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Local detection of magnetic fields is crucial for characterizing nano- andmicro-materials and has been implemented using various scanning techniques oreven diamond quantum sensors. Diamond nanoparticles (nanodiamonds) offer anattractive opportunity to chieve high spatial resolution because they caneasily be close to the target within a few 10 nm simply by attaching them toits surface. A physical model for such a randomly oriented nanodiamond ensemble(NDE) is available, but the complexity of actual experimental conditions stilllimits the accuracy of deducing magnetic fields. Here, we demonstrate magneticfield imaging with high accuracy of 1.8 $\mu$T combining NDE and machinelearning without any physical models. We also discover the field directiondependence of the NDE signal, suggesting the potential application for vectormagnetometry and improvement of the existing model. Our method further enrichesthe performance of NDE to achieve the accuracy to visualize mesoscopic currentand magnetism in atomic-layer materials and to expand the applicability inarbitrarily shaped materials, including living organisms. This achievement willbridge machine learning and quantum sensing for accurate measurements.

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