Label-free flow operators and stability operators from single-cell time courses: what local dynamical operators can and cannot identify

Flow operators estimated label-free from single-cell time courses separate fate-bifurcation from committed cells (AUC 0.89–1.00) and predict clonal displacement in LARRY (Spearman 0.56).

• Why it matters: Local Jacobians are used to flag unstable cells, but it is unclear what can be reliably identified from measured trajectories versus what remains unidentifiable. This work tests operator identifiability against independent truth.
• What they did: They introduce scJDO2, learning a score operator from any snapshot and a flow operator from sampled velocities using entropic optimal transport, then evaluate with pre-registered tests on synthetic, LARRY lineage data, and an independent simulator.
• The result: The flow operator validates the fitted velocity rather than {lambda}, detects 2/3 bifurcations and 2/3 cycles, and scales to 130,887 cells; however, neither operator recovers true Jacobians, and diffusion is not identifiable at typical sampling intervals.

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