CoordiNet: Constrained Dynamics Learning for State Coordination Over Graph

Abstract

A neural architecture to efficiently coordinate the transitions of state variables (states) over a graph is proposed. We consider the coordination of the time evolution of the state variables associated with the nodes on a graph. The states are associated with physical attributes of agents, e.g., the speed and/or location of vehicles. Efficient coordination then corresponds to the optimization of dynamics (how fast do vehicles travel) that may be subject to constraints (travel must be collision-free). The aim of this paper is (i) the formulation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">learnable constrained dynamics</i> which governs the transition of states under constraints over a graph and (ii) to show its industrial application. Firstly, we formulate continuous ordinary differential equations (ODEs), namely forward propagation of state transitions over a graph and backward propagation to optimize model parameters for the learnable constrained dynamics. Discretization of these continuous ODEs results in the neural architecture <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CoordiNet</i> . Secondly, as an application of CoordiNet, we address a traffic coordination problem by learning constrained dynamics such that vehicles can travel as fast as possible without collisions. Simulation experiments of traffic coordination confirm that our method maximizes the vehicles' speed states while avoiding collisions.