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：多自由度系统在多尺度上演化的动力学通常用随机微分方程建模。通常，这些方程的结构形式未知，系统动力学的唯一表现是离散时间点上的观测。尽管这些方法被广泛使用，但根据稀疏时间观测准确推断这些系统仍然具有挑战性。传统的推断方法要么侧重于观测的时间结构，忽略系统不变密度的几何特征，要么使用不变密度的几何近似，这仅限于保守驱动力的情形。为了解决这些局限性，本文提出了一种新颖的方法，将这两种视角统一起来。我们提出了一种路径增强方案，通过采用数据驱动控制来考虑不变系统密度的几何特征。对增强路径进行非参数推断，能够有效识别低采样率观测系统背后的确定性驱动力。