Hard Symplectic Graph Neural ODEs for Scalable Trajectory Reconstruction in Perturbed Relativistic N-Body Celestial Swarms: Scaling to One Million Bodies with Empirical NASA Ephemerides
This paper introduces SympG-NODE, a structure-preserving Graph Neural ODE framework that leverages symplectic geometry and equivariant graph networks to achieve scalable, high-accuracy trajectory reconstruction for perturbed relativistic N-body celestial swarms of up to one million bodies while strictly conserving Hamiltonian invariants and overcoming the phase-drift limitations of standard Physics-Informed Neural Networks.