Spectral Reconstruction with Deep Neural Networks https://arxiv.org/abs/1905.04305v1In conclusion, we believe that the suggested improvements will boost the performance of the proposed method to an as of yet unprecedented level and that neural networks will eventually replace existing state-of-the-art methods for spectral reconstruction|‹›
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 parametrised 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
labelled training data in a supervised setting and the freedom in defining an
optimisation 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.