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Modelling interactions is critical in learning complex dynamical systems,namely systems of interacting objects with highly non-linear and time-dependentbehaviour. A large class of such systems can be formalized as$\textit{geometric graphs}$, $\textit{i.e.}$, graphs with nodes positioned inthe Euclidean space given an $\textit{arbitrarily}$ chosen global coordinatesystem, for instance vehicles in a traffic scene. Notwithstanding the arbitraryglobal coordinate system, the governing dynamics of the respective dynamicalsystems are invariant to rotations and translations, also known as$\textit{Galilean invariance}$. As ignoring these invariances leads to worsegeneralization, in this work we propose local coordinate frames per node-objectto induce roto-translation invariance to the geometric graph of the interactingdynamical system. Further, the local coordinate frames allow for a naturaldefinition of anisotropic filtering in graph neural networks. Experiments intraffic scenes, 3D motion capture, and colliding particles demonstrate that theproposed approach comfortably outperforms the recent state-of-the-art.

Roto-translated Local Coordinate Frames For Interacting Dynamical Systems