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

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.