Rigid-body dynamics learning keeps its geometry: LieSPHGP separates dissipation from stochastic forcing for steadier long-horizon prediction
LieSPHGP combines port-Hamiltonian structure, Lie-group geometry, Gaussian processes and stochastic differential equations to learn controlled, dissipative rigid-body dynamics from noisy trajectories. Matérn-kernel Gaussian processes model mass, potential energy, dissipation, control and diffusion separately, while exponential-map updates keep rotations on the manifold. On a windy pendulum and a quadrotor benchmark, it improves prediction accuracy, long-horizon stability and manifold-constraint satisfaction over neural dynamics baselines.