The Non-Perturbative Adiabatic Invariant is All You Need

In this 19-minute talk from the Simons Foundation, explore Josh Burby's innovative approach to modeling highly-oscillatory dynamical systems through non-perturbative methods. Learn why traditional asymptotic averaging techniques fail in regimes with marginal timescale separation, particularly when studying charged particles in strong inhomogeneous magnetic fields. Discover the data-driven averaging method developed to overcome these limitations, which significantly outperforms conventional approaches even when accounting for higher-order corrections. Understand both the general principles of this non-perturbative technique and its specific application to charged particle dynamics. This presentation is part of the Simons Collaboration on Hidden Symmetries and Fusion Energy Annual Meeting 2025.