  The underlying physics behind an experimental observation often lacks a
simple analytical description. This is especially the case for scanning probe
microscopy techniques, where the interaction between the probe and the sample
is nontrivial. Realistic modeling to include the details of the probe is always
exponentially more difficult than its "spherical cow" counterparts. On the
other hand, a well-trained artificial neural network based on real data can
grasp the hidden correlation between the signal and sample properties. In this
work, we show that, via a combination of model calculation and experimental
data acquisition, a physics-infused hybrid neural network can predict the
tip-sample interaction in the widely used scattering-type scanning near-field
optical microscope. This hybrid network provides a long-sought solution for
accurate extraction of material properties from tip-specific raw data. The
methodology can be extended to other scanning probe microscopy techniques as
well as other data-oriented physical problems in general.
