Dynamics NL Dynamics w. Diffeomorphism Explore nonlinear dynamics properties without tracking Dynamics in Crab Crossing Explore the challenges of crab crosing in colliders Computation Auto-Diff in beam tracking Development of JuTrack code, focus on AD in self-field Data Driven Modeling ML Model for Beam Dynamics Apply machine learning in finding transformations to rotation ML based Control Methods Model predictive control enabled by data driven models