Magnetic field regression using artificial neural networks for cold atom experiments

Accurately measuring magnetic fields is essential for magnetic-field sensitive experiments in fields like atomic, molecular, and optical physics, condensed matter experiments, and other areas. However, since many experiments are conducted in an isolated vacuum environment that is inaccessible to experimentalists, it can be challenging to accurately determine the magnetic field. Here, we propose an efficient method for detecting magnetic fields with the assistance of an artificial neural network (NN). Instead of measuring the magnetic field directly at the desired location, we detect magnetic fields at several surrounding positions, and a trained NN can accurately predict the magnetic field at the target location. After training, we achieve a relative error of magnetic field magnitude (magnitude of error over the magnitude of magnetic field) below 0.3$\%$, and we successfully apply this method to our erbium quantum gas apparatus. This approach significantly simplifies the process of determining magnetic fields in isolated vacuum environments and can be applied to various research fields across a wide range of magnetic field magnitudes.