Title: Machine-learning-enhanced quantum sensors for accurate magnetic field imaging

Abstract: Local detection of magnetic fields is crucial for characterizing nano- and micro-materials and has been implemented using various scanning techniques or even diamond quantum sensors. Diamond nanoparticles (nanodiamonds) offer an attractive opportunity to chieve high spatial resolution because they can easily be close to the target within a few 10 nm simply by attaching them to its surface. A physical model for such a randomly oriented nanodiamond ensemble (NDE) is available, but the complexity of actual experimental conditions still limits the accuracy of deducing magnetic fields. Here, we demonstrate magnetic field imaging with high accuracy of 1.8 $\mu$T combining NDE and machine learning without any physical models. We also discover the field direction dependence of the NDE signal, suggesting the potential application for vector magnetometry and improvement of the existing model. Our method further enriches the performance of NDE to achieve the accuracy to visualize mesoscopic current and magnetism in atomic-layer materials and to expand the applicability in arbitrarily shaped materials, including living organisms. This achievement will bridge machine learning and quantum sensing for accurate measurements.