Do We Need an Encoder-Decoder to Model Dynamical Systems on Networks?

Understand

As deep learning gains popularity in modelling dynamical systems, we expose an underappreciated misunderstanding relevant to modelling dynamics on networks.

• Strongly influenced by graph neural networks, latent vertex embeddings are naturally adopted in many neural dynamical network models.
• However, we show that embeddings tend to induce a model that fits observations well but simultaneously has incorrect dynamical behaviours.
• Recognising that previous studies narrowly focus on short-term predictions during the transient phase of a flow, we propose three tests for correct long-term behaviour, and illustrate how an embedding-based dynamical model fails these tests, and analyse the causes, particularly through the lens of topological conjugacy.