High-Fidelity Radio Map Construction

Robots that localize a radio transmitter need more than a point estimate: in cluttered rooms, one measurement is often consistent with several transmitter locations and, because upper-mid-band antennas are directional, several headings. We present MAGNETAR, which infers a joint posterior over planar transmitter position and heading from a single asynchronous radio-frequency (RF) multipath snapshot, represented by angle-of-arrival and signal-to-noise-ratio estimates, given the room layout and receiver pose. Among our five neural scorers, MAGNETAR adopts a shared 2D U-Net conditioned on each candidate heading, jointly normalizing scores over a discretized position-heading grid. Training uses real-to-sim-calibrated 10 GHz simulations and a small measured subset. Grid-based joint posteriors outperform parametric ones on held-out simulations, the heading-conditioned scorer transfers best to robotic measurements, and fusing joint posteriors improves on fusing position-only marginals.

Reliable prediction of crystallographic texture in laser powder bed fusion is critical for linking process conditions with anisotropic response and for qualification. However, black-box models may fail under shift and cannot distinguish weak data support from loss of physical validity. This study develops a two-stage physics-based model for <001> || BD (build direction) texture in Inconel 718. Stage 1 maps process variables to melting mode and melt pool geometry. Stage 2 predicts texture by combining an empirical physics model with a random-forest residual model. A k-nearest-neighbor weight attenuates residual corrections for poorly supported queries, while a study-specific areal beam-power-density criterion withholds predictions outside the adopted conduction envelope. Conformal intervals are evaluated on the retained physics-valid set, and SHAP and Sobol analyses assess residual sensitivity. Under a controlled leave-one-defocus-out evaluation, the physics anchor achieved R^2 = 0.778, against -0.001 for the black-box model and 0.750 for the gated hybrid. Under leave-one-group-out cross-validation, the gated hybrid reached R^2 = 0.592 against 0.538 for the black-box model. Retained-set coverage was 92.9% at a mean full width of 3.65 multiples of a uniform distribution (MUD) under grouped cross-validation and 100% at a width of 3.21 MUD under transfer to a withheld +80 mm defocus regime. An illustrative mapping produced a retained BD elastic-modulus span of 127-187 GPa. On nine conditions from a separately built sample set, the framework withheld three, attenuated three, and matched the measured ordering for the rest. Separating data applicability, physics validity, and predictive uncertainty into distinct decisions lets the framework transfer where an unconstrained model does not, and withhold predictions where no model class performs adequately.

Radiomap blind prediction infers radiomaps from observable representations of the propagation environment and base station (BS) configuration without field measurements. These representations are inherently incomplete and cannot uniquely determine the target radiomap. Under squared loss, we identify the conditional-mean radiomap as the population-optimal deterministic target and decompose domain risk into target-approximation error and irreducible uncertainty. The train-test risk gap motivates propagation priors as cross-domain guidance, although their partial or simplified forms may bias the attainable predictor. We therefore propose RadioDecomp, which treats a prior-guided predictor as a correctable base and uses deterministic residual refinement to learn its remaining predictable discrepancy. We instantiate RadioDecomp as RadioLSR (LoS-Shadow-Residual). Experiments under cross-configuration and cross-environment settings show that RadioLSR is especially effective for cross-configuration generalization and provides overall gains over a controlled monolithic counterpart under cross-environment generalization.

Integrated sensing and communication (ISAC) provides a promising foundation for beam prediction in future vehicle-to-everything (V2X) networks. However, existing sensing-assisted beamforming methods still rely heavily on radio-frequency sensing, which may become unreliable in complex vehicular environments. Meanwhile, the growing availability of heterogeneous sensors, such as cameras and LiDAR, offers new opportunities to improve beam prediction through richer environmental perception. Motivated by this, this paper proposes a multi-modal beam prediction framework for V2X networks. Specifically, we develop BeamTransFuser, a hierarchical Transformer-based architecture that progressively fuses camera, LiDAR, radar, and GPS observations for robust beam prediction. In addition, to handle possible missing modalities in practical deployment, we introduce a generative module that reconstructs missing modality features from the available observations. Experimental results on a real-world multi-modal V2X dataset show that the proposed framework consistently outperforms representative baselines, while the generative module further improves robustness under incomplete sensing conditions.

