KoopCell：基于Koopman的生成模型，用于从分布快照学习单细胞动力学

中文摘要 AI 辅助

从时间上稀疏、未配对的分布快照中学习群体动力学是发育生物学中的一个基本挑战。近期基于神经微分方程和流匹配的方法能够在观测到的群体快照之间进行插值，但可能难以在训练时间范围之外进行外推，并且往往缺乏用于建模发育分支的显式机制。我们提出KoopCell，一个基于Koopman-Mori-Zwanzig理论的统一生成框架，该框架联合学习表示和预测性线性潜在动力学。理论上，利用弱连续性方程，我们从分布快照中推导出Koopman生成元的闭式最小二乘估计器，并在适当假设下建立收敛保证。为了建模分支动力学，我们进一步开发了KoopCell-M，该模型通过马尔可夫嵌入将非马尔可夫记忆纳入潜在Koopman动力学中。在合成系统和三个scRNA-seq数据集上的实验表明，我们的框架能够恢复Koopman谱、通过记忆建模分支，并扩展到预测高维基因表达分布，在所评估的方法中实现了最先进的性能。

英文摘要

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.

发表机构

• Fudan University（复旦大学）
• Research Institute of Intelligent Complex Systems, Fudan University（复旦大学智能复杂系统研究院）
• Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）

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