# Automatic differentiation approach for reconstructing spectral functions with neural networks

arXiv: https://arxiv.org/abs/2112.06206 · HTML: https://mlsanity.com/paper/2112.06206/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 12 Dec 2021.

## Builds on (most cited first, 4 of 4)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [Spectral Reconstruction with Deep Neural Networks](https://mlsanity.com/paper/1905.04305/) (2019)
- [Reconstructing spectral functions via automatic differentiation](https://mlsanity.com/paper/2111.14760/) (2021)

## Built on by (most cited first, 3 of 3)

- [Applications of Machine Learning to Lattice Quantum Field Theory](https://mlsanity.com/paper/2202.05838/) (2022)
- [Neural network approach to reconstructing spectral functions and complex poles of confined particles](https://mlsanity.com/paper/2203.03293/) (2022)
- [Neural Networks Asymptotic Behaviours for the Resolution of Inverse Problems](https://mlsanity.com/paper/2402.09338/) (2024)

## Abstract (arXiv)

Reconstructing spectral functions from Euclidean Green's functions is an important inverse problem in physics. The prior knowledge for specific physical systems routinely offers essential regularization schemes for solving the ill-posed problem approximately. Aiming at this point, we propose an automatic differentiation framework as a generic tool for the reconstruction from observable data. We represent the spectra by neural networks and set chi-square as loss function to optimize the parameters with backward automatic differentiation unsupervisedly. In the training process, there is no explicit physical prior embedding into neural networks except the positive-definite form. The reconstruction accuracy is assessed through Kullback-Leibler(KL) divergence and mean square error(MSE) at multiple noise levels. It should be noted that the automatic differential framework and the freedom of introducing regularization are inherent advantages of the present approach and may lead to improvements of solving inverse problem in the future.