KoopCell: Koopman-Based Generative Model for Learning Single-Cell Dynamics from Distribution Snapshots
Abstract
Learning population dynamics from temporally sparse, unpaired distribution snapshots is a fundamental challenge in developmental biology. Recent approaches based on neural differential equations and flow matching can interpolate between observed population snapshots, but may struggle to extrapolate beyond the training horizon and often lack an explicit mechanism for modeling developmental branching. We propose KoopCell, a unified generative framework based on Koopman-Mori-Zwanzig theory that jointly learns representations and predictive linear latent dynamics. Theoretically, using the weak continuity equation, we derive a closed-form least-squares estimator for the Koopman generator from distribution snapshots and establish convergence guarantees under suitable assumptions. To model branching dynamics, we further develop KoopCell-M, which incorporates non-Markovian memory into the latent Koopman dynamics through a Markovian embedding. Experiments on synthetic systems and three scRNA-seq datasets demonstrate the ability of our framework to recover Koopman spectra, model branching through memory, and scale to predicting high-dimensional gene expression distributions, achieving state-of-the-art performance among the evaluated methods.
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BibTeX
@misc{lu2026koopcell,
title = {{KoopCell: Koopman-Based Generative Model for Learning Single-Cell Dynamics from Distribution Snapshots}},
author = {Wanfeng Lu and Yutong Zhang and Keyi Zhou and Chenxin Ge and Wei Lin and Qunxi Zhu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33350},
eprint = {2609.33350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33350},
note = {CC0},
}
RIS
TY - UNPB
TI - KoopCell: Koopman-Based Generative Model for Learning Single-Cell Dynamics from Distribution Snapshots
AU - Wanfeng Lu
AU - Yutong Zhang
AU - Keyi Zhou
AU - Chenxin Ge
AU - Wei Lin
AU - Qunxi Zhu
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33350
UR - https://arxiv.org/abs/2609.33350
AB - Learning population dynamics from temporally sparse, unpaired distribution snapshots is a fundamental challenge in developmental biology. Recent approaches based on neural differential equations and flow matching can interpolate between observed population snapshots, but may struggle to extrapolate beyond the training horizon and often lack an explicit mechanism for modeling developmental branching. We propose KoopCell, a unified generative framework based on Koopman-Mori-Zwanzig theory that jointly learns representations and predictive linear latent dynamics. Theoretically, using the weak continuity equation, we derive a closed-form least-squares estimator for the Koopman generator from distribution snapshots and establish convergence guarantees under suitable assumptions. To model branching dynamics, we further develop KoopCell-M, which incorporates non-Markovian memory into the latent Koopman dynamics through a Markovian embedding. Experiments on synthetic systems and three scRNA-seq datasets demonstrate the ability of our framework to recover Koopman spectra, model branching through memory, and scale to predicting high-dimensional gene expression distributions, achieving state-of-the-art performance among the evaluated methods.
ER -