  Graph neural networks are useful for learning problems, as well as for
combinatorial and graph problems such as the Subgraph Isomorphism Problem and
the Traveling Salesman Problem. We describe an approach for computing Steiner
Trees by combining a graph neural network and Monte Carlo Tree Search. We first
train a graph neural network that takes as input a partial solution and
proposes a new node to be added as output. This neural network is then used in
a Monte Carlo search to compute a Steiner tree. The proposed method
consistently outperforms the standard 2-approximation algorithm on many
different types of graphs and often finds the optimal solution.
