Trajectory inference via Acceleration Matching

2026-08-04

AI Summary

This work addresses the challenge of inferring smooth trajectories from discrete, unpaired observational snapshots by proposing an efficient method that circumvents the need for costly preprocessing or trajectory simulation inherent in existing approaches. The method lifts the interpolation problem into phase space, where it learns an explicit conditional acceleration field via regression and leverages stochastic differential equations to generate smooth trajectories consistent with the given marginal distributions. Requiring only positional data for training—without trajectory alignment or simulation—it achieves substantial gains in computational efficiency and scalability. Experimental results demonstrate that the proposed approach matches or outperforms current state-of-the-art methods across multiple benchmark tasks, confirming its effectiveness and competitiveness.

Abstract

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.

Problem

• trajectory inference
• smooth trajectories
• discrete time points
• data interpolation
• unpaired snapshots

Innovation

• Trajectory inference
• Acceleration Matching
• Phase space
• Conditional acceleration field
• Smooth interpolation