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We develop an approach to learn an interpretable semi-parametric model of alatent continuous-time stochastic dynamical system, assuming noisyhigh-dimensional outputs sampled at uneven times. The dynamics are described bya nonlinear stochastic differential equation (SDE) driven by a Wiener process,with a drift evolution function drawn from a Gaussian process (GP) conditionedon a set of learnt fixed points and corresponding local Jacobian matrices. Thisform yields a flexible nonparametric model of the dynamics, with arepresentation corresponding directly to the interpretable portraits routinelyemployed in the study of nonlinear dynamical systems. The learning algorithmcombines inference of continuous latent paths underlying observed data with asparse variational description of the dynamical process. We demonstrate ourapproach on simulated data from different nonlinear dynamical systems.

Learning interpretable continuous-time models of latent stochastic dynamical systems