Automatic differentiation approach for reconstructing spectral functions with neural networks

Understand

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.