On The Temporal Domain of Differential Equation Inspired Graph Neural Networks
This work addresses a specific bottleneck in graph neural networks for researchers and practitioners, offering an incremental improvement over existing DE-GNNs.
The paper tackles the limitation of existing Differential Equation-Inspired Graph Neural Networks (DE-GNNs) that rely on fixed first or second-order temporal dependencies by proposing TDE-GNN, a neural extension that learns these dependencies, and demonstrates its benefits on graph benchmarks.
Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling complex relationships in graph-structured data. A recent innovation in this field is the family of Differential Equation-Inspired Graph Neural Networks (DE-GNNs), which leverage principles from continuous dynamical systems to model information flow on graphs with built-in properties such as feature smoothing or preservation. However, existing DE-GNNs rely on first or second-order temporal dependencies. In this paper, we propose a neural extension to those pre-defined temporal dependencies. We show that our model, called TDE-GNN, can capture a wide range of temporal dynamics that go beyond typical first or second-order methods, and provide use cases where existing temporal models are challenged. We demonstrate the benefit of learning the temporal dependencies using our method rather than using pre-defined temporal dynamics on several graph benchmarks.