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Generative models of cell dynamics: from Neural ODEs to flow matching.

Till Richter^1,2, Weixu Wang^1,2, Alessandro Palma^1,2

¹Helmholtz Munich, Munich, Germany.

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|February 27, 2026

Summary

Neural Ordinary Differential Equations (Neural ODEs) model complex dynamics in single-cell data. Innovations like Flow Matching enable efficient cell state transition modeling, advancing computational health research.

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Area of Science:

Computational Biology
Machine Learning
Dynamical Systems

Background:

Single-cell data presents significant challenges including noise, sparsity, and temporal limitations.
Neural Ordinary Differential Equations (Neural ODEs) offer a powerful framework for modeling complex dynamical systems.
Existing research highlights Neural ODEs' potential in mechanistic modeling of cellular development and population dynamics.

Purpose of the Study:

To investigate the suitability of Neural ODEs for modeling dynamic processes within single-cell data.
To explore applications in computational health, encompassing time-series analysis and generative models.
To examine the role of Flow Matching in efficient cell state transition modeling.

Main Methods:

Exploration of the mathematical properties of Neural ODEs for cellular dynamics.
Application of generative modeling, specifically simulation-free Flow Matching, for cell state transitions.
Analysis of standard time-series parameterizations and optimal transport-based generative models.

Main Results:

Neural ODEs effectively model the underlying dynamical laws in biological systems.
Flow Matching provides an efficient and expressive method for simulating cell state transitions without explicit simulation.
Neural ODEs demonstrate suitability for analyzing dynamic processes in cellular data.

Conclusions:

Neural ODEs are a robust machine learning framework for modeling dynamic processes in single-cell data.
Advancements in generative modeling, like Flow Matching, enhance the utility of Neural ODEs for computational health.
This approach promises to deepen the understanding of dynamics within cellular systems and drive future research.