PUN 神经算子：在噪声环境下学出噪声感知的导航价值场
Planning under Noise with Neural Operators
一篇做噪声下导航规划的新论文，用 Neumann 边界条件加 Monte Carlo 标签训练出能跨几何泛化的价值场，4D 重规划成功率 95% 以上还比对手快几十倍。
研究团队提出 Planning Under Noise（PUN），一个学习噪声感知价值场的神经算子，用于控制执行存在噪声时的规划任务。方法上将障碍物边界从零 Dirichlet 改为反射 Neumann 条件，并在目标处设 Dirichlet 条件，让采样路径可以继续探索自由空间直到抵达目标。为避免逐例完整求解 PDE，PUN 从部分收敛的 Monte Carlo 标签（基于 Walk on Stars 求解器）学习几何到场（geometry-to-field）的映射，推理时再用局部搜索做测试时扩展。在 4D 重规划基准的四种噪声水平上，PUN 达到 95-100% 成功率且运行时间最低；在最高噪声水平下相对其他方法成功率提升 10.7-60.6%，速度快 3.29-32.15 倍。
Planning under Noise with Neural Operators
Planning under uncertain control execution noise requires reliable feedback policies across diverse environments. We introduce Planning Under Noise (PUN), a neural operator that learns noise-aware value fields for planning in unseen geometries. Building on an established screened-Poisson formulation of stochastic optimal control, we address two challenges: specifying boundary conditions that support navigation across varying geometries and efficiently computing fields with reliable gradients. Zero-Dirichlet obstacle boundaries terminate sampled paths at walls, weakening the goal signal along long routes and making it harder to estimate reliably. We instead impose reflecting Neumann conditions on obstacles and a Dirichlet condition at the goal, allowing sampled paths to continue exploring free space until they reach the target. To solve the resulting PDE without a configuration-space mesh, we extend a Monte Carlo (MC) solver, Walk on Stars (WoSt), to higher dimensions. However, local MC fluctuations can reverse estimated gradient directions and cause planning failures, making direct planning require costly sampling. PUN amortizes this computation by learning geometry-to-field mappings from noisy, partially converged Monte Carlo labels, avoiding expensive convergence for every training example. At inference, test-time scaling uses bounded local search guided by the predicted global field. We evaluate PUN on planning tasks across dimensions. Across four noise levels, PUN matches or outperforms all compared planners, achieving 95-100% success on the 4D replanning benchmark while maintaining the lowest runtime. At the highest tested noise level in 4D, PUN achieves 10.7-60.6% relative gains in success rate over other methods while running 3.29-32.15 times faster.