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A Tutorial on Learning-Based Radio Map Construction: Data, Paradigms, and Physics-Awareness

Xiucheng Wang, Yuhao Pan, Nan Cheng, Çağkan Yapar, Ruijin Sun, Zhisheng Yin, Conghao Zhou, Wenchao Xu, Yuxiang Zhang, Jianhua Zhang, Shuguang Cui, Xuemin Shen

arXiv:2603.17499v7eess.SYeess.SP

TL;DR

Learning-based radio-map construction is constrained by ill-posed inversion, data precision limits, and mismatches between optical formulations and complex-valued RF propagation. The paper compares reconstruction paradigms and physics-aware methods, finding differentiated architecture trade-offs and improved physical fidelity from NeRF and 3DGS approaches.

  • Problem

    Radio-map reconstruction is ill-posed, while sparse or coarse measurements can lose information needed for phase-sensitive modeling and complex NLoS propagation.

  • Method

    The paper surveys measurement strategies, neural reconstruction architectures, diffusion acceleration, and optics-inspired NeRF and 3DGS methods for radio-map construction.

  • Results

    CNNs offer low cost above 5% sparsity, ViTs perform strongly at extreme sparsity, diffusion models provide broad capability with higher latency, and NeRF and 3DGS improve physical fidelity.

  • Takeaways & Limitations

    Architecture choice should reflect sparsity, latency, ground-truth availability, and the required level of physical fidelity.

  • Takeaways & Limitations

    Coarse 1 m datasets are unsuitable for phase-sensitive MIMO modeling, while optical NeRF formulations require substantial redesign for complex-valued RF propagation.

Abstract

from arXiv · show

Radio maps (RMs) provide the digital representation of the wireless propagation environment, mapping complex geographical and topological boundary conditions to critical spatial-spectral metrics that range from received signal strength to full channel state information matrices. The integration of artificial intelligence into next generation wireless networks further necessitates the accurate construction of RMs as a foundational prerequisite for electromagnetic digital twins. This paper presents a comprehensive survey of learning-based RM construction, systematically addressing three intertwined dimensions: data, paradigms, and physics-awareness. From the data perspective, we review physical measurement campaigns, ray tracing simulation engines, and publicly available benchmark datasets, identifying their respective strengths and fundamental limitations. From the paradigm perspective, we establish a core taxonomy that categorizes RM construction into source-aware forward prediction and source agnostic inverse reconstruction, and examine five principal neural architecture families spanning convolutional neural networks, vision transformers, graph neural networks, generative adversarial networks, and diffusion models. We further survey optics-inspired methods adapted from neural radiance fields and 3D Gaussian splatting for continuous wireless radiation field modeling. From the physics-awareness perspective, we introduce a three-level integration framework encompassing data-level feature engineering, loss-level partial differential equation regularization, and architecture level structural isomorphism. Open challenges including foundation model development, physical hallucination detection, and mortized inference for real-time deployment are discussed to outline future research directions. The project page is at https://github.com/UNIC-Lab/Awesome-Radio-Map-Categorized.

I. INTRODUCTION

Radio-map construction supports electromagnetic digital twins by representing wireless propagation across space, but data scarcity, computational cost, sparse inverse reconstruction, and physical inconsistency remain central challenges. The tutorial organizes these challenges through data sources, forward/inverse paradigms, neural architectures, generative and rendering methods, and physics-aware integration.

  • Radio maps digitally represent wireless propagation environments and are a prerequisite for electromagnetic digital twins.
  • Data ecosystem: Physical campaigns capture real propagation but incur high costs, limited coverage, difficult three-dimensional surveying, and device-dependent measurement noise.
  • Data ecosystem: Ray tracing and dominant-path methods synthesize physically grounded data, yet ray-tracing scalability and simulation latency limit city-scale dynamic and real-time use.
  • Problem paradigms: The tutorial distinguishes source-aware forward prediction from source-agnostic inverse reconstruction, where sparse observations require recovery of a global field.
  • Architectures: CNNs, ViTs, and GNNs address spatial modeling through localized mappings, global attention, and graph-based physical interactions, respectively.
  • Generative and rendering methods: GANs and diffusion models support generative reconstruction under severe sparsity, while NeRF and 3DGS model continuous wireless radiation fields but remain costly for dynamic scenes.
  • Physics awareness: Physics-informed methods incorporate electromagnetic laws into data representations, losses, or architectures to address physical hallucinations from unconstrained latent spaces.
  • Contributions: The tutorial contributes a data ecosystem, a forward-inverse architectural taxonomy, and a three-level physics-informed integration framework.

