# Purifying electron spectra from noisy pulses with machine learning using synthetic Hamilton matrices

## TL;DR

This paper introduces a deep neural network trained on synthetic data to effectively purify noisy photo-electron spectra from free-electron laser pulses, enabling accurate analysis of atomic and molecular ionization processes.

## Contribution

The study presents a novel machine learning approach using synthetic Hamilton matrices to purify electron spectra without system-specific training.

## Key findings

- Neural network successfully purifies noisy spectra
- Method generalizes to atomic and molecular systems
- Efficient Schrödinger equation propagation enables large training datasets

## Abstract

Photo-electron spectra obtained with intense pulses generated by free-electron lasers through self-amplified spontaneous emission are intrinsically noisy and vary from shot to shot. We extract the purified spectrum, corresponding to a Fourier-limited pulse, with the help of a deep neural network. It is trained on a huge number of spectra, which was made possible by an extremely efficient propagation of the Schr\"odinger equation with synthetic Hamilton matrices and random realizations of fluctuating pulses. We show that the trained network is sufficiently generic such that it can purify atomic or molecular spectra, dominated by resonant two- or three-photon ionization, non-linear processes which are particularly sensitive to pulse fluctuations. This is possible without training on those systems.