# Spectral functions in Minkowski quantum electrodynamics from neural reconstruction

arXiv: https://arxiv.org/abs/2510.24728 · HTML: https://mlsanity.com/paper/2510.24728/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 60 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 8 of 8)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks](https://mlsanity.com/paper/1905.04817/) (2019)
- [Gauge-covariant stochastic neural fields: Stability and finite-width effects](https://mlsanity.com/paper/2508.18948/) (2025)
- [A Tutorial on the Use of Physics-Informed Neural Networks to Compute the Spectrum of Quantum Systems](https://mlsanity.com/paper/2407.20669/) (2024)
- [Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics](https://mlsanity.com/paper/2411.02177/) (2024)

## Built on by (most cited first, 1 of 1)

- [Neural solutions of coupled ghost and gluon Dyson--Schwinger equations in Landau gauge](https://mlsanity.com/paper/2607.21548/) (2026)

## Abstract (arXiv)

We study neural reconstructions of quenched rainbow quantum electrodynamics (QED) Dyson--Schwinger benchmarks in Minkowski-related kinematics. Using the dispersive formulation as motivation, we separate the Euclidean Fukuda--Kugo equation, the spectral unitary equations, and the modified unitary equations. The Fukuda--Kugo benchmark is solved directly and shows the expected zero crossing above the critical region αc=π/3. Neural reconstructions with free output reproduce this behavior, while positivity-constrained ans"atze fail in the supercritical regime. Thus, spectral positivity should be treated as a diagnostic of the Lehmann representation, not imposed blindly as a neural constraint.