4) Intrinsic Properties:

The section introduces radio-map and related map concepts alongside diffusion, neural-rendering, and continuous-time formulations used to model spatial wireless fields. These frameworks trade representational fidelity, sampling requirements, and inference efficiency.

  • Diffusion models: Diffusion models generate plausible fields through forward noise injection and reverse denoising, with training commonly reduced to noise prediction.
  • Diffusion models: The DDPM formulation uses a timestep-dependent variance schedule and permits direct sampling at arbitrary diffusion times.
  • Continuous-time diffusion: Continuous-time SDE formulations generalize discrete diffusion and connect score-based inference with adaptive solvers and physics-informed stochastic control.
  • Neural rendering: NeRF represents scenes as continuous functions of spatial location and viewing direction, then synthesizes observations through differentiable volume rendering.
  • Neural rendering: RF rendering requires finer sampling than optical rendering because centimeter- and millimeter-scale propagation is phase-sensitive and dominated by multipath interference.

2) Positional Encoding:

Radio-map representations balance physical fidelity, computational cost, and generalization by encoding geometry, materials, semantics, transmitter conditions, and directional structure at different resolutions. Optical rendering primitives require substantial adaptation for complex-valued RF propagation.

  • Positional Encoding: Fourier features encode spatial coordinates at multiple frequencies, with RF resolution requirements tied to wavelength-scale variations.
  • Positional Encoding: Optical NeRF assumptions do not transfer directly to RF because wireless fields are complex-valued and shaped by multipath interference and diffraction.
  • 3D Gaussian Splatting: 3DGS replaces MLP-based ray marching with explicit anisotropic Gaussian primitives whose centers and covariances represent scene structure.
  • Directional Appearance: Spherical harmonics describe directional appearance, but RF angular fluctuations and complex signals motivate complex-valued Fourier-Legendre expansions.
  • Environment Representation: Environment tensors combine geometry, electromagnetic materials, and semantic labels as digital boundary conditions for electromagnetic modeling.
  • Environment Representation: Geometry encoding ranges from lightweight 2D occupancy maps to 2.5D height maps and full 3D voxel grids, trading fidelity against memory and representational scope.
  • Generalization Boundaries: The taxonomy table links deployment scenarios with environment representations, condition embedding strategies, and physical dimensions where models cannot generalize without retraining.
  • Transmitter Encoding: Transmitter conditions can use binary masks, differentiable Gaussian heatmaps, or embedded scalars such as power, frequency, and downtilt.

3) Condition Embedding Mechanisms:

Condition injection determines how effectively RM models use environmental and transmitter information, while generalization is bounded by the physical dimensions explicitly represented in the input. The section also distinguishes source-aware forward prediction from source-agnostic inverse reconstruction and relates architectural choices to propagation domains.

  • Condition injection strategies: Input concatenation is simple but treats all condition channels uniformly, whereas cross-attention separately encodes conditions and injects them through queries, keys, and values.RadioUNet uses building and transmitter maps as two channels; RadioDiff uses separate static and dynamic obstacle prompts.
  • Condition injection strategies: Adaptive layer normalization generates scale and shift parameters for scalar or low-dimensional conditions such as carrier frequency and transmit power.For spatially varying conditions such as building geometry, adaLN must be complemented by spatial conditioning.
  • Condition injection strategies: State-of-the-art frameworks combine input concatenation, convolutional spatial encoding, and adaLN for continuous beam vectors.Combining mechanisms matches different condition types to different injection pathways.
  • Generalization boundary: Generalization is bounded by the physical dimensions explicitly represented in the input; absent dimensions cannot be generalized over.Binary occupancy maps cannot distinguish building heights, hard-coded transmitter locations cannot support unseen positions, and implicit carrier frequency confines models to one band.
  • RM construction paradigms: Source-aware mapping predicts global electromagnetic coverage from environment and transmitter parameters, while source-agnostic mapping reconstructs complete fields from sparse measurements when transmitter parameters are unavailable.The source-aware task approximates physical solvers; the source-agnostic task is an ill-posed nonlinear inverse problem requiring structural priors.
  • Environmental domains: Indoor RM models require precise 3D structural representations, whereas outdoor models require global receptive fields to capture long-distance blockage correlations.Indoor settings emphasize wall penetration and dense multipath; outdoor settings emphasize line-of-sight blockage, shadowing, and diffraction.

