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.

本论文提出了一种使用本地坐标框架诱导几何图的旋转平移不变性和定义各向异性过滤器的方法，以建模交互动力系统，并在交通场景、三维运动捕捉和碰撞粒子实验中表现出优异的性能，超越了目前的最新技术水平。