We propose an implementation of GNN that predicts and imitates the motion be- haviors from observed swarm trajectory data. The network’s ability to capture interaction dynamics in swarms is demonstrated through transfer learning. We finally discuss the inherent availability and challenges in the scalability of GNN, and proposed a method to improve it with layer-wise tuning and mixing of data enabled by padding. In multi-agent systems (MAS) (Arai et al., 2002) , a group of agents has to effectively collaborate in order to solve a complex task in a parallel manner. Individual agents have to synchronize their actions and behaviors so as to produce a whole that is more than the sum of its parts. This synchronization is a core characteristics of MAS and is of vital importance to a wide range of modern application domains such as smart agriculture, military demining, or warehouse robotics. However, developing control strategies that allows a group of agents to perform a task jointly is still considered to be a complex challenge. This statement is particularly true for mobile agents that need to dynamically act in a physical space. To overcome this challenge, a variety of formalisms have been proposed to support the modeling and design of multi-agent and multi-robot systems. A prominent approach, called Boids or bird-oid, was proposed in Reynolds (1987) . In the Boids model, the system behavior emerges from the interplay of a few simple building-blocks. While simple to implement, it can be challenging to control the overall behavior of the swarm due to the emergent nature of the system dynamics. Other important formalisms for the specification of MAS are based on graph theory (Mesbahi & Egerstedt, 2010) , game theory, and formal languages. However, the latter approaches still require substantial modeling, coding, and verification efforts in order to yield practical controllers that can scale with the size of the system, i.e., the number of agents. Another obvious choice to reduce or eliminate modeling effort is to use machine learning. Reinforcement learning (Sartoretti et al., 2019) , in particular, has previously gained attention for synthesizing collective behavior in an MAS. However, due to the curse of dimensionality, reinforcement learning approaches often struggles to scale to systems with large number of agents. In this paper, we present an approach for learning multi-agent coordination through imitation (Schaal, 1999) . Rather than specifying the system dynamics, the designer only has to provide demonstrations of successful coordination behavior. In turn, this data set is used to learn a neural network representation of the underlying dynamics and rules of interaction. More specifically, we leverage recent insights regarding graph neural networks (GNN) (Battaglia et al., 2018) to learn a structured model of the dynamics. In contrast to traditional neural networks which take a vector, matrix or tensor as input, our graph neural network processes a graph representation of the multi-agent system. An implementation example of GNN can be seen in Kipf et al. (2018) , where the ability of GNN to better predict the motion of a simple physically interacting particles is highlighted. We show that the specific GNN implemented in this paper can accurately capture the dynamics of more complex multi-agent motion behaviors given a set of demonstrations. We also discuss and analyze difficulties in scaling learned models up to an MAS with a larger set of agents. Based on this discussion, we then propose a refinement training procedure to address these issues. The refinement procedure helps tuning a learned model to a system with a different number of agents, i.e., scalability along the size of the MAS. In this paper, we proposed an implementation of GNN that predicts and imitates the motion behaviors from observed swarm trajectory data. The network is combined with curriculum learning to achieve high accuracy prediction for arbitrary time steps. We demonstrated the network's ability to capture interaction dynamics in swarms through transfer learning. We discussed the availability and challenges in the scalability of GNN, and proposed a method to improve it, by using layer-wise tuning and mixing of data enabled by padding.
Improve the scalability of graph neural networks on imitation learning and prediction of swarm motion The paper proposes a new time series model for learning a sequence of graphs. This work considers sequence prediction problems in a multi-agent system.