Experimental Verification of Integrability in a Danilov-Nagaitsev Lattice using Machine Learning

In non-linear optics, achieving integrability can enhance the dynamic aperture in storage rings. We analyze turn-by-turn phase-space data from our Danilov-Nagaitsev lattice implementation at Fermilab's Integrable Optics Test Accelerator using machine learning. AI Poincar\'e estimates conserved quantities from experimental data without prior knowledge of the invariant structure, showing qualitative agreement with theoretical predictions. Additionally, one of the two learned invariants exhibits comparable or better conservation compared to known theoretical expressions.