Dynamic AFM is transitioning from a high-resolution imaging tool to a nanomechanical probe that can perform precise quantification of matter in fields as varied as microbiology, molecular metrology, and material science. To date, this has been achieved by estimating the nanoscale forces that exist between the probe and the sample, using empirical models that are merely approximations of the true probe-sample interaction physics. Here, we go beyond such approximations by making use of the recent advances in datascience and machine learning to distil nonlinear governing equations of dynamic AFM, and thus predict tip-sample forces directly from experimental raw deflection data. Our data-driven algorithm obtains physics-based models from experiments and is able to estimate time-resolved nanoscale interactions with sub-microsecond resolution.