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：本文研究了从无时间标签数据中重构动力系统的方法。无时间标签数据出现在许多应用场景中，例如分子动力学、单细胞RNA测序等。从时序数据重构动力系统的方法已被广泛研究，然而当时间标签未知时，这些方法不再适用。无时间标签使序列数据退化为分布数据。基于这一发现，我们提出将数据视为概率分布的样本，通过最小化分布损失（特别是切片Wasserstein距离）来重构潜在的动力系统。大量实验结果表明了所提方法的有效性。