# Physics-Informed Representation Alignment for Sparse Radio-Map Reconstruction

arXiv: https://arxiv.org/abs/2501.19160 · HTML: https://mlsanity.com/paper/2501.19160/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 18 references that are in the map.
- First posted on arXiv 31 Jan 2025.

## Builds on (most cited first, 5 of 5)

- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Efficient training of physics-informed neural networks via importance sampling](https://mlsanity.com/paper/2104.12325/) (2021)
- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [SATO: Stable Text-to-Motion Framework](https://mlsanity.com/paper/2405.01461/) (2024)
- [RadioGAT: A Joint Model-based and Data-driven Framework for Multi-band Radiomap Reconstruction via Graph Attention Networks](https://mlsanity.com/paper/2403.16397/) (2024)

## Built on by (most cited first, 11 of 11)

- [Generative Diffusion Models for Wireless Networks: Fundamental, Architecture, and State-of-the-Art](https://mlsanity.com/paper/2507.16733/) (2025)
- [RadioDiff-Flux: Efficient Radio Map Construction via Generative Denoise Diffusion Model Trajectory Midpoint Reuse](https://mlsanity.com/paper/2601.02790/) (2026)
- [Bridging Visual and Wireless Sensing via a Unified Radiation Field for 3D Radio Map Construction](https://mlsanity.com/paper/2601.19216/) (2026)
- [RadioDiff-FS: Physics-Informed Manifold Alignment in Few-Shot Diffusion Models for High-Fidelity Radio Map Construction](https://mlsanity.com/paper/2603.18865/) (2026)
- [Oracle Noise: Faster Semantic Spherical Alignment for Interpretable Latent Optimization](https://mlsanity.com/paper/2604.23540/) (2026)
- [Z2-Sampling: Zero-Cost Zigzag Trajectories for Semantic Alignment in Diffusion Models](https://mlsanity.com/paper/2604.23536/) (2026)
- [PGOT: A Physics-Geometry Operator Transformer for Complex PDEs](https://mlsanity.com/paper/2512.23192/) (2025)
- [Before the Body Moves: Learning Anticipatory Joint Intent for Language-Conditioned Humanoid Control](https://mlsanity.com/paper/2605.14417/) (2026)
- [Learning to Think in Physics: Breaking Shortcut Learning in Scientific Diffusion via Representation Alignment](https://mlsanity.com/paper/2605.20780/) (2026)
- [Traffic-CBM: A Structurally Interpretable Multimodal Framework for Encrypted Traffic Classification](https://mlsanity.com/paper/2606.29909/) (2026)
- [Radiomap Blind Prediction under Incomplete Observation: Error Characterization and Correctable Propagation-Prior Learning](https://mlsanity.com/paper/2609.32836/) (2026)

## Abstract (arXiv)

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.