Hybrid deep learning–mechanistic modeling of cellular dynamics from a spatiotemporal single-cell atlas

Single-cell measurement technologies provide a powerful framework for studying cellular heterogeneity, transitions, and regulatory networks, yet reconstructing the underlying dynamical processes governing these transitions remains a major challenge due to the high dimensionality of gene expression data. To address this, we develop a variational autoencoder (VAE)–latent neural ordinary differential equation (ODE) approach that learns a low-dimensional latent representation of cellular states and models their temporal evolution. We apply our framework to the single-cell fluorescence imaging spatiotemporal atlas of Drosophila melanogaster blastoderm embryos via spatial registration, which comprises six registered developmental time points prior to gastrulation. In our approach, gene expression profiles are encoded into a latent space where a neural ordinary differential equation (ODE) is trained to capture the continuous dynamics of cellular states over time, and a decoder subsequently maps these evolving latent representations back to the original high-dimensional gene expression space, enabling accurate reconstruction of observed transcriptional patterns. While such black-box deep learning approaches excel at capturing complex dynamical trajectories, they are inherently limited in their ability to predict the effects of combinatorial perturbations. To overcome this limitation, we leverage the inferred latent dynamics as a foundation for fitting a mechanistic Hill-function model of gene regulation, which—guided by the black-box representations—enables interpretable predictions by systematically perturbing couplings between specific gene pairs and thus provides mechanistic insight into developmental regulatory programs.