  The method of solar magnetic field calibration for the filter-based
magnetograph is normally the linear calibration method under weak-field
approximation that cannot generate the strong magnetic field region well due to
the magnetic saturation effect. We try to provide a new method to carry out the
nonlinear magnetic calibration with the help of neural networks to obtain more
accurate magnetic fields. We employed the data from Hinode/SP to construct a
training, validation and test dataset. The narrow-band Stokes I, Q, U, and V
maps at one wavelength point were selected from all the 112 wavelength points
observed by SP so as to simulate the single-wavelength observations of the
filter-based magnetograph. We used the residual network to model the nonlinear
relationship between the Stokes maps and the vector magnetic fields. After an
extensive performance analysis, it is found that the trained models could infer
the longitudinal magnetic flux density, the transverse magnetic flux density,
and the azimuth angle from the narrow-band Stokes maps with a precision
comparable to the inversion results using 112 wavelength points. Moreover, the
maps that were produced are much cleaner than the inversion results. The method
can effectively overcome the magnetic saturation effect and infer the strong
magnetic region much better than the linear calibration method. The residual
errors of test samples to standard data are mostly about 50 G for both the
longitudinal and transverse magnetic flux density. The values are about 100 G
with our previous method of multilayer perceptron, indicating that the new
method is more accurate in magnetic calibration.
