  To unravel pairing mechanism of a superconductor from limited, indirect
experimental data is always a difficult task. It is common but sometimes
dubious to explain by a theoretical model with some tuning parameters. In this
work, we propose that the machine learning might infer pairing mechanism from
observables like superconducting gap functions. For superconductivity within
the Migdal-Eliashberg theory, we perform supervised learning between
superconducting gap functions and electron-boson spectral functions. For simple
spectral functions, the neural network can easily capture the correspondence
and predict perfectly. For complex spectral functions, an autoencoder is
utilized to reduce the complexity of the spectral functions to be compatible to
that of the gap functions. After this complexity-reduction process, relevant
information of the spectral function is extracted and good performance
restores. Our proposed method can extract relevant information from data and
can be applied to general function-to-function mappings with asymmetric
complexities either in physics or other fields.
