01 December 2025
Graph neural networks (GNNs) have become a powerful framework for processing graph-structured data, enabling applications across various domains such as social networks, molecular biology, and more. Most GNNs are built upon the Message-Passing Neural Networks (MPNNs) framework, where information is exchanged between neighboring nodes, enabling effective learning from local graph structure. Despite their widespread use and success, a persistent challenge in GNNs is the effective modeling of long-range dependencies within graphs, as information propagation tends to degrade over extended distances.
Motivated by this, EMERGE partners from the University of Pisa introduce SONAR, a novel GNN architecture inspired by the dynamics of wave propagation in continuous media. SONAR models information flow on graphs as oscillations governed by the wave equation, allowing it to maintain effective propagation dynamics over long distances. By integrating adaptive edge resistances and state-dependent external forces, the method balances conservative and non-conservative behaviors, improving the ability to learn more complex dynamics. The authors provide a rigorous theoretical analysis of SONAR's energy conservation and information propagation properties, demonstrating its capacity to address the long-range propagation problem. Extensive experiments on synthetic and real-world benchmarks confirm that SONAR achieves state-of-the-art performance, particularly on tasks requiring long-range information exchange.
Read the paper in the link below.
More Information
