无模拟的带通用增长惩罚的非平衡动态最优传输

中文摘要 AI 辅助

从不配对的单细胞快照推断细胞动态需要同时建模状态转换和种群增长或死亡，非平衡动态最优传输（UDOT）通过对传输路径上的增长进行惩罚来解决这一问题，因此增长惩罚的选择是编码增殖和凋亡相关生物学先验的关键方式。然而，现有的UDOT求解器要么依赖计算成本高昂的神经常微分方程（NeuralODE）模拟，要么依赖条件路径的解析解，其效率仅局限于二次惩罚（即Wasserstein-Fisher-Rao（WFR）测地线）。为了实现适用于通用增长惩罚的高效UDOT求解器，我们首先证明凹增长惩罚会导致增长与传输分离的退化解。随后，我们提出SUDO（Simulation-free Unbalanced Dynamic Optimal transport，无模拟非平衡动态最优传输），这是一种适用于带通用非二次凸增长惩罚的UDOT的无模拟框架。SUDO学习条件路径和传输成本，求解诱导的半耦合问题，随后利用非平衡流匹配实现无模拟解。在WFR基准上，SUDO达到了高效解析解驱动算法的精度，同时在计算速度上优于基于模拟的方法。除WFR外，SUDO还支持编码增殖主导先验的非对称惩罚，并在合成数据集和单细胞数据集上生成更合理的轨迹和增长估计。

英文摘要

Inferring cellular dynamics from unpaired single-cell snapshots requires modeling both state transitions and population growth or death. Unbalanced dynamic optimal transport (UDOT) addresses this by penalizing growth along transport paths, making the choice of growth penalty a key way to encode biological priors on proliferation and apoptosis. However, existing UDOT solvers either rely on computationally expensive NeuralODE simulations or depend on analytical solutions of conditional paths, restricting their efficiency solely to quadratic penalties, i.e. Wasserstein-Fisher-Rao (WFR) geodesics. To enable an efficient UDOT solver for general growth penalties, we first show that concave growth penalties lead to degenerate solutions where growth and transport are separated. We then introduce \textbf{S}imulation-free \textbf{U}nbalanced \textbf{D}ynamic \textbf{O}ptimal transport (SUDO), a simulation-free framework for UDOT with general non-quadratic convex growth penalties. SUDO learns the conditional paths and transport costs, solves the induced semi-coupling problem, and subsequently leverages unbalanced flow matching to achieve a simulation-free solution. On WFR benchmarks, SUDO matches the accuracy of efficient, analytical solution-driven algorithms while outperforming simulation-based methods in computational speed. Beyond WFR, SUDO supports asymmetric penalties that encode proliferation-dominant priors and produce more plausible trajectories and growth estimates on synthetic and single-cell datasets.

发表机构

• Beijing International Center for Mathematical Research, Peking University（北京大学北京数学科学研究中心）
• Center for Quantitative Biology, Peking University（北京大学定量生物学中心）
• School of Mathematical Sciences, Peking University（北京大学数学科学学院）
• Center for Machine Learning Research, Peking University（北京大学机器学习研究中心）
• National Engineering Laboratory for Big Data Analysis and Applications（大数据分析与应用国家工程实验室）
• AI for Science Institute, Beijing（北京人工智能科学研究院）
• Institute for Artificial Intelligence, Peking University（北京大学人工智能研究院）

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