论文提出了AM算法做轨迹推断，不用模拟轨迹，训练只要位置数据，比现有方法省算力。
arXiv 新论文提出轨迹推断算法 Acceleration Matching (AM)。AM 将插值问题提升到相空间，学习条件加速度场来生成平滑轨迹。训练过程只用位置数据，免去轨迹模拟和昂贵预处理。在文献中的多个基准问题上，AM 达到与现有算法相当或更优的表现。
Trajectory inference via Acceleration Matching
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.