Roto-translated Local Coordinate Frames For Interacting Dynamical Systems

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 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.

In NeurIPS 2021. Source code: this https URL

Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2110.14961 [cs.LG]

(or arXiv:2110.14961v4 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2110.14961 Focus to learn more arXiv-issued DOI via DataCite

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