scMomenta: A Second-order Neural ODE Framework for Single-cell Temporal Prediction

Single-cell temporal prediction aims to reconstruct cell populations at unsampled time points from destructive measurements that provide only unpaired population snapshots. Most existing neural differential equation methods model latent cellular dynamics with a first-order equation, in which position and time alone determine the velocity. However, hidden kinetic variables, such as unspliced RNA, and dimensionality reduction can make latent dynamics depend on history that position does not record. We introduce scMomenta, a second-order neural ODE framework that augments the latent position with an explicit velocity state and learns a damped acceleration field. We also design an initial-velocity module that estimates each cell's velocity by optimal transport. On five time-course datasets, scMomenta achieves strong overall performance against six competing methods, improving the accuracy of single-cell temporal prediction. Experiments on latent dynamical order, trajectory crossing and velocity-space perturbation further show that an explicit velocity state captures temporal structure that position alone does not.