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文章背景与核心概要

准确的无线场建模（例如用于接入点部署、覆盖规划和定位的无线电图预测）长期以来一直受到高精度模拟高计算成本的限制。虽然机器学习提供了一种高效的替代方案，但大规模生成高保真训练数据仍然是一个挑战，因为低成本的标签通常来自带有残余蒙特卡洛噪声的有限射线模拟。

为了克服这一难题，作者推出了物理展开混合神经算子（Physics-Unrolled Hybrid Neural Operator, PU-HNO）。与将无线电图视为通用图像的做法不同，PU-HNO 被设计为一个结构化的三阶段级联网络，能够逐步捕获核心的无线电波传播现象：反射、衍射和散射。作者证明，在条件无偏标签噪声下，该模型能够成功学习到稳定的传播结构，甚至能够超越其训练标签本身的质量。在各种不同楼层平面图上进行的广泛实验表明，无论是在标准图像质量指标还是无线部署指标上，PU-HNO 都明显优于现有的图像到图像基线模型、无线学习模型以及单体神经算子。

Physics-Unrolled Neural Operator for Wireless Field Modeling

arXiv: 2608.18495 [cs.LG]
Submitted: August 19, 2026
Authors: Rafid Umayer Murshed, Saif Ur Rahman, Mingyue Tang, Elahe Soltanaghai
Primary Subject: Machine Learning (cs.LG), Artificial Intelligence (cs.AI)

arXiv: 2608.18495 [cs.LG]
Submitted: August 19, 2026
Authors: Rafid Umayer Murshed, Saif Ur Rahman, Mingyue Tang, Elahe Soltanaghai
Primary Subject: Machine Learning (cs.LG), Artificial Intelligence (cs.AI)

Summary

无线电图对于无线决策任务（如接入点部署、覆盖规划和定位）至关重要，但其精细的空间细节受复杂的传播效应支配，准确模拟的成本很高。机器学习提供了一条无需为每个场景运行昂贵的高保真模拟即可进行高保真无线电图预测的途径。

然而，大规模生成高质量的训练标签也很困难：经济实惠的标签来自有限射线模拟，这些模拟比低保真输入更丰富，但带有残余的蒙特卡洛噪声。为了应对这一挑战，我们引入了物理展开混合神经算子（PU-HNO），这是一个三阶段级联网络，它通过逐步捕获反射、衍射和散射效应，而不是将无线电图视为通用图像，从低保真射线追踪输出和场景先验中预测高保真室内无线电图。

我们证明，在条件无偏标签噪声下，该模型可以学习稳定的传播结构并优于其自身的训练标签。跨不同楼层平面图的实验表明，PU-HNO 在图像质量和无线部署指标上均优于图像到图像基线、无线学习模型和单体神经算子。

Summary

Accurate wireless field modeling—such as radio-map prediction for access-point placement, coverage planning, and localization—is traditionally bottlenecked by the high computational cost of fine-grained simulations. While machine learning offers an efficient alternative, generating high-fidelity training data at scale remains a challenge because affordable labels are typically derived from finite-ray simulations burdened by residual Monte Carlo noise.

To overcome this, the authors introduce the Physics-Unrolled Hybrid Neural Operator (PU-HNO). Rather than treating radio maps as generic images, PU-HNO is designed as a structured three-stage cascade that progressively captures core wireless propagation phenomena: reflection, diffraction, and scattering. The authors prove that under conditionally unbiased label noise, the model successfully learns stable propagation structures and can even surpass the quality of its own training labels. Extensive experiments across diverse floorplans demonstrate that PU-HNO outperforms existing image-to-image baselines, wireless learning models, and monolithic neural operators across both standard image-quality and wireless deployment metrics.

Abstract

无线电图对于接入点部署、覆盖规划和定位等无线决策任务至关重要，但其精细的空间细节受复杂的传播效应控制，且精确模拟成本高昂。机器学习提供了一条途径，无需为每个场景运行昂贵的高保真模拟即可实现高保真无线电图预测。

然而，大规模生成高质量的训练标签也很困难：经济实惠的标签来自有限射线模拟，这些模拟比低保真输入更丰富，但也带有残余的蒙特卡洛噪声。我们通过物理展开混合神经算子（PU-HNO）来应对这一挑战，这是一个三阶段级联，它从低保真射线追踪输出和场景先验中预测高保真室内无线电图，通过逐步捕获反射、衍射和散射效应，而不是将无线电图视为通用图像。

我们证明，在条件无偏标签噪声下，该模型可以学习稳定的传播结构，并超越其自身的训练标签。跨不同楼层平面图的实验表明，PU-HNO 在图像质量和无线部署指标上均优于图像到图像基线、无线学习模型和单体神经算子。

Abstract

Radio maps are essential for wireless decision-making tasks such as access-point placement, coverage planning, and localization, but their fine spatial details are governed by complex propagation effects and are costly to simulate accurately. Machine learning offers a path to high-fidelity radio-map prediction without running expensive high-fidelity simulations for every scene.

However, generating high-quality training labels at scale is also difficult: the affordable labels come from finite-ray simulations, which are richer than low-fidelity inputs but carry residual Monte Carlo noise. We address this challenge with Physics-Unrolled Hybrid Neural Operator (PU-HNO), a three-stage cascade that predicts high-fidelity indoor radio maps from low-fidelity ray-tracing outputs and scene priors by progressively capturing reflection, diffraction, and scattering effects, rather than treating radio maps as generic images.

We prove that, under conditionally unbiased label noise, the model can learn stable propagation structure and outperform its own training labels. Experiments across diverse floorplans show that PU-HNO outperforms image-to-image baselines, wireless learning models, and monolithic neural operators across both image-quality and wireless deployment metrics.

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