TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamics
This work addresses the limitation of first-order dynamics in optimal transport for generative modeling and single-cell omics, which often fail to capture regulatory momentum and time-delayed responses, providing a more expressive model for these fields.
This paper introduces TracingFlow, a simulation-free Flow Matching framework that infers continuous system evolution from sparse temporal snapshots by modeling second-order dynamics. It achieves superior accuracy in distributional reconstruction and trajectory faithfulness on complex synthetic and large-scale scRNA-seq datasets compared to first-order methods.
Inferring continuous system evolution from sparse temporal snapshots is a key challenge in generative modeling and single-cell omics. While Optimal Transport (OT) is popular, existing frameworks are largely restricted to first-order dynamics, assuming memoryless velocity fields. This limits expressiveness, as first-order systems fail to account for regulatory momentum and time-delayed responses inherent in processes like cell differentiation. Here, we introduce TracingFlow, a simulation-free Flow Matching framework generalizing to second-order dynamics. By using neural networks to regress the acceleration field, TracingFlow provides an exact, efficient solution to the Dynamical Optimal Acceleration Transport (DOAT) problem. Unlike first-order methods yielding over-smoothed trajectories, our second-order formulation captures high-curvature transitions and nonlinear evolutions by learning the underlying force fields. Evaluated on complex synthetic and large-scale scRNA-seq datasets, TracingFlow achieves superior accuracy in distributional reconstruction and trajectory faithfulness. Moreover, by integrating lineage tracing priors, it recovers dynamical structures that are both mathematically optimal and biologically plausible.