Geometric path augmentation for inference of sparsely observed stochastic nonlinear systems
This addresses a challenging inference problem in science for systems with sparse observations, but it is incremental as it builds on existing paradigms.
The paper tackles the problem of identifying deterministic driving forces in stochastic nonlinear systems from sparse-in-time observations by proposing a data-driven path augmentation scheme that reconciles temporal and geometric paradigms, achieving efficient inference for low sampling rates.
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.