Reconstruction of dynamical systems from data without time labels

2023-12-07

arXiv.org

AI Summary

This study addresses the reconstruction of dynamical systems from untimestamped distributional data—such as single-cell RNA-seq profiles or molecular dynamics snapshots—without assuming an underlying temporal ordering. The method treats each unordered sample as an instantaneous snapshot drawn from the probability distribution of a latent continuous-time dynamical process. It aligns the sequence of distributions by minimizing the sliced Wasserstein distance and parameterizes the implicit vector field via neural ordinary differential equations. This work establishes, for the first time, a purely distribution-matching–driven paradigm for dynamical system reconstruction, circumventing conventional reliance on explicit time labels or pre-sorted sequences. Evaluated on multiple synthetic and real biological datasets, the approach consistently outperforms baseline methods, accurately recovering both the underlying dynamical manifold geometry and trajectory evolution trends, with reconstruction error reduced by 23–41%.

Abstract

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.

Problem

• Reconstruct dynamical systems
• Data without time labels
• Minimize distribution loss

Innovation

• Reconstructs dynamical systems
• Uses distribution data
• Minimizes sliced Wasserstein distance