arXiv：cs.LG· Fedor Sergeev, Markus Heinonen, Daniel Waxman, Tim Cooijmans, Ricardo Baptista, Dmitry Batenkov, Eli Bingham·· 3 小时前AI 评分38
Double-Stitch：无仿真学习 Wasserstein 拉格朗日残差的人群动力学
Simulation-Free Learning of Population Dynamics with Wasserstein Lagrangian Residuals
AI 导读
研究者提出 Double-Stitch，一种无需仿真的方法，通过学习种群路径上运动方程残差来学习 Wasserstein 空间中的拉格朗日力学，该方程由无需梯度速度的 Clebsch 变分原理导出。在合成、单细胞和海洋涡旋数据集上，该方法在多数任务上匹配或超越梯度流方法与基于仿真的 WLM，训练速度比 WLM 快 4-14 倍。JAX 实现已公开。
正文
Abstract: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 velocities, and show that the residual vanishes exactly when the equation holds. We test Double-Stitch on synthetic, single-cell and ocean vortex datasets and find that it matches or outperforms gradient-flow methods and simulation-based WLM on most tasks, while training $4$-$14$ times faster than WLM. We provide a JAX implementation of Double-Stitch at this https URL.
| Comments: | 34 pages, 11 figures |
| Subjects: | Machine Learning (cs.LG); Methodology (stat.ME); Machine Learning (stat.ML) |
| Cite as: | arXiv:2610.03679 [cs.LG] |
| (or arXiv:2610.03679v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.03679 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Daniel Waxman [view email]
[v1]
Fri, 2 Oct 2026 17:46:52 UTC (6,553 KB)
来源：arXiv：cs.LG · arxiv.org