Graph Neural Reaction Diffusion Models

TL;DR

This paper introduces a novel Graph Neural Reaction Diffusion (RDGNN) model inspired by Turing instabilities, demonstrating its effectiveness across diverse data types and its competitive or superior performance compared to existing methods.

Contribution

The paper proposes a new GNN architecture based on neural reaction diffusion systems, inspired by Turing patterns, with theoretical analysis and empirical validation.

Findings

Effective on homophilic, heterophilic, and spatio-temporal data

Improves or matches state-of-the-art performance

Theoretically grounded in reaction diffusion dynamics

Abstract

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.