F. Target RM and Mapping Function

This section defines radio maps as multidimensional channel tensors and distinguishes forward surrogate modeling from inverse spatial interpolation and latent-source estimation. It then connects measurement and simulation workflows to their respective fidelity, scalability, and sampling trade-offs.

  • Target RM representation: The target radio map is a tensor M ∈ R^H×W×C_M whose channels encode wireless metrics such as RSS, ToA, and SINR.A three-channel example contains RSS in dBm, ToA in nanoseconds, and SINR in dB.
  • Mapping functions: Forward RM construction uses a differentiable surrogate solver, whereas inverse construction uses a spatial interpolator and latent-source estimator.The inverse setting reconstructs a complete field from sparse observations when transmitter parameters are latent or unavailable.
  • Sampling paradox: Three non-collinear line-of-sight measurements suffice for free-space trilateration in an idealized 2D setting, but multipath fluctuations of 5–15 dB create substantial practical errors.Urban diffraction, blockage, and frequency-selective fading can invalidate geometric inversion.
  • Sampling paradox: Physics-aware adaptive sampling targets diffraction corners, shadow boundaries, high-entropy zones, and uncertain NLoS regions rather than uniformly sampling predictable LoS areas.Active learning can use predictive uncertainty to select high-variance locations and improve sample efficiency.
  • Data acquisition: Physical measurements provide ground truth and real-channel stochasticity, while simulations offer scalability but may simplify complex multipath scattering and hardware impairments.Drive and walk tests collect geolocated signal-quality indicators, and campaigns remain operationally constrained.
  • Data acquisition: Crowdsourced UE and UAV measurements expand temporal and three-dimensional coverage but require device calibration and energy-constrained trajectory design.UE reports include device-specific noise and antenna-gain variation; UAV planning can maximize information gain in uncertain regions.
  • Ray tracing simulation: SBR provides high-fidelity phase-aware multipath modeling but scales with ray count, object count, and interaction order, making city-scale generation expensive.Its complexity is expressed as O(N_rays × N_obj^K_max).
  • Ray tracing simulation: DPM reduces complexity to approximately O(N_Rx × N_obj) by retaining dominant paths, trading high-order interaction fidelity for orders-of-magnitude faster dataset generation.The method exploits the observation that over 95% of received energy comes from a sparse set of dominant paths.

C. Data Preprocessing and Representation

RM preprocessing converts spatial data into standardized tensors while embedding geometric and material features that approximate propagation-relevant boundary conditions. Public datasets broaden evaluation coverage but remain limited by synthetic-data gaps, quantization, and coarse spatial resolution.

  • Rasterization discretizes vector-based CAD or GIS maps into binary occupancy grids, while feature engineering adds physical priors.
  • Edge maps highlight building walls and corners where reflection losses and diffraction are concentrated.Sobel or Laplacian kernels compute edge intensity maps, while UTD motivates emphasizing structural corners.
  • Material-property maps encode relative permittivity and conductivity, but deterministic assignments contribute to the simulation-to-reality gap.The composite environment tensor concatenates these channels with other inputs.
  • Public benchmarks span 2D, indoor, 3D, multimodal, temporal, beam-specific, and channel-matrix RM tasks.RadioMapSeer contains 56,080 simulated 2D maps, while UrbanRadio3D provides 11.2 million labeled points across 20 height layers.
  • Synthetic solvers create domain gaps, 8-bit encoding introduces approximately 0.4 dB quantization steps over 100 dB, and 1 m grids can alias centimeter-wavelength phase information.These limitations motivate calibrated measurements, higher precision, finer resolution, and frequency-dependent material models.

V. LEARNING-BASED METHODS FOR SOURCE-AWARE RADIO MAPPING

Source-aware RM construction has evolved across architectures that trade off latency, data efficiency, spatial modeling, and output modality. CNNs provide strong baselines, while attention and specialized spatial mechanisms address long-range dependencies, sparse inputs, and three-dimensional structure.

