Learning to reconstruct the bubble distribution with conductivity maps using Invertible Neural Networks and Error Diffusion

TL;DR

This paper introduces a novel method using Invertible Neural Networks to accurately reconstruct conductivity maps from magnetic field measurements, aiding in bubble detection during electrolysis.

Contribution

The study presents a new application of INNs for high-resolution conductivity map reconstruction from magnetic field data, outperforming traditional regularization techniques.

Findings

INNs significantly improve reconstruction accuracy.

The method effectively estimates bubble size and location.

Quantitative results show superior performance over Tikhonov regularization.

Abstract

Electrolysis is crucial for eco-friendly hydrogen production, but gas bubbles generated during the process hinder reactions, reduce cell efficiency, and increase energy consumption. Additionally, these gas bubbles cause changes in the conductivity inside the cell, resulting in corresponding variations in the induced magnetic field around the cell. Therefore, measuring these gas bubble-induced magnetic field fluctuations using external magnetic sensors and solving the inverse problem of Biot-Savart Law allows for estimating the conductivity in the cell and, thus, bubble size and location. However, determining high-resolution conductivity maps from only a few induced magnetic field measurements is an ill-posed inverse problem. To overcome this, we exploit Invertible Neural Networks (INNs) to reconstruct the conductivity field. Our qualitative results and quantitative evaluation using random error diffusion show that INN achieves far superior performance compared to Tikhonov regularization.