发表机构
Center for Machine Learning Research, Peking University; School of Mathematical Sciences, Peking University; Center for Quantitative Biology, Peking University; National Engineering Laboratory for Big Data Analysis and Applications, Beijing; AI for Science Institute, Beijing（北京大学机器学习研究中心; 北京大学数学科学学院; 北京大学定量生物学中心; 北京大数据分析与应用国家工程实验室; 北京科学智能研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
TracingFlow是一种无模拟的二阶动力学轨迹推断框架，通过回归加速度场解决动力最优加速度传输问题，在合成与scRNA-seq数据集上实现了更优的分布重构与轨迹保真度，还能恢复兼具数学最优性与生物学合理性的动力学结构。
AI 中文摘要
从稀疏时间快照推断连续系统演化是生成建模和单细胞组学的核心挑战。最优传输（OT）虽应用广泛，但现有框架大多局限于一阶动力学，假设速度场无记忆，这限制了表达能力，因为一阶系统无法解释细胞分化等过程中固有的调控动量和延迟响应。本文提出TracingFlow，一种可推广至二阶动力学的无模拟Flow Matching框架。通过使用神经网络回归加速度场，TracingFlow为动力最优加速度传输（DOAT）问题提供了精确且高效的解决方案。与产生过度平滑轨迹的一阶方法不同，TracingFlow的二阶公式通过学习潜在力场捕捉高曲率过渡和非线性演化。在复杂合成数据集和大规模scRNA-seq数据集上的评估显示，TracingFlow在分布重构和轨迹保真度方面实现了更优的准确性；此外，通过整合谱系示踪先验，它恢复了兼具数学最优性和生物学合理性的动力学结构。
英文摘要
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.
