# Physics-Unrolled Neural Operator for Wireless Field Modeling

arXiv: https://arxiv.org/abs/2608.18495 · HTML: https://mlsanity.com/paper/2608.18495/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 53 references that are in the map.
- First posted on arXiv 19 Aug 2026.

## Builds on (most cited first, 30 of 31)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Image Quality Assessment: Unifying Structure and Texture Similarity](https://mlsanity.com/paper/2004.07728/) (2020)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [RadioUNet: Fast Radio Map Estimation with Convolutional Neural Networks](https://mlsanity.com/paper/1911.09002/) (2019)
- [Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport](https://mlsanity.com/paper/2204.06684/) (2022)
- [Multi-Grid Tensorized Fourier Neural Operator for High-Resolution PDEs](https://mlsanity.com/paper/2310.00120/) (2023)
- [Sionna RT: Differentiable Ray Tracing for Radio Propagation Modeling](https://mlsanity.com/paper/2303.11103/) (2023)
- [Pretraining Codomain Attention Neural Operators for Solving Multiphysics PDEs](https://mlsanity.com/paper/2403.12553/) (2024)
- [Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems](https://mlsanity.com/paper/2204.09157/) (2022)
- [NeRF2: Neural Radio-Frequency Radiance Fields](https://mlsanity.com/paper/2305.06118/) (2023)
- [NeWRF: A Deep Learning Framework for Wireless Radiation Field Reconstruction and Channel Prediction](https://mlsanity.com/paper/2403.03241/) (2024)
- [Dataset of Pathloss and ToA Radio Maps With Localization Application](https://mlsanity.com/paper/2212.11777/) (2022)
- [Learning Radio Environments by Differentiable Ray Tracing](https://mlsanity.com/paper/2311.18558/) (2023)
- [GSRF: Complex-Valued 3D Gaussian Splatting for Efficient Radio-Frequency Data Synthesis](https://mlsanity.com/paper/2502.01826/) (2025)
- [Radio Frequency Ray Tracing with Neural Object Representation](https://mlsanity.com/paper/2411.18635/) (2024)
- [Physics-Informed Generative Modeling of Wireless Channels](https://mlsanity.com/paper/2502.10137/) (2025)
- [Toward Real-Time Digital Twins of EM Environments: Computational Benchmark of Ray Launching Software](https://mlsanity.com/paper/2406.05042/) (2024)
- [Accelerating Ray Tracing-Based Wireless Channels Generation for Real-Time Network Digital Twins](https://mlsanity.com/paper/2504.09751/) (2025)

## Abstract (arXiv)

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.