Learning interpretable continuous-time models of latent stochastic dynamical systems

TL;DR

This paper introduces a semi-parametric, interpretable model for latent continuous-time stochastic dynamical systems using Gaussian processes, enabling flexible and understandable representations of complex dynamics from noisy, unevenly sampled data.

Contribution

It presents a novel approach combining Gaussian processes with stochastic differential equations to learn interpretable dynamical models from high-dimensional, irregularly sampled data.

Findings

Successfully modeled nonlinear dynamical systems with noisy data

Provided interpretable portraits of system dynamics

Demonstrated effectiveness on simulated datasets

Abstract

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time 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 representation corresponding directly to the interpretable portraits routinely employed in the study of nonlinear dynamical systems. The learning algorithm combines inference of continuous latent paths underlying observed data with a sparse variational description of the dynamical process. We demonstrate our approach on simulated data from different nonlinear dynamical systems.