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's 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.

--Electromagnetic stimulation of the human brain is a key tool for the neurophysiological characterization and diagnosis of several neurological disorders. Transcranial magnetic stimulation (TMS) is one procedure that is commonly used clinically. However, personalized TMS requires a pipeline for accurate head model generation to provide target-specific stimulation. This process includes intensive segmentation of several head tissues based on magnetic resonance imaging (MRI), which has significant potential for segmentation error, especially for low-contrast tissues. Additionally, a uniform electrical conductivity is assigned to each tissue in the model, which is an unrealistic assumption based on conventional volume conductor modeling. This paper proposes a novel approach to the automatic estimation of electric conductivity in the human head for volume conductor models without anatomical segmentation. A convolutional neural network is designed to estimate personalized electrical conductivity values based on anatomical information obtained from T1-and T2-weighted MRI scans. This approach can avoid the time-consuming process of tissue segmentation and maximize the advantages of position-dependent conductivity assignment based on water content values estimated from MRI intensity values. The computational results of the proposed approach provide similar but smoother electric field results for the brain when compared to conventional approaches. In electromagnetic dosimetry applications, the use of computational models that imitate human anatomy is an essential process [1].