Spectral Reconstruction with Deep Neural Networks
This addresses a classic challenge in computational physics for researchers in condensed matter and quantum many-body systems, representing an incremental improvement over existing methods.
The paper tackles the ill-posed inverse problem of reconstructing spectral functions from imaginary time Green's functions using deep neural networks, achieving accuracy comparable to or better than Bayesian methods, especially at higher noise levels.
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.