# Spectral Reconstruction with Deep Neural Networks

arXiv: https://arxiv.org/abs/1905.04305 · HTML: https://mlsanity.com/paper/1905.04305/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2019.

## Built on by (most cited first, 6 of 6)

- [Applications of Machine Learning to Lattice Quantum Field Theory](https://mlsanity.com/paper/2202.05838/) (2022)
- [Machine learning spectral functions in lattice QCD](https://mlsanity.com/paper/2110.13521/) (2021)
- [Automatic differentiation approach for reconstructing spectral functions with neural networks](https://mlsanity.com/paper/2112.06206/) (2021)
- [Neural network approach to reconstructing spectral functions and complex poles of confined particles](https://mlsanity.com/paper/2203.03293/) (2022)
- [Machine learning Hadron Spectral Functions in Lattice QCD](https://mlsanity.com/paper/2112.00460/) (2021)
- [Inverting Non-Injective Functions with Twin Neural Network Regression](https://mlsanity.com/paper/2601.05378/) (2026)

## Abstract (arXiv)

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.