Roto-translated Local Coordinate Frames For Interacting Dynamical Systems

Miltiadis Kofinas, Naveen Shankar Nagaraja, Efstratios Gavves

Keywords: Trajectory forecasting, interacting dynamical systems, graph neural networks, roto-translation equivariance, equivariance, invariance, geometric graphs

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

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TL;DR: Roto-translated local coordinate frames for all nodes-objects in the geometric graphs of interacting dynamical systems

Code: https://github.com/mkofinas/locs