Reconstructing spatiotemporal fields from partial observations is fundamental to scientific inference, from inferring atmospheric states from satellite data to recovering fluid states from imaging. When observations are incomplete, the inverse problem is fundamentally ill-posed: even when the underlying PDE dynamics are Markovian in the full state, partial observation operators induce a non-Markovian posterior that cannot be resolved from a single timestep. We propose a history-bootstrapped autoregressive flow matching (HB-ARFM) for spatiotemporal inverse reconstruction under partial observability. Observation history bootstraps the initial reconstruction via conditional flow matching, reducing ambiguities. The same conditional transport model is then applied autoregressively, conditioning on both new observations and past predictions to propagate the reconstruction forward in time. We evaluate the method on boiling dynamics reconstruction, recovering full velocity and temperature fields from interface geometry and motion. Across two inverse tasks with varying observation sparsity, HB-ARFM produces physically and temporally valid reconstructions where other models fail.

翻译：摘要：从部分观测中重建时空场是科学推理的基础，涵盖从卫星数据推断大气状态到从成像恢复流体状态等多个领域。当观测不完整时，逆问题本质上是不适定的：即使底层偏微分方程动力学在全状态空间中是马尔可夫的，部分观测算子也会导致非马尔可夫的后验分布，该后验无法从单个时间步中求解。我们提出了一种基于历史引导的自回归流匹配方法（HB-ARFM），用于解决部分可观测性下的时空逆重建问题。观测历史通过条件流匹配引导初始重建，减少歧义性。随后，相同的条件传输模型以自回归方式应用，同时基于新观测和过去预测将重建结果随时间向前传播。我们在沸腾动力学重建任务上评估该方法，从界面几何与运动恢复完整的速度场和温度场。在两种不同观测稀疏度的逆任务中，HB-ARFM 能够生成物理与时域有效的重建结果，而其他模型则无法实现。