In this paper, we study the method to reconstruct dynamical systems from data without time labels. Data without time labels appear in many applications, such as molecular dynamics, single-cell RNA sequencing etc. Reconstruction of dynamical system from time sequence data has been studied extensively. However, these methods do not apply if time labels are unknown. Without time labels, sequence data becomes distribution data. Based on this observation, we propose to treat the data as samples from a probability distribution and try to reconstruct the underlying dynamical system by minimizing the distribution loss, sliced Wasserstein distance more specifically. Extensive experiment results demonstrate the effectiveness of the proposed method.

翻译：本文研究从无时间标签数据中重构动力学系统的方法。无时间标签数据广泛存在于分子动力学、单细胞RNA测序等应用场景。基于时间序列数据的动力学系统重构已有深入研究，但这些方法在时间标签未知时无法适用。当时间标签缺失时，序列数据转化为分布数据。基于此观察，我们提出将数据视为概率分布的采样样本，并通过最小化分布损失（具体采用切片Wasserstein距离）来重构底层动力学系统。大量实验结果验证了所提方法的有效性。