从离散时间快照中推断连续动态，解决时间标签模糊问题。
CT-OT Flow: Estimating Continuous-Time Dynamics from Discrete Temporal Snapshots
- 用部分最优传输对齐相邻时间段，恢复高精度时间标签
- 通过时间核平滑重建分布，生成邻近时间点对训练ODE/SDE模型
- 适用于单细胞测序与台风轨迹等真实数据，误差显著更低
在单细胞RNA测序、移动感知和环境监测等场景中，数据仅以有限时间窗内的聚合快照形式观测，常伴有噪声或不确定的时间戳，且无法获得连续轨迹。本文研究如何从此类快照中估计连续时间动态。提出连续时间最优传输流（CT-OT Flow），采用两阶段框架：(i) 通过部分最优传输（POT）对齐相邻区间，推断高分辨率时间标签；(ii) 利用时间核平滑重建连续时间数据分布，并从中采样相邻时间点对，用于训练标准的常微分方程/随机微分方程（ODE/SDE）模型。该方法显式建模快照聚合与时间标签不确定性，并引入筛选与小批量POT等实用加速策略，适用于大规模数据集。在合成基准及两个真实数据集（scRNA-seq和台风路径）上，相比OT-CFM、[SF]²M、TrajectoryNet、MFM和ENOT，CT-OT Flow显著降低分布误差与轨迹误差。
原文摘要 · Abstract (English)
In many real-world settings--e.g., single-cell RNA sequencing, mobility sensing, and environmental monitoring--data are observed only as temporally aggregated snapshots collected over finite time windows, often with noisy or uncertain timestamps, and without access to continuous trajectories. We study the problem of estimating continuous-time dynamics from such snapshots. We present Continuous-Time Optimal Transport Flow (CT-OT Flow), a two-stage framework that (i) infers high-resolution time labels by aligning neighboring intervals via partial optimal transport (POT) and (ii) reconstructs a continuous-time data distribution through temporal kernel smoothing, from which we sample pairs of nearby times to train standard ODE/SDE models. Our formulation explicitly accounts for snapshot aggregation and time-label uncertainty and uses practical accelerations (screening and mini-batch POT), making it applicable to large datasets. Across synthetic benchmarks and two real datasets (scRNA-seq and typhoon tracks), CT-OT Flow reduces distributional and trajectory errors compared with OT-CFM, [SF]\(^{2}\)M, TrajectoryNet, MFM, and ENOT.
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