  The electron-boson spectral density (or glue) function can be obtained from
measured optical scattering rate by solving a generalized Allen formula, which
relates the two quantities with an integral equation and is an inversion
problem. Thus far, numerical approaches, such as the maximum entropy method
(MEM) and the least squares fitting method, have been applied for solving the
generalized Allen formula. Here, we developed a new method to obtain the glue
functions from the optical scattering rate using a machine learning approach
(MLA). We found that the MLA is more robust against random noise compared with
the MEM. We applied the new developed MLA to experimentally measured optical
scattering rates and obtained reliable glue functions in terms of their shapes
including the amplitudes. We expect that the MLA can be a useful and rapid
method for solving other inversion problems, which may contain random noise.
