TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamics

TL;DR - TracingFlow is a simulation-free flow-matching framework that infers trajectories from sparse temporal snapshots using second-order dynamics. By learning acceleration rather than only velocity, it better captures nonlinear, high-curvature processes such as cell differentiation.

• Provides an exact, efficient solution to the Dynamical Optimal Acceleration Transport problem.
• Learns force fields that model regulatory momentum and delayed responses absent from memoryless first-order methods.
• Improves distribution reconstruction and trajectory faithfulness on synthetic and large-scale scRNA-seq datasets.
• Incorporates lineage-tracing priors to recover mathematically optimal and biologically plausible dynamics.