Geometric path augmentation for inference of sparsely observed stochastic nonlinear systems

TL;DR

This paper introduces a novel geometric path augmentation method that improves the inference of stochastic nonlinear systems from sparse observations by integrating geometric information with non-parametric inference.

Contribution

It combines geometric and temporal approaches for system identification, enabling efficient inference from low-sampling-rate data.

Findings

Effective in identifying deterministic forces from sparse data

Reconciles geometric and temporal inference paradigms

Applicable to systems with stochastic and nonlinear dynamics

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.