The evolution toward sixth-generation (6G) wireless networks is driving larger antenna arrays and highly directional multi-beam transmission, making accurate knowledge of beam-dependent spatial coverage important for beam management and environment-aware network operation. Radio maps (RMs) provide such a representation, yet conventional RM prediction assumes omnidirectional or transmitter-level radiation. In beamformed multiple-input multiple-output (MIMO) systems, one propagation scene instead gives rise to many configuration-dependent beam radio maps (BeamRMs), creating challenges in beam representation and generalization. Existing methods either condition prediction on beam descriptors or use beam maps as auxiliary inputs to generic architectures. We propose BeamRMX, which, to the best of our knowledge, is the first dedicated framework to treat the spatial radiation pattern as the primary BeamRM query and learn how scene geometry transforms it into the received power field. XBase learns multiscale interactions between the radiation query and scene geometry, while an optional Evidence Adapter uses a few cross-configuration BeamRMs from the same scene. Matched-domain and zero-shot experiments show consistent gains over deterministic and diffusion baselines, including mean absolute error reductions of 26.1% on unseen scenes and 47.8% on an unseen configuration. Cross-configuration evidence further improves reconstruction and intra-sector beam refinement.

Radio maps describe how wireless signals propagate across space and are essential for wireless communication, sensing, and network planning. However, constructing accurate radio maps traditionally requires either dense measurements or computationally expensive physical simulations, which limits scalability and real-time deployment. Recent advances in generative artificial intelligence offer a promising alternative, but existing approaches lack fine-grained control and physical consistency when applied to real-world wireless environments. Here we present \textbf{ControlRadio}, a controllable generative framework that produces radio maps from natural-language descriptions and environmental layouts, including building structures and transmitter locations. Joint semantic and spatial conditioning enables interpretable, propagation-plausible generation, while a controlled latent prior and layout-aware conditioning improve stability and structural consistency. Extensive experiments demonstrate that ControlRadio achieves state-of-the-art accuracy and strong generalization across diverse urban scenarios, while reducing computation time by more than four orders of magnitude compared with conventional simulation-based methods. Such results suggest a new paradigm for scalable and controllable wireless environment modeling, with broad implications for next-generation communication systems and data-driven radio sensing.

High-fidelity radio fields are typically simulated for every scene--transmitter configuration or fitted separately to each scene, failing to exploit propagation structures shared across environments. We present Point2Radio, a foundation model that learns a transferable propagation prior from multiple environments. Given a material-aware point cloud and a transmitter (TX) setting, a common encoder produces a TX-conditioned scene representation that can be queried at arbitrary receiver (RX) locations. Task-specific query decoders map this representation to different radio quantities, e.g., three-dimensional (3D) path-gain (PG) fields and power angular spectra (PAS). At inference for a new scene, the model uses only a material-aware point cloud and transceiver queries, running in milliseconds on a single GPU without meshes or explicit path tracing. We evaluate PG prediction on a scene-disjoint split of a 337-scene corpus containing 86,272 TX-conditioned fields. Point2Radio achieves 0.871 dB mean absolute error (MAE), reducing error by 76.7% relative to a same-split UNet-style baseline. The same encoder also supports PAS prediction via a task-specific decoder. Experiments further show that light target-scene fine-tuning improves adaptation to a specific environment.

Accurately predicting directional radio maps is essential for wireless applications, yet prior approaches primarily focus on omnidirectional signals and typically treat transmitter localization and signal map reconstruction as separate tasks. In omnidirectional settings, predicting the maximum signal location often coincides with the transmitter position, which limits the need for explicit joint modeling. However, in directional propagation where angular effects, reflections, and building occlusions play critical roles, this assumption no longer holds. To address this gap, we propose SymNet, a unified framework that jointly predicts directional radio maps and transmitter locations from sparse signal measurements. SymNet incorporates a prediction head for transmitter localization alongside radio map reconstruction, enabling simultaneous learning of both tasks. This joint formulation leverages their complementary information and leads to consistent improvements over treating them separately. Experiments on challenging directional scenarios demonstrate that SymNet outperforms state-of-the-art baselines, achieving superior accuracy in both radio map reconstruction and transmitter localization.

