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

Abstract

The integration of artificial intelligence into next-generation wireless networks necessitates the accurate construction of radio maps (RMs) as a foundational prerequisite for electromagnetic digital twins. A RM provides 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. This tutorial 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 amortized inference for real-time deployment are discussed to outline future research directions.

Figures (4)

• Figure 1: The illustration of RM data collection. A comprehensive workflow bridging physical measurements and ray tracing simulations to generate standardized multi-dimensional benchmark datasets.
• Figure 2: Two primary paradigms of neural RM construction. (A) Source-aware modeling, where neural networks act as deterministic surrogates for ray tracing using known environment and transmitter inputs. (B) Source-agnostic reconstruction, representing an ill-posed inverse problem that leverages probabilistic generation to interpolate complete radio fields from sparse, incomplete measurements.
• Figure 3: The progression illustrates a paradigm shift towards increasing spatial and physical modeling capabilities. Early CNNs rely on local receptive fields but struggle with long-range diffraction. ViTs overcome this via global self-attention to capture macro-shadowing dependencies. GNNs embed physics-informed priors by modeling non-Euclidean multipath topologies. Recently, generative modelsreframe the task as probabilistic inference, enabling the reconstruction of high-fidelity radio maps from extreme sparsity while overcoming physical hallucinations.
• Figure 4: The paradigm of physics-informed neural networks for radio map construction. The framework is fundamentally grounded in the Helmholtz equation, which governs electromagnetic wave propagation behaviors such as diffraction and reflection (left). Physical priors are integrated through a dual-driven mechanism: (top right) data-level injection via electromagnetic feature engineering, which utilizes the effective wavenumber ($k_{\text{eff}}^2$) to locate spatial singularities and guide generative models; and (bottom right) loss-level regularization, which embeds partial differential equation (PDE) residuals, Dirichlet boundary conditions, and source node losses into a joint constraint loop ($\mathcal{L}_{\text{PLN}}$) to force latent representations to strictly conform to physical wave dynamics.