# Spectral Reconstruction with Deep Neural Networks

## TL;DR

This paper introduces a supervised deep learning approach for reconstructing spectral functions from Green's functions, showing comparable or better accuracy than traditional Bayesian methods, especially under high noise conditions.

## Contribution

It presents a novel neural network-based method for spectral reconstruction that leverages supervised learning and prior knowledge, offering potential improvements over existing techniques.

## Key findings

- Reconstruction accuracy is comparable or superior to Bayesian inference.
- Method performs well at higher noise levels.
- Supervised learning offers advantages in defining optimization objectives.

## 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.