Joint Velocity-Growth Flow Matching for Single-Cell Dynamics Modeling

TL;DR

This paper introduces VGFM, a novel method for modeling single-cell dynamics from snapshot data by jointly learning velocity and growth, effectively handling unpaired and unbalanced data with flow matching and neural network approximation.

Contribution

VGFM is the first framework to jointly model velocity and growth in single-cell dynamics using flow matching and semi-relaxed optimal transport.

Findings

VGFM outperforms existing methods on synthetic datasets.

VGFM accurately captures biological dynamics in real data.

The approach effectively handles unpaired, unbalanced snapshot data.

Abstract

Learning the underlying dynamics of single cells from snapshot data has gained increasing attention in scientific and machine learning research. The destructive measurement technique and cell proliferation/death result in unpaired and unbalanced data between snapshots, making the learning of the underlying dynamics challenging. In this paper, we propose joint Velocity-Growth Flow Matching (VGFM), a novel paradigm that jointly learns state transition and mass growth of single-cell populations via flow matching. VGFM builds an ideal single-cell dynamics containing velocity of state and growth of mass, driven by a presented two-period dynamic understanding of the static semi-relaxed optimal transport, a mathematical tool that seeks the coupling between unpaired and unbalanced data. To enable practical usage, we approximate the ideal dynamics using neural networks, forming our joint velocity and growth matching framework. A distribution fitting loss is also employed in VGFM to further improve the fitting performance for snapshot data. Extensive experimental results on both synthetic and real datasets demonstrate that VGFM can capture the underlying biological dynamics accounting for mass and state variations over time, outperforming existing approaches for single-cell dynamics modeling.