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.
Ilze Amanda Auzina (University of Amsterdam)
Çağatay Yıldız (University of Tübingen)
Efstratios Gavves (University of Amsterdam)
Dr. Efstratios Gavves is an Associate Professor at the University of Amsterdam in the Netherlands, an ELLIS Scholar, and co-founder of Ellogon.AI. He is a director of the QUVA Deep Vision Lab with Qualcomm, and the POP-AART Lab with the Netherlands Cancer Institute and Elekta. Efstratios received the ERC Career Starting Grant 2020, and NWO VIDI grant 2020 to research on the Computational Learning of Time for spatiotemporal sequences and video. His background is in Computer Vision. Currently, his research interests lie in the Machine Learning of Time and Dynamics, and its applications to Vision and Sciences.
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