Stochastic evolution equations describing the dynamics of systems under the influence of both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying these systems from sparse-in-time observations remains still a challenging endeavour. Existing approaches focus either on the temporal structure of the observations by relying on conditional expectations, discarding thereby information ingrained in the geometry of the system's invariant density; or employ geometric approximations of the invariant density, which are nevertheless restricted to systems with conservative forces. Here we propose a method that reconciles these two paradigms. We introduce a new data-driven path augmentation scheme that takes the local observation geometry into account. By employing non-parametric inference on the augmented paths, we can efficiently identify the deterministic driving forces of the underlying system for systems observed at low sampling rates.

翻译：描述在确定力和随机力影响下的系统动态的斯托孔进化方程式在所有科学领域都很普遍。然而,从零星的时空观测中查明这些系统仍然是一项挑战性的工作。现有的方法要么侧重于观测的时间结构,依靠有条件的预期,从而抛弃系统不变化密度几何学中固有的信息;要么采用不变化密度的几何近似值,但仍局限于有保守力的系统。我们在此提出一种调和这两种模式的方法。我们采用了一种新的数据驱动路径增强计划,将当地观测几何纳入考虑。在扩大的路径上采用非参数推论,我们可以有效地确定低采样率所观测系统的基本系统的确定力。