Geometric path augmentation for inference of sparsely observed stochastic nonlinear systems

Abstract

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. * https://dimitra-maoutsa.gitlab.io/ 2 Here we employ the term path augmentation to refer to what is widely known as data augmentation. We resorted to this term because we consider it as more elegant and better descriptive of the proposed augmentation process, while the term 'data augmentation' is considerably vague.