  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.
