切线 Schrödinger 桥匹配：利用机制敏感性学习随机输运

中文摘要 AI 辅助

预测随机系统对粘度、反应速率或外力变化的响应需要昂贵的模拟，这促使开发可复用的学习模型。然而，仅匹配观测到的结果分布并不能确保准确的干预响应。我们引入了切线 Schrödinger 桥匹配（Tangent-SBM），该方法从端点观测和机制敏感性中学习随机输运。它在轨迹传播的同时传播参数导数，并根据提供的目标对其进行监督。对于平均响应目标，单次 rollout 的平方误差也会惩罚响应变异性；我们的目标使用两次独立的 rollout 来匹配均值，而无需此额外惩罚。我们建立了敏感性精度约束有限变化预测误差和决策遗憾的条件。在高斯系统、随机双阱系统、PDEBench 反应-扩散系统和随机 Navier-Stokes 系统中，Tangent-SBM 在敏感性和有限变化预测方面优于匹配的条件桥基线，同时保持相当的端点和分布精度。控制实验考察了目标正确性、响应目标和模拟器预算分配。为了测试决策实用性，我们评估了 Navier-Stokes 中的校准粘度选择：Tangent-SBM 在每项评估任务上都降低了相对于不采取行动的跟踪误差。

英文摘要

Predicting how stochastic systems respond to changes in viscosity, reaction rates, or external forces requires costly simulations, motivating reusable learned models. Yet matching observed outcome distributions does not ensure accurate intervention responses. We introduce Tangent Schrödinger Bridge Matching (Tangent-SBM), which learns stochastic transports from endpoint observations and mechanistic sensitivities. It propagates parameter derivatives alongside trajectories and supervises them against supplied targets. For average-response targets, single-rollout squared error also penalizes response variability; our objective uses two independent rollouts to match the mean without this additional penalty. We establish conditions under which sensitivity accuracy bounds finite-change prediction error and decision regret. Across Gaussian, stochastic double-well, PDEBench reaction--diffusion, and stochastic Navier--Stokes systems, Tangent-SBM improves sensitivity and finite-change prediction over matched conditional-bridge baselines while maintaining comparable endpoint and distributional accuracy. Controls examine target correctness, response objectives, and simulator-budget allocation. To test decision usefulness, we evaluate calibrated viscosity selection in Navier--Stokes: Tangent-SBM reduces tracking error relative to taking no action on every evaluated task.

发表机构

• University of Michigan（密歇根大学）

机构由 AI 辅助整理，请以论文原文为准。