Roto-translated Local Coordinate Frames For Interacting Dynamical Systems

arXiv:2110.14961v4 Announce Type: replace 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 extit{geometric graphs}, extit{i.e.}, graphs with nodes positioned in the Euclidean space given an extit{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 extit{Galilean invariance}. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.

Source: arXiv cs.LG | 2026-10-02