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Stochastic evolution equations describing the dynamics of systems under theinfluence of both deterministic and stochastic forces are prevalent in allfields of science. Yet, identifying these systems from sparse-in-timeobservations remains still a challenging endeavour. Existing approaches focuseither on the temporal structure of the observations by relying on conditionalexpectations, discarding thereby information ingrained in the geometry of thesystem's invariant density; or employ geometric approximations of the invariantdensity, which are nevertheless restricted to systems with conservative forces.Here we propose a method that reconciles these two paradigms. We introduce anew data-driven path augmentation scheme that takes the local observationgeometry into account. By employing non-parametric inference on the augmentedpaths, we can efficiently identify the deterministic driving forces of theunderlying system for systems observed at low sampling rates.

Geometric path augmentation for inference of sparsely observed stochastic nonlinear systems