scChrono: Learning a Transcriptomic Virtual Embryo through Multi-Rate Developmental Dynamics

Virtual Embryo aims to construct a data-backed digital twin of embryogenesis that computationally describes continuous development. At the transcriptomic level, this requires recovering continuous developmental dynamics from discrete single-cell observations. However, transcriptional changes occur at different temporal rates, with sustained developmental progression coexisting with more localized state changes, making the complete developmental process difficult to capture with a single dynamical process. We introduce scChrono, a neural stochastic differential equation (SDE) for learning multi-rate developmental dynamics and constructing a transcriptomic virtual embryo. scChrono decomposes deterministic dynamics into Persistent Dynamics for sustained progression and Fast-Transition Dynamics for temporally gated corrections, while stochastic diffusion models population-level heterogeneity. scChrono reconstructs intermediate states, completes unobserved developmental intervals, forecasts unseen future transcriptomic distributions, and transfers learned developmental representations to downstream Cell Fate Prediction. Across the two primary forecasting settings on the Mouse Developmental Cell and Lineage Atlas (mdCLA), scChrono reduces normalized mean absolute error (NMAE) by 14.1-16.0% and Co-expression Structure Score (CSS) by 4.5% in highly variable gene (HVG) space, and Sinkhorn divergence by 16.1-21.9% in principal component analysis (PCA) space, relative to the strongest baseline for each metric, while achieving the best performance on all six metrics in both temporal completion settings. On lineage-resolved LARRY, transfer improves dominant top-1 fate accuracy by 6.2% over training from scratch. These results support multi-rate developmental dynamics as a framework for building continuous transcriptomic virtual embryos from cross-sectional single-cell atlases. Code is available at https://anonymous.4open.science/r/scChrono-54CC/.