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

• URL: http://arxiv.org/abs/2608.21070v1
• Date: Fri, 21 Aug 2026 13:11:29 GMT
• Title: TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamics
• Abstract summary: Inferring continuous system evolution from sparse temporal snapshots is a key challenge in generative modeling and single-cell omics.<n>Here, we introduce TracingFlow, a simulation-free Flow Matching framework generalizing to second-order dynamics.<n>By using neural networks to regress the acceleration field, TracingFlow provides an exact, efficient solution to the Dynamical Optimal Acceleration Transport (DOAT) problem.
• Score: 7.088148340428723
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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