The graph identification problem consists of discovering the interactions
among nodes in a network given their state/feature trajectories. This problem
is challenging because the behavior of a node is coupled to all the other nodes
by the unknown interaction model. Besides, high-dimensional and nonlinear state
trajectories make difficult to identify if two nodes are connected. Current
solutions rely on prior knowledge of the graph topology and the dynamic
behavior of the nodes, and hence, have poor generalization to other network
configurations. To address these issues, we propose a novel learning-based
approach that combines (i) a strongly convex program that efficiently uncovers
graph topologies with global convergence guarantees and (ii) a self-attention
encoder that learns to embed the original state trajectories into a feature
space and predicts appropriate regularizers for the optimization program. In
contrast to other works, our approach can identify the graph topology of unseen
networks with new configurations in terms of number of nodes, connectivity or
state trajectories. We demonstrate the effectiveness of our approach in
identifying graphs in multi-robot formation and flocking tasks.

该研究提出了一种基于学习的方法，结合了强凸规划和自注意力编码器，可以有效地揭示图的拓扑结构以及预测适当的正则化参数，从而解决了网络配置不同的情况下图拓扑的识别问题。