[论文] Simulation-Free Learning of Population Dynamics with Wasserstein Lagra...

论文概要

研究领域: ML 作者: Fedor Sergeev, Markus Heinonen, Daniel Waxman, Tim Cooijmans, Ricardo Baptista, Dmitry Batenkov, Eli Bingham 发布时间: 2026-10-02 arXiv: 2610.03679

中文摘要

细胞、生物体和流体的动力学通常被建模为随时间演化的概率分布。从非配对快照中重建和外推这种演化需要对底层过程做出假设。Wasserstein 梯度流是常见选择，但无法描述保守或周期性动力学。Wasserstein 空间中的拉格朗日力学可以涵盖两者，但现有的学习方法基于仿真：每步训练都要运行数值求解器，使训练代价高昂。我们提出 Double-Stitch——一种无仿真方法，通过惩罚学习到的群体路径上的运动方程残差来学习这些力学。我们从不需要梯度速度的 Clebsch 变分原理推导出该方程，并证明残差仅在方程成立时精确为零。我们在合成、单细胞和海洋涡旋数据集上测试 Double-Stitch，发现它在大多数任务上匹配或优于梯度流方法和基于仿真的 WLM，同时训练速度比 WLM 快 4-14 倍。我们在 https://github.com/BasisResearch/stitching 提供了 JAX 实现。

原文摘要

The dynamics of cells, organisms, and fluids are often modeled as probability distributions evolving over time. Reconstructing and extrapolating this evolution from unpaired snapshots requires assumptions about the underlying process. Wasserstein gradient flows are a common choice, but they cannot describe conservative or periodic dynamics. Lagrangian mechanics in Wasserstein space covers both, but existing methods for learning it are simulation-based: they run a numerical solver at every training step, which makes training expensive. We propose Double-Stitch, a simulation-free method that learns these mechanics by penalizing the residual of the equation of motion along a learned population path. We derive this equation from a Clebsch variational principle that does not require gradient ve...

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