TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics

TL;DR

TrajectoryNet introduces a novel approach linking continuous normalizing flows with dynamic optimal transport to model continuous, non-linear cellular trajectories over time, improving upon static models in single-cell RNA sequencing data analysis.

Contribution

It presents TrajectoryNet, a method that controls continuous paths between distributions, enabling dynamic modeling of cellular trajectories in biomedical data.

Findings

TrajectoryNet effectively models continuous cellular dynamics.

It outperforms static optimal transport models in scRNA-seq data.

The method captures non-linear cellular trajectories.

Abstract

It is increasingly common to encounter data from dynamic processes captured by static cross-sectional measurements over time, particularly in biomedical settings. Recent attempts to model individual trajectories from this data use optimal transport to create pairwise matchings between time points. However, these methods cannot model continuous dynamics and non-linear paths that entities can take in these systems. To address this issue, we establish a link between continuous normalizing flows and dynamic optimal transport, that allows us to model the expected paths of points over time. Continuous normalizing flows are generally under constrained, as they are allowed to take an arbitrary path from the source to the target distribution. We present TrajectoryNet, which controls the continuous paths taken between distributions to produce dynamic optimal transport. We show how this is particularly applicable for studying cellular dynamics in data from single-cell RNA sequencing (scRNA-seq) technologies, and that TrajectoryNet improves upon recently proposed static optimal transport-based models that can be used for interpolating cellular distributions.