基于Wasserstein拉格朗日残差的免模拟群体动力学学习
Simulation-Free Learning of Population Dynamics with Wasserstein Lagrangian Residuals
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中文总结 AI 辅助
提出免模拟的Double-Stitch方法，通过惩罚运动方程残差学习Wasserstein空间中的拉格朗日动力学，在多个数据集上优于或匹配现有方法，训练速度提升4-14倍。
中文摘要 AI 辅助
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。从不成对的快照中重建并外推这种演化需要对潜在过程做出假设。Wasserstein梯度流是一种常见选择，但它无法描述保守或周期性动力学。Wasserstein空间中的拉格朗日力学涵盖了这两种情况，但现有的学习方法基于模拟：它们在每个训练步骤运行数值求解器，这使得训练成本高昂。我们提出了Double-Stitch，一种免模拟方法，通过沿学习到的群体路径惩罚运动方程的残差来学习这些力学。我们从Clebsch变分原理推导出该方程，该原理不需要梯度速度，并证明当方程成立时残差恰好消失。我们在合成数据集、单细胞数据集和海洋涡流数据集上测试了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模拟的WLM，同时训练速度比WLM快4-14倍。我们在此https URL提供Double-Stitch的JAX实现。
英文摘要
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 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 https://github.com/BasisResearch/stitching.
发表机构
- Basis Research Institute（Basis研究院）
- ETH Zurich（苏黎世联邦理工学院）
- Helmholtz AI（亥姆霍兹人工智能）
- MIT（麻省理工学院）
- University of Toronto（多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。