Reliable wireless connectivity is essential for urban air mobility (UAM) networks in dense urban environments. It is therefore imperative to carefully plan the supporting communication infrastructure for UAM flight corridors. Most existing works optimize communication infrastructure and UAV flight paths independently, often leading to unnecessary base station (BS) deployment or excessive flight detours. This paper studies the joint optimization of BS deployment and UAV flight corridors in complex urban environments, aiming to minimize both infrastructure investment and flight distance while satisfying communication quality constraints. We propose CR-CMAB, a channel reciprocity-guided combinatorial multi-armed bandit framework. The framework constructs high-fidelity radio maps using 3D ray tracing, selects BS combinations via coverage-aware CMAB search, and dynamically expands the search space by identifying promising BS locations through channel reciprocity. Experimental results from a detailed case study demonstrate that CR-CMAB outperforms baseline methods with moderate computational time, yielding more strategically positioned BSs and shorter flight corridors. This study offers a practical planning perspective for cost-effective and communication-reliable UAM deployment in future smart cities.

Radio map (RM) estimation aims to reconstruct the spatial distribution of wireless signal characteristics, such as received signal strength (RSS), from sparse measurements, a task that is critical for spectrum management, interference mitigation, and localization in modern wireless networks. Traditional approaches, including interpolation and deep learning, either struggle to capture complex propagation effects or require large-scale retraining for each new sampling pattern, which limits their generalization. More recently, prior-based methods have combined pre-trained generative models with measurements to reduce the need for deployment-time model fine-tuning, but they typically treat the prior as a simple regularizer and lack explicit transmitter-aware integration. In this paper, we propose RadioTrace, a novel RM estimation framework without deployment-time fine-tuning that tightly integrates sparse RSS measurements with a frozen pre-trained diffusion prior. RadioTrace incorporates transmitter (Tx) location estimation directly into the denoising loop, iteratively refining Tx coordinates based on reconstruction quality to guide the generative process. To further enhance robustness, we introduce a propagation-guided K-means initialization that mitigates poor local minima in the Tx update and provides a geometry-consistent starting point. Moreover, we provide a stochastic stability analysis for the Tx-coordinate refinement component, showing that the Tx update remains stable under perturbations induced by diffusion sampling and Tx-map relaxation. Extensive experiments demonstrate that RadioTrace achieves competitive performance with state-of-the-art learning-based methods under random sampling, and maintains strong reconstruction quality under restricted-area sampling, highlighting its adaptability, robustness, and practical relevance.

Angular radio maps describe the received-power distribution over the angle of arrival and underpin beam selection and receiver localization in sixth-generation (6G) networks. Predicting the angular power spectrum (APS) from geometry is difficult, because the mapping is ill-posed in non-line-of-sight (NLOS) conditions and must generalize to unseen environments. Distortion-minimizing regressors return the conditional mean, which over-smooths the spectrum and erases the multipath structure that downstream tasks need. We cast the task as a perception-distortion problem and propose RadioDiff-v2, a dual-branch one-dimensional diffusion transformer trained with flow matching. It couples periodic angular encoding, adaptive layer-normalization conditioning, a Fourier angular mixer, and joint velocity and clean-signal heads. A per-metric estimator portfolio reads every deployment quantity from this single model, so that samples carry the distribution, the clean-signal head supplies a regression-grade point estimate, Bayes-optimal rules select beams, and the conditional likelihood localizes the receiver. We prove that a concentrated conditional yields a straight probability-flow trajectory that one step integrates exactly, identifying deterministic transport as the correct inductive bias. On a zero-shot test of 99 environments and one million links, RadioDiff-v2 leads every baseline on every metric, with a 0.39 dB Wasserstein-1 distance, per-bin error below the regression baseline, a 2.43 dB eight-beam NLOS sweep loss, and a 20.6-pixel localization error with four base stations. Code is available at https://github.com/UNIC-Lab/RadioDiff-v2.

