The dynamics of systems of many degrees of freedom evolving on multiple scales are often modeled in terms of stochastic differential equations. Usually the structural form of these equations is unknown and the only manifestation of the system's dynamics are observations at discrete points in time. Despite their widespread use, accurately inferring these systems from sparse-in-time observations remains challenging. Conventional inference methods either focus on the temporal structure of observations, neglecting the geometry of the system's invariant density, or use geometric approximations of the invariant density, which are limited to conservative driving forces. To address these limitations, here, we introduce a novel approach that reconciles these two perspectives. We propose a path augmentation scheme that employs data-driven control to account for the geometry of the invariant system's density. Non-parametric inference on the augmented paths, enables efficient identification of the underlying deterministic forces of systems observed at low sampling rates.

翻译：多自由度系统在多个时间尺度上演化的动力学，通常通过随机微分方程建模。然而，这些方程的结构形式往往未知，系统动力学的唯一表现为离散时间点的观测数据。尽管此类模型被广泛使用，但基于稀疏时间观测准确推断这些系统仍具挑战性。传统的推断方法要么聚焦于观测的时间结构而忽略系统不变密度的几何特性，要么采用仅限于保守驱动力的不变密度几何近似。为突破这些局限，本文提出一种融合两种视角的新方法。我们设计了一种路径增广方案，通过数据驱动控制策略来刻画系统不变密度的几何特征。对增广路径进行非参数推断，能够高效识别低采样率观测系统背后的确定性驱动力。