mlsanityData to 14 Oct 2026

First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systems

arXiv 2606.11138 ↗First posted 9 Jun 2026cs.LG cs.NA math.NAcited by 1

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Abstract (arXiv)

We introduce First-Order Trajectory Matching (FTM), a surrogate-modeling method that learns the first-order local transport of probability mass from trajectories of stochastic systems. By matching the symmetric first-order motion of trajectories, FTM learns the probability current velocity, whose flow preserves time marginals to match ensemble averages, while also capturing current-like trajectory quantities such as fluxes, circulations, and barrier-crossing currents. FTM learns the current velocity directly from trajectories, avoiding drift, diffusion, and score estimation. Our stability analysis separates discretization error from sampling variance and shows that the one-step simulation-free FTM loss is stable when temporal resolution and sample size are properly balanced. Across stochastic dynamical systems and PDE examples, we empirically demonstrate that FTM provides trajectory-aware ensemble predictions at low, deterministic-rollout cost.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 42 of its 60 references that are in the map. First posted on arXiv 9 Jun 2026.

Builds on

42 of 60 references.

References · 42

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30 more
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Citing papers per year: 2026: 1.

1 paper.

  1. 2026One-Step Generative Surrogate Models via Block-Triangular Joint Driftingcited by 0