Spectral reconstruction with deep neural networks
Lukas Kades, Jan M. Pawlowski, Alexander Rothkopf, Manuel Scherzer, Julian M. Urban, Sebastian J. Wetzel, Nicolas Wink, Felix P. G. Ziegler
Abstract
We explore artificial neural networks as a tool for the reconstruction of spectral functions from imaginary time Green's functions, a classic ill-conditioned inverse problem. Our ansatz is based on a supervised learning framework in which prior knowledge is encoded in the training data and the inverse transformation manifold is explicitly parametrized through a neural network. We systematically investigate this novel reconstruction approach, providing a detailed analysis of its performance on physically motivated mock data, and compare it to established methods of Bayesian inference. The reconstruction accuracy is found to be at least comparable and potentially superior in particular at larger noise levels. We argue that the use of labeled training data in a supervised setting and the freedom in defining an optimization objective are inherent advantages of the present approach and may lead to significant improvements over state-of-the-art methods in the future. Potential directions for further research are discussed in detail.