Radio frequency (RF) maps provide a compact representation of multipath propagation characteristics and are fundamental to channel modeling, coverage analysis, and environment-aware wireless optimization. This paper proposes a unified RF map construction framework based on a physics-informed neural network (PINN) and a graph neural network (GNN), supporting both cross-scene generation and in-scene completion with 2D and 2.5D environmental representations. The PINN embeds electromagnetic propagation constraints to establish a physically consistent mapping from receiver locations to multipath parameters, including path gain, time of arrival, and angles, while the GNN enforces spatial consistency by modeling correlations among neighboring receivers. To comprehensively evaluate multipath reconstruction quality, we propose a peak-weighted dynamic time warping metric that jointly accounts for amplitude errors and peak delay misalignment in channel impulse responses. Extensive experiments demonstrate that the proposed method consistently outperforms image-based, diffusion-based, and interpolation baselines across both map-level and multipath-level metrics, achieving robust generalization and high-fidelity RF map construction under sparse observations.

Low-altitude Unmanned Aerial Vehicles (UAVs) often need to infer channel knowledge across a range of heights from only sparse observations collected at a few altitude layers. To address this challenge, this paper studies height-conditioned cross-height channel knowledge map (CKM) prediction for UAV-assisted communications in geometry-rich urban environments. We develop a geometry-aware conditional prediction framework that combines urban scene priors, sparse multi-altitude observations, and target-height descriptors to reconstruct dense CKMs at unobserved target heights. An uncertainty head is further introduced to characterize prediction confidence and to support cost-aware online UAV sensing under motion and safety constraints. Experiments on a layered aerial CKM benchmark show that the proposed Feature Pyramid Network (FPN)-Transformer achieves the best overall performance under both unseen-scene zero-shot and legacy patch-random protocols, reducing the Root Mean Square Error (RMSE) to 5.347dB and 1.111dB, respectively, compared with 6.937dB and 1.221dB for the strongest baseline 3D-RadioDiff. Moreover, after applying our unseen-scene few-shot adaptation, the RMSE further decreases from 5.347dB in zero-shot prediction to 3.518dB with 10-shot two-height support, while the uncertainty-guided cost-aware sensing policy improves active reconstruction from 6.94dB at initialization to 4.79dB at sensing budget 40, outperforming uncertainty-only sensing at 5.08dB and random aerial sampling at 5.84dB.

LiDAR semantic segmentation often degrades under real-world deployment due to evolving sensing conditions, while collecting new annotations for retraining is impractical. Test-time adaptation (TTA) updates model parameters online using pseudo-label supervision, but directly applying standard TTA strategies to LiDAR data is challenging. Because pseudo-label reliability is spatially heteroscedastic under range-dependent sparsity and occlusion, uniform updates on globally shared parameters can inject unstable gradients and destabilize adaptation. We propose a geometry-constrained test-time prompt tuning framework for LiDAR semantic segmentation. Our method estimates per-location sensing reliability from depth-consistent beam terminations and neighborhood support, and uses it to reweight spatial supervision. Adaptation is confined to lightweight prompt adapters inserted into a frozen backbone, with spatial gating to prevent unreliable regions from perturbing globally shared representations. A temporally smoothed prototype alignment strategy further stabilizes online updates by accumulating reliable semantic evidence over time. Experiments on standard LiDAR benchmarks demonstrate improved adaptation stability and segmentation performance under deployment variations without additional annotations.

