基于加速度匹配的轨迹推断
Trajectory inference via Acceleration Matching
浏览论文内容
中文总结 AI 辅助
针对轨迹推断现有算法计算成本高的问题，提出加速度匹配（AM）算法，通过提升至相空间回归条件加速度场，在基准问题上表现优于或相当现有算法。
中文摘要 AI 辅助
轨迹推断是众多科学领域中的基础问题：给定一组离散时间点上未配对的观测快照，目标是生成最贴合并插值数据的平滑轨迹。现有算法存在计算挑战：它们要么依赖预处理子程序来强制平滑性，要么依赖基于模拟的训练目标，两者都可能成本高昂。为克服这些限制，我们提出一种名为加速度匹配（Acceleration Matching，简称AM）的新算法。我们的方法包括将原始插值问题提升至相空间，然后回归到显式条件加速度场，该场会生成符合指定边际分布的随机平滑轨迹。重要的是，我们得到的训练算法仅需位置数据，训练期间无需轨迹模拟，且无需昂贵的预处理。我们提供了充足的数值证据，表明AM在现有文献中的多个基准问题上与现有算法相当或更优。
英文摘要
Trajectory inference is a fundamental problem in many scientific domains: given a collection of unpaired snapshots of observations at discrete time points, the goal is to generate smooth trajectories that best resemble and interpolate the data. Existing algorithms exhibit computational challenges: they either rely on preprocessing subroutines to enforce smoothness or on simulation-based training objectives, both of which can be expensive. In order to overcome these limitations, we propose a new algorithm called Acceleration Matching (\texttt{AM}). Our approach consists of lifting the original interpolation problem to phase space and then regressing onto an explicit conditional acceleration field that induces random, smooth trajectories that agree with the prescribed marginals. Importantly, our resulting training algorithm only requires positional data, avoids trajectory simulation during training, and is devoid of expensive preprocessing. We provide ample numerical evidence suggesting that \texttt{AM} is competitive with or superior to existing algorithms on several benchmark problems from the existing literature.
发表机构
- University of Padova（帕多瓦大学）
- École polytechnique（巴黎综合理工学院）
- Yale University（耶鲁大学）
机构由 AI 辅助整理，请以论文原文为准。