  • The source-aware architecture landscape includes CNNs, ViTs, GNNs, GANs, and diffusion models, with no single family dominating every trade-off.
  • CNN-based methods: CNN encoder-decoder models establish image-to-image RM prediction, but pooling and fixed receptive fields can lose boundary detail and long-range dependencies.RadioUNet uses building maps and transmitter position as inputs, while PPNet preserves pooling indices during decoding.
  • CNN-based methods: PPNet’s two-phase training and preserved pooling indices stabilize convergence and improve accuracy near building boundaries.
  • CNN-based methods: Atrous, deformable, and pyramid-based convolutions expand receptive fields to capture propagation structures across spatial scales.The tutorial recommends atrous convolutions for regular grids and deformable convolutions for irregular propagation-relevant structures.
  • CNN-based methods: 2D tensor designs can encode discrete vertical information without full 3D convolutions, but they cannot represent continuous vertical interactions such as interfloor wave guiding.R2Net uses height-indexed inputs and output channels for 3D path-loss prediction.
  • ViT-based methods: RMTransformer achieves an RMSE of 0.0071 on USC, approximately 62% lower than RadioUNet and 32% lower than PMNet.Its MaxViT encoder combines block attention for local boundaries with grid attention for global structure.
  • ViT-based methods: With only 50 sampling points, DAT-Unet reduces RMSE by approximately 12% compared to RadioUNet.Deformable attention learns offsets toward structurally relevant regions such as building corners and observation points.

C. GNN-Based Methods

Graph and generative approaches model propagation beyond ordinary pixel mappings. GNNs represent heterogeneous, non-Euclidean interactions, while GANs and diffusion models generate spatially coherent or probabilistic maps under sparse and incomplete observations.

  • GNN-based methods: GNNs represent spatial or spectral elements as nodes and physical interactions as edges, accommodating heterogeneous entities and non-uniform sampling.
  • GNN-based methods: RadioGAT constructs radio-depth features from obstruction, distance fading, and frequency fading, enabling masked semisupervised training.
  • GNN-based methods: GNN-MDAR uses a variational information bottleneck to discard domain-specific graph noise after propagation-relevant structure stabilizes.
  • GNN-based methods: WirelessNet uses heterogeneous message passing with separate user-equipment and base-station node types and distinct communication and interference edges.
  • GNN-based methods: Dense graphs with millions of nodes remain a scalability limitation for GNN message passing.
  • Generative methods: GANs generate spatially coherent maps with sharper shadow boundaries, while physics-embedded objectives can align generation with operational spectrum-management requirements.TiRE-GAN uses a radio-depth input and task-incentivized regularization from a pretrained outage-detection network.

1) Foundational Methods and Sparse Scenarios:

Diffusion and related generative methods address increasingly sparse and ill-posed RM reconstruction, while acceleration techniques target real-time deployment. Their probabilistic outputs support nonlinear downstream expectations, but stochastic sampling does not provide explicit parameter uncertainty.

  • Foundational methods and sparse scenarios: Diffusion methods model RM construction as conditional generation for dynamic, indoor, vehicular, transmitter-unknown, super-resolution, and 3D scenarios.
  • Real-time acceleration: Iterative denoising creates a real-time latency bottleneck, motivating pruning, latent caching, flow matching, and token-prediction alternatives.
  • Real-time acceleration: RadioDiff-Turbo reduces sampling from 1000 to 10 steps and reaches approximately 60 ms inference latency without network retraining.
  • Real-time acceleration: Caching shared-environment diffusion states delivers 3.5–58× acceleration with less than 0.15% accuracy degradation.Early denoising recovers shared building topology, while later steps refine scene-specific details.
  • Real-time acceleration: RadioFlow achieves single-step generation with 63 ms latency and 8.3× parameter reduction by replacing stochastic diffusion with continuous normalizing flows.
  • Probabilistic reconstruction: Diffusion sampling estimates expectations of nonlinear RM functionals such as channel capacity and bit error rate, unlike deterministic point estimates.
  • Probabilistic reconstruction: The generated variability represents aleatoric uncertainty, not explicit epistemic uncertainty over model parameters.
  • Sparse scenarios: Source-agnostic reconstruction becomes severely ill-posed as sampling decreases, motivating a transition from deterministic completion toward probabilistic generation.

3) High-Dimensional Tensor Extension:

High-dimensional RM reconstruction extends beyond dense image regression by using tensor completion, attention, equivariance, generative models, and latent representations for sparse or structured observations.

