Predicting Time Series of Networked Dynamical Systems without Knowing Topology

TL;DR

This paper introduces a novel framework that learns the dynamics of networked systems directly from time series data without requiring prior knowledge of the network topology, enabling accurate forecasting and generalization across diverse networks.

Contribution

The proposed method leverages continuous graph neural networks with attention to infer latent topologies from data, addressing the challenge of unknown or incomplete network structures.

Findings

Successfully predicts future network states without topology knowledge

Generalizes well across different network topologies

Outperforms existing methods on real and synthetic data

Abstract

Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for forecasting system behaviors and making informed decisions. However, existing methods for modeling networked time series often assume known topologies, whereas real-world networks are typically incomplete or inaccurate, with missing or spurious links that hinder precise predictions. Moreover, while networked time series often originate from diverse topologies, the ability of models to generalize across topologies has not been systematically evaluated. To address these gaps, we propose a novel framework for learning network dynamics directly from observed time-series data, when prior knowledge of graph topology or governing dynamical equations is absent. Our approach leverages continuous graph neural networks with an attention mechanism to construct a latent topology, enabling accurate reconstruction of future trajectories for network states. Extensive experiments on real and synthetic networks demonstrate that our model not only captures dynamics effectively without topology knowledge but also generalizes to unseen time series originating from diverse topologies.