Physics-Informed Representation Alignment for Sparse Radio-Map Reconstruction

TL;DR

This paper introduces PhyRMDM, a physics-informed neural network framework that aligns physical principles with data-driven features to improve sparse radio map reconstruction accuracy.

Contribution

It presents a novel dual-learning framework combining PINNs with representation alignment to effectively incorporate physical constraints into neural network models.

Findings

Achieves NMSE of 0.0031 in static scenarios

Attains NMSE of 0.0047 in dynamic scenarios

Provides 37.2% accuracy improvement in ultra-sparse conditions

Abstract

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.