Accurate, site-specific channel information is crucial for optimizing next-generation wireless networks. Among various approaches, localized statistical channel modeling (LSCM), which models the channel multipath angular power spectrum (APS) from the reference signal received power (RSRP) measurement, has emerged as a state-of-the-art method tailored for efficient network optimization. However, despite its effectiveness, LSCM cannot predict APS at the vast majority of locations where no measurements are available, which significantly restricts its applicability in large-scale, real-world scenarios. To address this challenge, we present \emph{point-cloud-assisted tangent Gaussian splatting} (PC-TGS), the first framework to \emph{extrapolate} APS to unmeasured outdoor grids by integrating sparse radio measurements with dense LiDAR-based geometry. PC-TGS represents environmental scatterers as anisotropic 3D Gaussians, initialized and refined through a relaxed-mean reparameterization of the raw point cloud. A tangent-plane projection accurately maps each Gaussian into the local angular domain, while a depth-aware electromagnetic splatting process aggregates their contributions. To ensure practical deployment, we derive a closed-form Gaussian-weighted average (GWA) for APS bin integration and provide a provable error bound. { Evaluations on a LiDAR-scanned city-scale dataset (5M points, 6,310 RSRP samples) demonstrate that PC-TGS achieves better APS and RSRP prediction performance compared to state-of-the-art baselines and faster inference time for APS extrapolation task. These results highlight the potential of PC-TGS to enable geometry-aware and data-efficient channel prediction in large-scale wireless digital twins.

Diffusion models achieve high-fidelity radio map construction through iterative denoising, yet their sampling cost limits practicality in dynamic wireless systems where radio maps must be refreshed repeatedly. Meanwhile, classical propagation models encode valuable scene-level knowledge that standard diffusion inference discards entirely by initializing from pure Gaussian noise. This paper bridges propagation priors and diffusion refinement through a mid-start sampling strategy. A matched propagation prior is perturbed to an intermediate diffusion timestep, and the pretrained diffusion backbone executes only the remaining reverse steps, focusing computation on multipath-aware refinement rather than full reconstruction from noise. We provide theoretical analysis establishing an upper bound on the initialization gap, a sufficient condition under which truncation improves reconstruction fidelity, and a formal characterization of prior-quality sensitivity under aggressive truncation. Experiments on IRT4HighRes show that, at $P_{\text{start}}=0.5$, the proposed method achieves a $2.01\times$ speedup while simultaneously improving NMSE, RMSE, SSIM, and PSNR over the full-step baseline. A prior-quality ablation across three propagation models of different fidelity confirms that reconstruction quality tracks prior quality, with the sensitivity amplified under shorter reverse trajectories, consistent with the theoretical predictions. These results also suggest that mid-start reconstruction quality can serve as a proxy for ranking the scene-level fidelity of different propagation models.

Radiated noise in unmanned underwater vehicles (UUVs) is an important indicator for characterizing acoustic signatures and evaluating platform performance. To address the strong dependence of traditional physics-based modeling and numerical simulation methods on target structural information and environmental boundary conditions, and their inability to achieve continuous spatial spectrum-response modeling in three-dimensional scenes, this paper proposes a neural radiated-noise field (NRNF). An NRNF represents the UUV radiated-noise spectrum as a continuous function of the three-dimensional UUV position, the three-dimensional hydrophone position, the UUV yaw angle, and the frequency, enabling query-based prediction at arbitrary spatial locations. The proposed method employs sinusoidal encoding for position and frequency, and introduces a learnable three-dimensional scene feature grid to explicitly represent environmental structure and propagation effects. A spectrum-prediction dataset is constructed from lake trials, and the proposed model is evaluated under three settings: horizontal extrapolation, depth extrapolation, and cross-run generalization. Results show that the NRNF achieves an average prediction error of 3.5 dB in the 50 to 5000 Hz band. Horizontal extrapolation is easiest, depth extrapolation is the most challenging, and cross-run generalization is of intermediate difficulty. Further ablation results demonstrate that the scene feature grid significantly improves the prediction stability and spatial generalization of the model.

With the emergence of wireless applications in three-dimensional environments, such as the low-altitude airspace and 3D heterogeneous networks, radio map estimation is increasingly required to characterize signal propagation across both horizontal and vertical dimensions. However, extending radio map estimation from 2D to 3D remains challenging due to increased spatial sparsity and limited supervision across continuous altitudes. In this paper, we propose \textbf{\textit{RadioFormer3D}}, a specialized model for volumetric spectrum reconstruction under weak supervision. Building on the dual-stream, multi-granularity fusion architecture of \textit{RadioFormer}, \textit{RadioFormer3D} introduces a Fourier-based sampling encoder and a volumetric decoder to efficiently process sparse measurements in 3D space. To alleviate the lack of vertical supervision, we propose the \textbf{\textit{Joint Spectrum Integrity Loss}}, which integrates volume-level pseudo-label supervision, map-level geometry-aware radio rendering, and pixel-level localized constraints within a unified optimization scheme. This design enables the model to capture complex vertical structural relationships more effectively under sparse supervision. Extensive experiments across several radio map datasets show that \textit{RadioFormer3D} achieves superior overall performance compared to representative existing methods. In particular, it demonstrates improved reconstruction quality at unlabeled altitudes while maintaining a favorable trade-off between accuracy and inference efficiency, positioning it as a highly promising solution for future 3D environment-aware wireless networks.

