Learning interpretable continuous-time models of latent stochastic dynamical systems

Abstract

We develop an approach to learn an interpretable
\nsemi-parametric model of a latent continuoustime stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear stochastic differential equation (SDE) driven by a Wiener process, with a drift evolution function drawn from a Gaussian process (GP) conditioned on a set of learnt fixed points and corresponding local Jacobian matrices. This form yields a flexible nonparametric model of the dynamics, with a
\nrepresentation corresponding directly to the interpretable portraits routinely employed in the study
\nof nonlinear dynamical systems. The learning algorithm combines inference of continuous latent
\npaths underlying observed data with a sparse variational description of the dynamical process. We
\ndemonstrate our approach on simulated data from
\ndifferent nonlinear dynamical systems.