Structure-preserving Gaussian Process Dynamics

RWTH Publications (RWTH Aachen)

Abstract

Most physical processes posses structural properties such as constant energies, volumes, and other invariants over time. When learning models of such dynamical systems, it is critical to respect these invariants to ensure accurate predictions and physically meaningful behavior. Strikingly, state-of-the-art methods in Gaussian process (GP) dynamics model learning are not addressing this issue. On the other hand, classical numerical integrators are specifically designed to preserve these crucial properties through time. We propose to combine the advantages of GPs as function approximators with structure preserving numerical integrators for dynamical systems, such as Runge-Kutta methods. These integrators assume access to the ground truth dynamics and require evaluations of intermediate and future time steps that are unknown in a learning-based scenario. This makes direct inference of the GP dynamics, with embedded numerical scheme, intractable. Our key technical contribution is the evaluation of the implicitly defined Runge-Kutta transition probability. In a nutshell, we introduce an implicit layer for GP regression, which is embedded into a variational inference-based model learning scheme.

Authors 4

1. Katharina Ensinger Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University · Robert Bosch (Germany)

   Affiliation as printed

   Bosch Center for Artificial Intelligence , Renningen , Germany

   Institute for Data Science in Mechanical Engineering , RWTH Aachen University , Aachen , Germany

2. Friedrich Solowjow Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering , RWTH Aachen University , Aachen , Germany

3. Sebastian Ziesche

   Robert Bosch (Germany)

   Affiliation as printed

   Bosch Center for Artificial Intelligence , Renningen , Germany

4. Sebastian Trimpe Aachen Institute for Data Science in Mechanical Engineering

   RWTH Aachen University

   Affiliation as printed

   Institute for Data Science in Mechanical Engineering , RWTH Aachen University , Aachen , Germany