On The Temporal Domain of Differential Equation Inspired Graph Neural
  Networks
Moshe Eliasof Eldad Haber Eran Treister Carola-Bibiane Schönlieb
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.