用物理规律约束神经网络，提升稀疏数据下无线地图重建精度
Physics-Informed Representation Alignment for Sparse Radio-Map Reconstruction
- 通过双路径学习实现物理规律与神经特征的跨域对齐
- 在静态/动态场景下分别达到0.0031和0.0047的低均方误差
- 极端稀疏条件下（1%采样率）性能提升37.2%，适合通信系统优化
无线地图重建对实现先进应用至关重要，但复杂信号传播与稀疏观测数据限制了实际场景中的重建精度。现有方法常无法在稀疏测量下将物理约束与数据驱动特征对齐。为此，我们提出物理对齐无线地图扩散模型（PhyRMDM），通过双学习路径建立物理原理与神经网络特征间的跨域表示对齐。模型融合物理信息神经网络（PINNs）与显式强制满足亥姆霍兹方程约束及环境传播模式的一致性机制。实验表明，该方法在静态无线地图（SRM）条件下达到0.0031的归一化均方误差（NMSE），动态无线地图（DRM）下为0.0047，且在超稀疏情形（1%采样率）中实现37.2%的准确率提升，验证了其在融合物理建模与深度学习方面的有效性。
原文摘要 · Abstract (English)
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.
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