Can neural networks learn navigation rules that work in unseen environments?

Neural Navigation Functions embed learning into the mathematical structure of motion planning, using neural networks to adapt a PDE-based planner to new environments without retraining. By mapping geometric features to planner coefficients while preserving the underlying math, the approach guarantees collision avoidance and monotonic progress toward the goal by construction. On diverse geometries the method achieves zero-shot transfer with 5× faster convergence than learned competitors.