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

2026-08-21

AI Summary

本文提出TracingFlow框架，通过神经网络回归加速度场解决第二阶动力学问题，以提高稀疏时间快照下系统演化推断的准确性。

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.

Problem

• Optimal Transport
• first-order dynamics
• cell differentiation
• second-order dynamics
• trajectory inference

Innovation

• Second-Order Dynamics
• Acceleration Field
• Dynamical Optimal Acceleration Transport (DOAT)
• High-Curvature Transitions
• Lineage Tracing Priors