Interacting ODEs with Gaussian Processes

Abstract

A broad spectrum of dynamical systems consists of multiple interacting objects. Since their interplay is typically a priori unknown, learning interaction dynamics of objects from data has become an emerging field in dynamical systems. In this talk, we will present a new method that allows uncertainty-aware modelling of such systems based on Gaussian Processes. Our formulation decomposes the dynamics into independent and interaction dynamics. The first one governs the motion of an object in isolation, the latter describes the effects that result from interactions with neighbouring objects. By employing Gaussian process ordinary differential equations, our model infers both components with reliable uncertainty estimates. The dynamics are embedded into a latent space in order to allow for missing dynamic or static information. We will show that efficient inference for this model family is possible with modern variational sparse Gaussian process inference techniques. We will conclude the talk with showing empirical results that demonstrate that our model leads to improved disentanglement and improved calibration of long-term predictions.

Notes

• References:

  • Learning Interacting Dynamical Systems with Latent Gaussian Process ODEs

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