Learning-based radio map estimation (RME) plays a critical role in UAV-assisted wireless sensing, enabling tasks such as coverage prediction and network optimization. Most current methods assume an independently and identically distributed (i.i.d.) training and testing setting based on random sampling. However, practical UAV measurements are collected sequentially along feasible trajectories, resulting in highly structured and spatially correlated patterns. This mismatch introduces a sampling distribution shift that increases the intrinsic difficulty of spatial field recovery and compromises the generalization of models trained under i.i.d. assumptions. To mitigate this issue, we propose a trajectory-aware training paradigm based on Stochastic-Triggered Trajectory-Based Sampling (ST-TBS), which preserves trajectory continuity while introducing sampling variability. Moreover, from a statistical perspective, we show that trajectory-based sampling reduces spatial diversity and increases information redundancy compared to random sampling. Extensive experiments on the RadioMapSeer and SpectrumNet datasets demonstrate that models trained with random sampling suffer significant performance degradation under trajectory-based observations, with RMSE increasing from 0.0391 to 0.2632 on SpectrumNet. Conversely, our proposed ST-TBS method effectively reduces the RMSE to 0.0571. These results highlight the necessity of aligning training and deployment sampling distributions for reliable RME.

Building a site-specific propagation model typically requires either ray-tracing over detailed 3D maps or dense measurement campaigns. Both approaches are expensive and often infeasible for rapid deployments where geographic data is unavailable or outdated. We present PropSplat, a map-free propagation modeling method that reconstructs radio frequency (RF) fields using 3D anisotropic Gaussian primitives. Each Gaussian encodes a scalar path loss offset relative to an explicit baseline path loss model with a learnable path loss exponent. Gaussians are initialized along observed transmitter--receiver paths and optimized end-to-end to learn the propagation environment without external information like floor plans, terrain databases, or clutter data. We evaluate PropSplat against wireless radiance field methods NeRF$^2$, GSRF, and WRF-GS+ on two real-world datasets. On large-scale outdoor drive-tests spanning multiple topographical regions at six sub-6 GHz frequencies, PropSplat achieves 5.38 dB RMSE when training measurements are spaced 300m apart and outperforms WRF-GS+ (5.87 dB), GSRF (7.46 dB), and NeRF$^2$ (14.76 dB). On indoor Bluetooth Low Energy measurements, PropSplat achieves 0.19m mean localization error, an order of magnitude better than NeRF$^2$ (1.84m), while achieving near-identical received signal strength prediction accuracy. These results show that accurate site-specific propagation reconstruction is achievable from sparse RF-native measurements. The need for geographic data as a prerequisite for scalable RF environment modeling is reduced.

Channel-gain maps provide the channel gain between any two locations in a geographical region. They find numerous applications, from resource allocation and interference control to path planning for autonomous vehicles. Channel-gain map estimation (CGME) is considerably more challenging than conventional radio map estimation (RME) because channel-gain maps are functions over a 6-dimensional input space. This calls for specialized methods, which currently rely on the (inaccurate) radio tomographic model or require a prohibitively large number of measurements since they do not exploit any spatial structure. This paper overcomes this issue by leveraging spatial patterns that channel-gain maps exhibit across environments, as dictated by the laws of physics and typical environmental characteristics (e.g. building materials and layouts). Adopting a metalearning perspective, a transformer-based estimator is proposed to implicitly learn this common structure from measurements collected in multiple environments. This enables CGME in new environments from significantly fewer measurements (five times less in our experiments). To maximize learning efficiency, the transformer is composed with a feature map that enforces the invariances of CGME, such as those following from reciprocity. Numerical experiments corroborate the merits of the proposed estimator relative to existing methods.

