Data-Driven Discovery of Beam Centroid Dynamics

TL;DR

This paper applies Sparse Identification of Nonlinear Dynamics (SINDy) to derive interpretable equations for beam centroid dynamics in accelerators, offering a data-driven approach that balances prediction accuracy and interpretability without relying on detailed first-principles models.

Contribution

The study demonstrates the use of SINDy to learn evolution equations for beam dynamics directly from data, providing an interpretable alternative to traditional machine learning models in accelerator physics.

Findings

SINDy accurately predicts beam centroid evolution.

SINDy offers better interpretability than black-box models.

Comparison shows SINDy balances prediction and computational efficiency.

Abstract

Understanding and predicting complex dynamics in accelerators is necessary for their successful operation. A grand challenge in accelerator physics is to develop predictive virtual accelerators that mitigate design cost and schedule risk. Data-driven techniques greatly appeal to generating virtual accelerators due to their limited dimensionality compared with first-principle simulation, yet require significant up-front investment and lack interpretability in the context of governing equations. This paper uses an alternative, interpretable, data-driven technique called Sparse Identification of Nonlinear Dynamics (SINDy) developed by University of Washington researchers to study nonlinear beam centroid dynamics excited by realistic beam injection. We propose evolution equations based solely on data analysis and intuition of the underlying lattice structure, without recourse to an underlying first-principles centroid model nor the actual lattice forcing functions. We do this to mimic an application environment where analytic models are inadequate or where detailed lattice forcing functions are unknown. In the context of the accurate centroid model, we report and interpret SINDy's beam evolution equations learned from the training data and show favorable prediction results. We compare with an alternative machine learning model used on the same training data and contrast its prediction ability, computational expense, and interpretability with SINDy's results.