  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.
