ETD

• adaptive dissipativity
• dynamical systems
• graph neural networks
• graph representation learning
• machine learning
• ordinary differential equations

Modeling dynamic graphs, where both topology and node attributes evolve over time, remains a fundamental challenge in machine learning, primarily due to the challenge of capturing long-range spatiotemporal dependencies. Existing dynamic Graph Neural Network (GNN) architectures are effective at local information aggregation but often struggle to propagate signals across distant nodes and time steps, limiting their applicability to real-world systems characterized by complex and delayed interactions.

This thesis investigates the problem of capturing long-range spatiotemporal dependencies in dynamic graph models. Many existing approaches describe graph evolution using ordinary differential equations (ODEs). While such methods leverage properties like non-dissipativity, where information is conserved over time, they often underperform in scenarios where not all information has to be propagated indefinitely.

We propose novel architectures that adaptively learn to balance dissipative and non-dissipative dynamics according to the underlying data characteristics. Furthermore, we introduce benchmark datasets and evaluation protocols specifically designed to assess models’ capacity to handle long-range spatiotemporal dependencies, addressing a significant gap in current research on dynamic graphs.

Our theoretical analysis provides insights into the representational power and effectiveness of the proposed methods. Extensive experiments on both synthetic and real-world datasets demonstrate that our approaches outperform or match state-of-the-art baselines, particularly in scenarios requiring extended-range dependency modeling. To the best of our knowledge, this work is among the first to study the equilibrium between conservation and dissipation in dynamic graphs. Overall, our contributions advance dynamic graph representation learning and facilitate more accurate modeling of complex evolving systems in domains such as biomedicine, infrastructure, and social networks.