  Reconstructing spectral functions from Euclidean Green's functions is an
important inverse problem in physics. The prior knowledge for specific physical
systems routinely offers essential regularization schemes for solving the
ill-posed problem approximately. Aiming at this point, we propose an automatic
differentiation framework as a generic tool for the reconstruction from
observable data. We represent the spectra by neural networks and set chi-square
as loss function to optimize the parameters with backward automatic
differentiation unsupervisedly. In the training process, there is no explicit
physical prior embedding into neural networks except the positive-definite
form. The reconstruction accuracy is assessed through Kullback-Leibler(KL)
divergence and mean square error(MSE) at multiple noise levels. It should be
noted that the automatic differential framework and the freedom of introducing
regularization are inherent advantages of the present approach and may lead to
improvements of solving inverse problem in the future.

Computational Physics;Machine Learning;High Energy Physics - Lattice