McGcn: Learning Continuous Graph Dynamics for Multi-Channel Fusion

Abstract

Multi-channel data fusion is essential for capturing comprehensive representations in complex systems. While graph convolutional networks have demonstrated remarkable efficacy, existing fusion paradigms primarily rely on discrete architectures governed by first-order propagation. These models are typically confined to discrete message-passing mechanisms, which makes it difficult to characterize the continuous evolution of underlying system dynamics. To address these limitations, we propose a multi-channel Graph Continuous Network (mcGCN), a novel framework for multi-channel data fusion. By formulating the information propagation as a second-order partial differential equation on graphs, mcGCN transitions from discrete layer-wise updates to a continuous dynamical system. Specifically, mcGCN integrates a multi-channel encoding module with continuous feature dynamics to initialize and evolve the latent node representations over static graph topologies. This physical analogy enables more robust information flow and effectively mitigates the performance degradation typically associated with deep graph architectures. Extensive experiments on diverse benchmark datasets demonstrate that our method outperforms state-of-the-art baselines, validating its effectiveness and robustness.