用二阶动力学建模细胞演化轨迹，更准更真实。
TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamics
- 用神经网络预测加速度场，突破一阶动力学限制。
- 在真实单细胞数据上，轨迹重建准确率显著提升。
- 适合研究细胞分化等具有惯性与延迟响应的生物过程。
从稀疏时间快照中推断连续系统演化是生成建模与单细胞组学的关键挑战。尽管最优传输（OT）广受欢迎，现有方法多局限于一阶动力学，假设速度场无记忆性。这限制了模型表达能力，因一阶系统无法捕捉细胞分化等过程中固有的调控惯性与时滞响应。本文提出TracingFlow，一种无需模拟的流匹配框架，可推广至二阶动力学。通过神经网络回归加速度场，TracingFlow为动态最优加速度传输（DOAT）问题提供精确高效的解。相比一阶方法产生的过度平滑轨迹，二阶形式能捕捉高曲率转变与非线性演化，学习底层力场。在复杂合成数据与大规模scRNA-seq数据集上的评估显示，TracingFlow在分布重构与轨迹保真度方面均表现更优。此外，结合谱系追踪先验，其恢复的动力学结构兼具数学最优性与生物学合理性。
原文摘要 · Abstract (English)
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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