Latent GP-ODEs with Informative Priors

Ilze Amanda Auzina, Cagatay Yildiz, Efstratios Gavves

Keywords: dynamical modeling, gaussian processes, generative modeling, informative priors

Abstract:

For many complex systems the parametric form of the differential equation might be
unknown or infeasible to determine. Earlier works have explored to model the unknown
ODE system with a Gaussian Process model, however, the application has been limited to
a low dimensional data setting. We propose a novel framework by combining a generative and a
Bayesian nonparametric model. Our model learns a physically meaningful latent representation (position,
momentum) and solves in the latent space an ODE system. The use of GP allows us to account
for uncertainty as well as to extend our work with informative priors. We demonstrate our
framework on an image rotation dataset. The method demonstrates its ability to learn
dynamics from high dimensional data and we obtain state-of-the-art performance compared to
earlier GP-based ODEs models on dynamic forecasting.