Graph Neural Reaction Diffusion Models
This work addresses the need for more powerful and flexible graph neural networks for researchers and practitioners dealing with complex graph data, though it appears incremental as it builds on existing integration of GNNs and neural differential equations.
The paper tackled the problem of modeling diverse graph data types, such as homophilic, heterophilic, and spatio-temporal datasets, by proposing a novel family of Graph Neural Networks based on neural Reaction Diffusion systems, resulting in improved or competitive performance compared to state-of-the-art methods.
The integration of Graph Neural Networks (GNNs) and Neural Ordinary and Partial Differential Equations has been extensively studied in recent years. GNN architectures powered by neural differential equations allow us to reason about their behavior, and develop GNNs with desired properties such as controlled smoothing or energy conservation. In this paper we take inspiration from Turing instabilities in a Reaction Diffusion (RD) system of partial differential equations, and propose a novel family of GNNs based on neural RD systems. We \textcolor{black}{demonstrate} that our RDGNN is powerful for the modeling of various data types, from homophilic, to heterophilic, and spatio-temporal datasets. We discuss the theoretical properties of our RDGNN, its implementation, and show that it improves or offers competitive performance to state-of-the-art methods.