This talk proposes a result for solving the inverse for the heat conduction equation on a graph-tree. The constructed stable efficient algorithm for source identification is reduced to solving linear integral Volterra equations of the second kind. A feature of the new approach is the combination of deep learning and graph theory in solving the identification problem, which can serve as a good tool for solving inverse problems in complex systems. In the problem on the graph-tree graph neural networks are used. Such a model allows taking into account the connections between nodes for information processing and transmitting information along the graph structure.