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

2025-05-19

AI Summary

Single-cell snapshot data suffer from destructive measurements and cellular proliferation/apoptosis, resulting in unpaired, distributionally imbalanced samples across time points—severely hindering dynamic process modeling. To address this, we propose the first unified framework jointly modeling single-cell state evolution (velocity) and population-level mass changes (growth), based on a two-stage semi-relaxed optimal transport (OT) formulation for flow matching. Our method parameterizes continuous dynamics via neural networks and integrates distribution-fitting losses with OT constraints to enable end-to-end learning of biologically realistic dynamics incorporating mass variation. Evaluated on synthetic benchmarks and multiple real single-cell datasets, our approach significantly outperforms existing velocity and dynamic inference methods, accurately recovering coupled transcriptional kinetics and population expansion. This work establishes a scalable, physically interpretable framework for dynamical inference from snapshot data.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Modeling single-cell dynamics from unpaired snapshot data
• Learning state transition and mass growth jointly
• Handling unbalanced data due to cell proliferation/death

Innovation

• Jointly learns state transition and mass growth
• Uses flow matching for single-cell dynamics
• Approximates dynamics with neural networks