It is a little jarring to hear "data-driven" and "nonperturbative" in the same sentence. It sounds a little bit like saying you designed a boat with a better lift-to-drag ratio. "Wait, is it a boat or a plane?". So, I opened the paper fully expecting to not understand anything, and I was pleasantly surprised.<p>> First we deduce formally-exact non-perturbative guiding center
equations of motion assuming a hidden symmetry with associated conserved quantity J. We refer to J as the non-perturbative adiabatic invariant.<p>Simply: this is not just some kind of unsupervised ML black-box magic. There is a formal mathematical solution to <i>something</i>, but it has a certain gap, namely precisely what quantity is conserved and how to calculate it.<p>> Then we describe a data-driven method for learning J from a dataset of full-orbit α-particle trajectories. [...] Our proposed method for learning J applies on a per-magnetic field basis; changing B requires re-training. This makes it well-suited to stellarator design assessment tasks, such as α-loss fraction uncertainty quantification.<p>With the formal simplification of the dynamics in hand, the researchers believe that a trained model can then give a useful approximation of the invariant, which allows the formal model, with its unknown parameters now filled in, to be used to model the dynamics.<p>In a crude way, I think I have a napkin-level sketch of what they're doing here. Suppose we are modeling a projectile, and we know nothing of kinematics. They have determined that the projectile has a parabolic trajectory (the formal part) and then they are using data analysis to find the <i>g</i> coefficient that represents gravitational acceleration (the data-driven part). Obviously, you would never need machine learning in such a very simple case as I have described, but I think it approximates the main idea.