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Comparative analysis of Realistic EMF Exposure Estimation from Low Density Sensor Network by Finite & Infinite Neural Networks

Mohammed Mallik, Laurent Clavier, Davy P. Gaillot

TL;DR

The paper addresses reconstructing RF-EMF exposure maps over a $1\ \mathrm{km}^2$ region from sparse real-world sensors. It compares finite-width and infinite-width convolutional networks via the CNTK framework (EME-CNTK and EME-CNTK+EigenPro) against a Generative Local Image Prior approach (GLIP), all guided by a Local Image Prior (LIP). Results on Lille, France data show that EME-CNTK+EigenPro achieves the best accuracy on high-resolution grids (128×128) with RMSEs as low as $1.99\times 10^{-1}$ V/m in Wazemmes and $4.59\times 10^{-1}$ V/m in Euratechnologies, using input from less than 1% of the area; GLIP underperforms under sparse sensing, and exact CNTK is impractical for large grids. The work demonstrates the practical viability of infinite-width CNNs with eigenvalue-aware preconditioning for real-world EMF exposure estimation and highlights the importance of sensor density and prior structure for accurate mapping. This has implications for scalable, real-time exposure assessment in urban environments and informs sensor deployment strategies in regulatory risk assessments.

Abstract

Understanding the spatial and temporal patterns of environmental exposure to radio-frequency electromagnetic fields (RF-EMF) is essential for conducting risk assessments. These assessments aim to explore potential connections between RF-EMF exposure and its effects on human health, as well as on wildlife and plant life. Existing research has used different machine learning tools for EMF exposure estimation; however, a comparative analysis of these techniques is required to better understand their performance for real-world datasets. In this work, we present both finite and infinite-width convolutional network-based methods to estimate and assess EMF exposure levels from 70 real-world sensors in Lille, France. A comparative analysis has been conducted to analyze the performance of the methods' execution time and estimation accuracy. To improve estimation accuracy for higher-resolution grids, we utilized a preconditioned gradient descent method for kernel estimation. Root Mean Square Error (RMSE) is used as the evaluation criterion for comparing the performance of these deep learning models.

Comparative analysis of Realistic EMF Exposure Estimation from Low Density Sensor Network by Finite & Infinite Neural Networks

TL;DR

The paper addresses reconstructing RF-EMF exposure maps over a region from sparse real-world sensors. It compares finite-width and infinite-width convolutional networks via the CNTK framework (EME-CNTK and EME-CNTK+EigenPro) against a Generative Local Image Prior approach (GLIP), all guided by a Local Image Prior (LIP). Results on Lille, France data show that EME-CNTK+EigenPro achieves the best accuracy on high-resolution grids (128×128) with RMSEs as low as V/m in Wazemmes and V/m in Euratechnologies, using input from less than 1% of the area; GLIP underperforms under sparse sensing, and exact CNTK is impractical for large grids. The work demonstrates the practical viability of infinite-width CNNs with eigenvalue-aware preconditioning for real-world EMF exposure estimation and highlights the importance of sensor density and prior structure for accurate mapping. This has implications for scalable, real-time exposure assessment in urban environments and informs sensor deployment strategies in regulatory risk assessments.

Abstract

Understanding the spatial and temporal patterns of environmental exposure to radio-frequency electromagnetic fields (RF-EMF) is essential for conducting risk assessments. These assessments aim to explore potential connections between RF-EMF exposure and its effects on human health, as well as on wildlife and plant life. Existing research has used different machine learning tools for EMF exposure estimation; however, a comparative analysis of these techniques is required to better understand their performance for real-world datasets. In this work, we present both finite and infinite-width convolutional network-based methods to estimate and assess EMF exposure levels from 70 real-world sensors in Lille, France. A comparative analysis has been conducted to analyze the performance of the methods' execution time and estimation accuracy. To improve estimation accuracy for higher-resolution grids, we utilized a preconditioned gradient descent method for kernel estimation. Root Mean Square Error (RMSE) is used as the evaluation criterion for comparing the performance of these deep learning models.

Paper Structure

This paper contains 15 sections, 7 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Inverse problem formulation
  4. EME-CNTK
  5. EME-CNTK+EigenPro
  6. GLIP
  7. Model details
  8. Results
  9. Evaluation metrics
  10. Implementation Details and Dataset
  11. Visual Analysis
  12. EME-CNTK & GLIP
  13. Quantitative Analysis
  14. Comparative Analysis of Time Efficiency
  15. Conclusion

Figures (3)

  • Figure 1: Visualization of the region of interest. This showcases the experimental 1$km^2$ areas in Wazemmes and Euratechnologies, where black circles show the sensors kept for error calculation: 2 and 4 in Euratechnologies and 4, 24, 29 and 34 in Wazemmes, respectively.
  • Figure 2: Experimental results for EME-CNTK$_{EigenPro}$ & GLIP by 46 and 18 sensors in Wazemmes and Euratechnologies districts, respectively.
  • Figure 3: The results of the CNTK and GLIP models showcases the reference and estimated EMF exposure levels. The 1st row presents the graphs of CNTK and GLIP for both reference and estimated exposure for sensors 4, 24, 29, and 33 in the Wazemmes district. In the 2nd row, the graphs depict the reference and estimated exposure for sensors 2 and 4 in the Euratechnologies district, with the first two graphs corresponding to CNTK and the latter two to GLIP. All results are shown when LIP prior is used.