Roto-translated Local Coordinate Frames For Interacting Dynamical Systems
This addresses generalization issues in learning dynamical systems for applications like traffic simulation and motion capture, though it is incremental as it builds on existing geometric graph frameworks.
The paper tackled the problem of modelling interactions in complex dynamical systems by proposing local coordinate frames to enforce roto-translation invariance, which comfortably outperformed recent state-of-the-art methods in experiments on traffic scenes, 3D motion capture, and colliding particles.
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.