Geometric constraints improve inference of sparsely observed stochastic dynamics
This work addresses a critical problem in modeling complex systems with sparse data, offering a method that improves inference accuracy for researchers in fields like physics and biology, though it appears incremental by reconciling existing perspectives.
The paper tackles the challenge of inferring stochastic differential equations from sparse-in-time observations by introducing a novel approach that combines temporal structure with geometric constraints of the invariant density, enabling efficient identification of deterministic forces at low sampling rates.
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.