Unsupervised learning spectral functions with neural networks

Reconstructing spectral functions from Euclidean Green's functions is an ill-posed inverse problem that is crucial for understanding the properties of many-body systems. In this proceeding, we propose an automatic differentiation (AD) framework utilizing neural network representations for spectral reconstruction from propagator observables. We construct spectral functions using neural networks and optimize the network parameters unsupervisedly based on the reconstruction error of the propagator. Compared to the maximum entropy method, the AD framework demonstrates better performance in situations with high noise levels. It is noteworthy that neural network representations provide non-local regularization, which has the potential to significantly improve the solution of inverse problems.