Stuart-Landau Oscillatory Graph Neural Network

TL;DR

This paper introduces the Stuart-Landau Graph Neural Network (SLGNN), a physics-inspired deep learning architecture that leverages complex oscillator dynamics to improve performance on various graph tasks.

Contribution

The paper presents the first GNN architecture based on Stuart-Landau oscillators, allowing dynamic amplitude and phase evolution, which enhances expressiveness and control in oscillatory graph neural networks.

Findings

SLGNN outperforms existing OGNNs on multiple graph tasks.

The model effectively manages amplitude and phase dynamics.

Experimental results demonstrate improved accuracy and robustness.

Abstract

Oscillatory Graph Neural Networks (OGNNs) are an emerging class of physics-inspired architectures designed to mitigate oversmoothing and vanishing gradient problems in deep GNNs. In this work, we introduce the Complex-Valued Stuart-Landau Graph Neural Network (SLGNN), a novel architecture grounded in Stuart-Landau oscillator dynamics. Stuart-Landau oscillators are canonical models of limit-cycle behavior near Hopf bifurcations, which are fundamental to synchronization theory and are widely used in e.g. neuroscience for mesoscopic brain modeling. Unlike harmonic oscillators and phase-only Kuramoto models, Stuart-Landau oscillators retain both amplitude and phase dynamics, enabling rich phenomena such as amplitude regulation and multistable synchronization. The proposed SLGNN generalizes existing phase-centric Kuramoto-based OGNNs by allowing node feature amplitudes to evolve dynamically according to Stuart-Landau dynamics, with explicit tunable hyperparameters (such as the Hopf-parameter and the coupling strength) providing additional control over the interplay between feature amplitudes and network structure. We conduct extensive experiments across node classification, graph classification, and graph regression tasks, demonstrating that SLGNN outperforms existing OGNNs and establishes a novel, expressive, and theoretically grounded framework for deep oscillatory architectures on graphs.