Roto-translated Local Coordinate Frames For Interacting Dynamical Systems
arXiv (Cornell University)(2021)
摘要
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
geometric graphs, i.e., graphs with nodes positioned in
the Euclidean space given an 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
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.
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关键词
local coordinate frames,dynamical
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