Applications of ML-Based Statistical Distance to the Modeling of Nonlinear dynamics in High-Intensity Beams

Measures of discrepancy between probability distributions are widely used in the fields of artificial intelligence and machine learning. Although two-sample algorithms for estimating statistical distance typically have high computational complexity, we show that some measures of statistical distance (and statistical dependence) can be implemented efficiently as numerical diagnostics in simulations involving charged-particle beams with large particle ensembles. Such diagnostics are useful for comparing two particle populations, for matching a particle beam successfully into a periodic transport system, and for detecting high-dimensional nonlinear correlations in the beam phase space. The resulting diagnostics provide sensitive measures of dynamical processes (such as mixing and relaxation) important for understanding the long-time phase space evolution of beams in nonlinear or high-intensity systems. Applications are illustrated using several benchmark problems and examples involving intense beams. While the focus is on charged-particle beams, these methods may also be applied to other many-body systems such as plasmas or gravitational systems.