aiqbench analysis
First-Order Trajectory Matching (FTM) offers a novel surrogate-modeling approach for stochastic systems that learns probability current velocity directly from trajectories, bypassing the need for explicit drift, diffusion, or score estimation. By ensuring stability through a balanced trade-off between temporal resolution and sample size, the method achieves low-cost, deterministic-rollout ensemble predictions while accurately capturing complex dynamics like fluxes and barrier-crossing currents. This advancement provides a robust framework for trajectory-aware predictions in chaotic and turbulent environments without relying on traditional simulation-heavy techniques.
First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systems
arXiv:2606.11138v1 Announce Type: new Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Numerical Analysis (math.NA)
arXiv:2606.11138 [cs.LG]
(or arXiv:2606.11138v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.11138 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 218 words