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.

电解是环保氢气生产的关键，但在该过程中产生的气泡阻碍反应，降低电池效率并增加能耗。测量气泡引起的磁场波动，利用反比萨伐尔定律的逆问题来估算电池内的电导率、气泡的大小和位置等；我们利用可逆神经网络（INNs）重建电导率场，定性和定量结果表明INN相较于Tikhonov正则化具有更卓越的性能。

使用可逆神经网络和误差扩散学习基于电导率图的气泡分布重建