Reconstruction of dynamical systems from data without time labels
This addresses a practical issue for researchers in computational biology and physics where time-stamped data is unavailable, though it is an incremental extension of existing methods to a new data type.
The paper tackles the problem of reconstructing dynamical systems from data lacking time labels, which is common in fields like molecular dynamics and single-cell RNA sequencing, by treating the data as samples from a probability distribution and minimizing the sliced Wasserstein distance, with extensive experiments showing its effectiveness.
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.