  • High-Dimensional Tensor Extension: Online robust 4D tensor completion tracks low-rank subspaces across streaming space-frequency-time measurements while rejecting outliers.ROASMP combines temporal pre-filling, attention-based forgetting, CP decomposition, ℓ1 regularization, ADMM, and recursive least squares.
  • CNN-Based Methods: CNN inverse methods remain computationally efficient for edge devices but cannot represent diverse reconstructions or uncertainty below 5% sampling.The limitation becomes important when sparse observations make the inverse solution non-unique.
  • ViT-Based Methods: ViTs process variable-sized sparse point sets as tokens, avoiding zero-padding and information dilution from dense-grid rasterization.Their attention mechanism also captures long-range spatial structure and supports physical equivariance designs such as STORM.
  • GAN-Based Methods: GAN methods generate global RM patterns from environmental inputs and can operate without intermediate RSS measurements using satellite imagery.Satellite inputs provide fine spatial resolution but omit building heights, material properties, and temporal updates.
  • Diffusion-Based Methods: Diffusion approaches provide probabilistic reconstruction and can combine learned priors with latent-space or multi-scale conditioning.RadioDiff-Inverse uses a pretrained prior, while other approaches reduce dimensionality or accelerate inference through latent representations.

3) Handling Extreme Observational Degradations:

Extreme observational degradation motivates probabilistic and physics-aware reconstruction, while optics-inspired fields provide continuous representations but face RF-specific modeling and deployment constraints.

  • Extreme Observational Degradations: Under one-percent sampling, physics-informed sensor placement enables sub-meter NLoS source localization without power calibration.RadioDiff-Loc places sensors near building vertices using Fisher-information guidance.
  • Extreme Observational Degradations: Below the non-uniqueness threshold, reconstruction must shift from deterministic regression to probabilistic generation whose quality depends on the learned prior.This follows because observations no longer uniquely determine the underlying RM.
  • Optics-Inspired Methods: NeRF adaptations model RF propagation with complex-valued micro-voxels and Huygens-Fresnel-inspired secondary sources.They use complex attenuation and re-emitted signals to represent volumetric propagation.
  • Optics-Inspired Methods: RF neural rendering must account for absorption, reflection, diffraction, scattering, phase, and sparse hardware sampling unlike optical rendering.These differences create physical challenges when transferring NeRF formulations into the RF domain.
  • Generalizable Radio-Frequency Radiance Fields: GRaF achieves zero-shot cross-scene generalization, reducing MSE by 26.9% and improving PSNR by 10.2% over NeRF2 without retraining.Its generated spatial spectra also reduce AoA estimation errors by 61.6% compared with using only 50% of real data.

B. 3DGS-Based Methods

3DGS-based RM methods replace optical compositing with complex electromagnetic representations and coherent superposition, improving rendering efficiency while retaining scene-specific limitations.

  • B. 3DGS-Based Methods: 3DGS replaces NeRF ray marching with explicit anisotropic Gaussian primitives and parallelizable rasterization for RF rendering.RF adaptations also require complex-domain representations and hemispherical antenna models.
  • B. 3DGS-Based Methods: WRF-GS models Gaussians as virtual transmitters and substitutes signal strength and attenuation for optical color and opacity.Its Mercator projection is suitable for terrestrial links with elevation angles below 30° but requires compensation for high-elevation links.
  • B. 3DGS-Based Methods: RF splatting uses complex wave attenuation, deformable Gaussians, Fourier-Legendre expansions, and frequency-domain consistency losses.These designs separate static and dynamic fading or encode amplitude and phase without MLPs.
  • B. 3DGS-Based Methods: nGRF uses unordered complex superposition rather than normalized alpha blending because RF waves exhibit constructive and destructive interference.Covariance scaling preserves energy conservation, and nGRF reports 220× faster inference than NeRF baselines.
  • Discussion: 3DGS methods provide higher physical fidelity and angle-power-spectrum modeling, but environmental or transmitter changes can require retraining lasting tens of minutes.Traditional networks can instead encode transmitters explicitly and generalize without retraining.
  • Future Directions: Hybrid representations and amortized inference aim to update only dynamic Gaussian subsets or predict field parameters in a single feed-forward pass.The latter targets construction-time reductions from minutes to milliseconds.

A. A Taxonomy of Embeddable Physical Knowledge

Physical knowledge can enter RM construction through geometric features, electromagnetic response features, or PDE-based constraints, with increasing physical depth and computational cost.

