Using "AI Poincare" to analyze non-linear integrable optics

TL;DR

This paper evaluates AI Poincare, an AI-based method, for analyzing conserved quantities in non-linear integrable systems relevant to accelerator physics, demonstrating its effectiveness on simulated and experimental data.

Contribution

The study introduces an improved neural network architecture and provides a comprehensive evaluation of AI Poincare's performance in identifying conserved quantities in complex dynamical systems.

Findings

AI Poincare accurately estimates conserved quantities in simulated data.

Optimal perturbation range enhances manifold extraction performance.

Successful application to experimental data from Fermilab's accelerator.

Abstract

This study dives into the applicability of using automated discovery of conserved quantities in dynamical systems relevant to accelerator physics. Specifically, we explore the performance of AI Poincar\'e in analyzing numerical trajectory data obtained using the McMillan system of non-linear integrable optics. A comprehensive evaluation of the algorithm's performance is conducted through diverse methodologies. These include the analysis of the estimated number of conserved quantities embedded in a dataset and the deviation of interpolated points on the inferred manifold with respect to points in actually in the dataset. the investigation identifies an optimal range of perturbation distances where the underlying manifold extraction algorithm inside AI Poincar\'e exhibits optimal performance. Additionally, an improved neural network architecture is proposed based on the observed results. Finally, we apply the algorithm to preliminary experimental data from the Integrable Optics Test Accelerator at Fermilab to successfully infer the number of conserved quantities even in the presence of fast decoherence of the measured signal.