无需模拟即可快速预测混沌系统的集合轨迹，效率高且精度优。
First-Order Trajectory Matching: Fast Ensemble Predictions of Chaotic, Turbulent, Stochastic Systems
- 直接从轨迹学习概率流速度，跳过传统扩散与得分估计步骤。
- 在多个随机动力系统和偏微分方程中实现低开销的精准集合预测。
- 适合需要高效、稳定预测复杂随机系统的研究人员或工程应用。
我们提出一阶轨迹匹配（FTM），一种代理建模方法，通过学习随机系统轨迹的一阶局部概率质量传输来建模。通过匹配轨迹的对称一阶运动，FTM 学习概率流速度，其流动保持时间边缘分布以匹配集合平均值，同时捕捉类似通量、环流和穿越屏障电流等轨迹量。FTM 直接从轨迹学习当前速度，避免了漂移、扩散和得分估计。我们的稳定性分析将离散化误差与采样方差分离，并表明当时间分辨率与样本量合理平衡时，一步模拟无须的 FTM 损失是稳定的。在多个随机动力系统和偏微分方程示例中，我们实证证明了 FTM 能以低开销、确定性滚动成本实现轨迹感知的集合预测。
原文摘要 · Abstract (English)
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.
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