Data-driven discovery of beam centroid dynamics

We propose a method for understanding and predicting charged-particle beam dynamics using an interpretable, data-driven approach whose output is directly identifiable to terms in underlying evolution equations. In particular, we introduce a technique called Sparse Identification of Nonlinear Dynamics (SINDy), previously developed for other applications, and we apply SINDy to an elementary test problem for nonlinear beam dynamics in an electron ring. We generate the SINDy evolution equations solely on the basis of data—with no recourse to an underlying first-principles model. This methodology has the advantage that it applies to environments where analytic models do not suffice. Finally, we compare our methodology with both a machine learning technique and a first-principles model, and we show that SINDy can learn interpretable equations for nonlinear beam dynamics at lower computational cost while achieving comparable accuracy. • The development of an interpretable, data-driven model. • The development of a methodology for capturing beam dynamics in situations where analytic models are inadequate. • A comparison made to both another machine learning technique and first-principles model.