.02788/) (2026)
- [Generalizable Motion Planning via Operator Learning](https://mlsanity.com/paper/2410.17547/) (2024)
- [Physics-informed Neural Motion Planning on Constraint Manifolds](https://mlsanity.com/paper/2403.05765/) (2024)
- [Physics-informed Temporal Difference Metric Learning for Robot Motion Planning](https://mlsanity.com/paper/2505.05691/) (2025)
- [Train-Once Plan-Anywhere Kinodynamic Motion Planning via Diffusion Trees](https://mlsanity.com/paper/2508.21001/) (2025)
- [Physics-informed sensor coverage through structure preserving machine learning](https://mlsanity.com/paper/2509.10363/) (2025)
- [PC-Planner: Physics-Constrained Self-Supervised Learning for Robust Neural Motion Planning with Shape-Aware Distance Function](https://mlsanity.com/paper/2410.12805/) (2024)
- [Physics-informed Neural Motion Planning via Domain Decomposition in Large Environments](https://mlsanity.com/paper/2506.12742/) (2025)
- [Physics-informed Neural Time Fields for Prehensile Object Manipulation](https://mlsanity.com/paper/2508.02976/) (2025)
- [Motion Planning With Gamma-Harmonic Potential Fields](https://mlsanity.com/paper/1606.09278/) (2016)
- [KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planning](https://mlsanity.com/paper/2509.09074/) (2025)
- [Multi-robot Multi-source Localization in Complex Flows with Physics-Preserving Environment Models](https://mlsanity.com/paper/2509.14228/) (2025)
- [Online Hierarchical Policy Learning using Physics Priors for Robot Navigation in Unknown Environments](https://mlsanity.com/paper/2510.01519/) (2025)
- [A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds](https://mlsanity.com/paper/2605.08436/) (2026)

## Abstract (arXiv)

We introduce Neural Navigation Functions (Neural-NF), a learned reactive navigation function capable of zero-shot transfer across unseen environment geometries. Neural-NF places data-driven adaptation within a structured elliptic planner, where the navigation objective is learned while planner structure is preserved by construction. Specifically, intrinsic Laplacian-derived features are mapped to local PDE coefficients, and solving the resulting boundary value problem produces a globally consistent value function on each target domain. For every admissible learned model, the resulting policy is collision-free, provides monotonic descent and a global minimum at the goal by construction. This admits a linearly-solvable optimal-control interpretation for any parameter setting. Empirically, Neural-NF achieves strong zero-shot transfer across diverse geometries and outperforms learned planners that directly predict the value function by up to a 5× improvement.