Spectrum cartography reconstructs spatial radio fields from sparse and heterogeneous wireless measurements, underpinning many sensing and optimization tasks in wireless networks. Attention mechanisms have recently enabled adaptive measurement aggregation via attention kernel-based formulations. However, the resulting exponential kernels exhibit severe spectral imbalance, inducing large condition numbers that render standard iterative solvers ineffective for regularized attention kernel regression. This paper proposes a Learning-based Attention Kernel Regression (LAKER) algorithm for accelerating regularized attention kernel regression in spectrum cartography. The key idea is to learn a data-dependent preconditioner that captures the inverse spectral structure of the attention kernel system, directly reducing the condition number bottleneck. The preconditioner is obtained by solving a regularized maximum-likelihood estimation problem via a shrinkage-regularized convex--concave procedure, and is integrated with a preconditioned conjugate gradient solver for efficient optimization, whose solution is used for radio map reconstruction. Extensive experiments demonstrate that LAKER significantly reduces condition numbers by up to three orders of magnitude, accelerates convergence by over twenty-fold compared to baselines, and maintains high reconstruction accuracy, establishing learning-based preconditioning as an effective approach for attention kernel regression in spectrum cartography.

Optimal wireless transmitter placement is a central task in radio-network planning, and exhaustive search becomes prohibitively expensive at scale. This paper studies the single-transmitter setting under a learned propagation model, enabling exhaustive per-pixel assessment at scale in a regime where measurement-based labeling is infeasible and ray-tracing-based labeling is computationally out of reach. We introduce a dataset of 167525 urban scenarios (RadioMapSeer-Deployment) with dual ground-truth labels for coverage-optimal and power-optimal transmitter locations. Benchmark analysis reveals an asymmetric coverage-power trade-off: coverage-optimal placement sacrifices 13.86% of received-power, whereas power-optimal placement sacrifices 5.50% of coverage; the best balanced placement lies at $\bar{d}=2.60$ from the ideal point (100%,100%). We evaluate two learning formulations: indirect heatmap-based models predicting received-power radio maps, and direct score-map models predicting the objective landscape over feasible transmitter locations. Within the heatmap family, discriminative models deliver one-shot predictions 1350-2400$\times$ faster than exhaustive search, while diffusion models additionally support multi-sample inference that improves single-objective performance and, by reusing the same sample pool under a balanced criterion, recovers strong balanced placements without explicit multi-objective training. Dual score-map strategies combining power and coverage score-maps match the exhaustive balanced optimum ($\bar{d}=2.60$) and remain close to it across smaller candidate budgets, at 14-22$\times$ speedups including the cost of evaluating shortlisted candidates. Dual score-map methods are strongest overall, whereas heatmap formulations remain attractive for their physically meaningful intermediate maps and, in the diffusion setting, for inference-time search.

Radio astronomy plays a crucial role in understanding the universe, particularly within the realm of non-thermal astrophysics. Images of celestial objects are derived from the signals (called visibility) measured by radio telescopes. Such imaging results, called dirty images, contain artifacts due to factors such as sparsity and therefore require reconstruction to improve imaging quality. Existing methods typically restrict reconstruction to a unimodal domain, either to the dirty image after imaging or to the sparse visibility prior to imaging. Focusing solely on each unimodal reconstruction results in the loss of complementary in-context information in either the visibility or image domain, leading to an incomplete modeling of mutual dependency and consistency. To address these challenges, we propose CDCRec, a multimodal radio interferometric data reconstruction method that explicitly models cross-domain consistency. We design a hierarchical multi-task and multi-stage framework to enhance the exploration of interplays between domains during reconstruction. Our experimental results demonstrate that CDCRec improves imaging performance through enhanced cross-domain correlation extraction. In particular, our self-supervised complementary modeling strategy is better than current methods at interferometric domain translations that rely heavily on recovering dense information from constrained source-domain data.