Robust Reconstruction of the Void Fraction from Noisy Magnetic Flux Density Using Invertible Neural Networks

Electrolysis stands as a pivotal method for environmentally sustainable hydrogen production. However, the formation of gas bubbles during the electrolysis process poses significant challenges by impeding reactions, diminishing cell efficiency, and dramatically increasing energy consumption. Furthermore, the inherent difficulty in detecting these bubbles arises from the non-transparency of the wall of electrolysis cells. Fortunately, these gas bubbles induce alterations in the cell’s conductivity, leading to corresponding fluctuations in the surrounding magnetic flux density. In this context, we can leverage external magnetic sensors to measure the magnetic flux density fluctuations induced by gas bubbles. Next, by solving the inverse problem of the Biot-Savart Law, we can estimate the conductivity, bubble size, and location within the cell. Nevertheless, reconstructing a high-resolution conductivity map from limited induced magnetic flux density measurements poses a formidable challenge as an ill-posed inverse problem. To overcome this challenge, we employ Invertible Neural Networks (INNs) to reconstruct the conductivity field. The inherent property of INNs, characterized by a bijective mapping between the input and output space, makes them exceptionally well-suited for resolving ill-posed inverse problems. We conducted extensive qualitative and quantitative evaluations to compare the performance of INNs with traditional approaches such as Tikhonov regularization. Our experiments demonstrate that, particularly in the presence of noise in the magnetic sensor data, our INN-based approach outperforms Tikhonov regularization in accurately reconstructing bubble distributions and conductivity fields. We hope that, given the efficacy of INNs shown in this work, they will become an indispensable deep-learning based approach for addressing inverse problems not only in Process Tomography but across various other domains.