  • A. A Taxonomy of Embeddable Physical Knowledge: Geometric features such as building maps, LoS ratios, and edge detectors are inexpensive, backbone-agnostic inputs but do not encode electromagnetic responses.They identify where wave-obstacle interactions occur using GIS or CAD data.
  • A. A Taxonomy of Embeddable Physical Knowledge: Electromagnetic features include FSPL, Fresnel reflection and transmission coefficients, diffraction losses, and projected antenna radiation patterns.They encode quantitative responses but require frequency-dependent parameters.
  • A. A Taxonomy of Embeddable Physical Knowledge: PDE-level knowledge uses the Helmholtz equation ∇2u + k2u = −f as preprocessing or loss-level constraints.This provides the strongest physical regularization but requires evaluating differential operators and is computationally demanding.
  • Data-Level Integration: Projected antenna features support cross-frequency generalization for fixed-downtilt antennas but discard volumetric radiation in active 3D beamforming.Full 3D tensor representations are needed when beam direction varies in three dimensions.
  • Data-Level Integration: PDE-derived effective-wavenumber masks improve diffusion conditioning by identifying electromagnetic singularities such as deep fading and sharp shadowing boundaries.RadioDiff-k2 reports a 45.5% NMSE reduction from this conditioning strategy.
  • Loss-Level Integration: Source-agnostic settings make transmitter-dependent LoS constraints ill-posed unless localization is added or the constraint becomes relative spatial consistency.A ReLU-based penalty can additionally enforce NLoS delays above the theoretical LoS minimum.
  • Architecture and Loss Integration: PEFNet embeds the volume integral equation and method-of-moments discretization, achieving R2 > 0.99 with approximately 1.1-second inference on RadioMapSeer.The reported latency is compared with hours for classical numerical solvers.

3) Gradient Pathologies and Dynamic Balancing:

Combining physical and data losses creates severe gradient-scale imbalances, motivating dynamic weighting and warmup strategies. The section also surveys physics-aware architectures and their benefits, costs, and remaining risk of physical hallucinations.

  • Gradient Pathologies: Physical-loss gradients operate on electric-field residuals while data-loss gradients operate on path loss, often differing by two to three orders of magnitude.
  • Dynamic Balancing: Dynamic adjustment, uncertainty weighting, and adaptive annealing rebalance competing objectives and prevent premature enforcement of strong physical constraints.
  • Helmholtz Equation Embedding: Helmholtz-based regularization combines PDE, boundary-condition, and source constraints to enforce wave-propagation dynamics beyond measured regions.
  • Helmholtz Equation Embedding: 37.2% NMSE improvement at 1–10% sampling rates is reported for combined regularization over diffusion-only baselines, but discretization error can become substantial at 28 GHz.
  • Algorithm Unrolling: Algorithm unrolling embeds classical optimization into trainable cascaded networks, achieving 25.81 dB PSNR at 10% sampling and reconstruction from nine measurements.
  • Physics-Informed Generative Architectures: Physics-informed generative architectures inject geometric-optics priors into denoising, while architecture-level methods still cannot guarantee Maxwell compliance in non-physical latent spaces.
  • Physical Hallucinations: Physical hallucinations include violations of energy conservation, reciprocity, or boundary conditions, motivating post-generation PDE and conservation checks.

1) Scenario-Specific Recommendations:

The survey maps physics-aware integration levels to deployment scenarios, data availability, and latency requirements. It also identifies unresolved challenges in beam-aware modeling, complex environments, source ambiguity, foundation models, amortized inference, and hallucination detection.

  • Scenario-Specific Recommendations: Data-level integration is recommended for offline network planning when several seconds of latency are acceptable and backbone modification should be avoided.
  • Scenario-Specific Recommendations: Loss-level integration is recommended below 10% sampling because PDE and multipath constraints restrict sparse reconstructions to feasible electromagnetic manifolds.
  • Scenario-Specific Recommendations: Architecture-level integration with flow matching or lightweight diffusion is recommended for real-time digital-twin synchronization below 100 ms, alongside post-hoc consistency checks.
  • Scenario-Specific Recommendations: Combining data- and loss-level integration is recommended below 1,000 labeled samples, with RadioDUN reconstructing from nine measurement points.
  • Beam-Aware RM Construction: Beam-aware RM construction remains constrained by scarce datasets and high-dimensional continuous beam conditioning, with BeamCKM identified as the only public benchmark.
  • Complex Scenarios: Source-agnostic methods generally address one source, while multi-source settings lack theoretical identifiability guarantees under sparse observations.
  • Amortized Inference: NeRF and 3DGS require per-scene optimization, making amortized feed-forward prediction of scene representations an open route toward millisecond-scale inference.
  • Physical Hallucination Detection: Operational physical-hallucination detection remains absent, motivating differentiable verification, constrained generation, and standardized metrics.
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