Physics-Informed Representation Alignment for Sparse Radio-Map Reconstruction

Radio map reconstruction is essential for enabling advanced applications, yet challenges such as complex signal propagation and sparse observational data hinder accurate reconstruction in practical scenarios. Existing methods often fail to align physical constraints with data-driven features, particularly under sparse measurement conditions. To address these issues, we propose **Phy**sics-Aligned **R**adio **M**ap **D**iffusion **M**odel (**PhyRMDM**), a novel framework that establishes cross-domain representation alignment between physical principles and neural network features through dual learning pathways. The proposed model integrates **Physics-Informed Neural Networks (PINNs)** with a **representation alignment mechanism** that explicitly enforces consistency between Helmholtz equation constraints and environmental propagation patterns. Experimental results demonstrate significant improvements over state-of-the-art methods, achieving **NMSE of 0.0031** under *Static Radio Map (SRM)* conditions, and **NMSE of 0.0047** with **Dynamic Radio Map (DRM)** scenarios. The proposed representation alignment paradigm provides **37.2%** accuracy enhancement in ultra-sparse cases (**1%** sampling rate), confirming its effectiveness in bridging physics-based modeling and deep learning for radio map reconstruction.