Predicting Time Series of Networked Dynamical Systems without Knowing Topology

TL;DR

The paper tackles forecasting in networked dynamical systems without known topology by learning latent interactions from a short observation window using a topology-agnostic neural ODE framework (TAGODE). It introduces either fixed or time-varying latent edges, the latter via attention, to capture evolving interactions and predict future nodal states. Through transductive and inductive experiments on real COVID-19 data and synthetic networks across multiple dynamical regimes, TAGODE and its time-varying variant consistently outperform strong baselines, with particularly strong generalization in long-horizon and OOD settings. This approach enables robust prediction and analysis of complex networked systems where topology is incomplete or evolving, offering practical benefits for forecasting in epidemiology, ecology, neuroscience, and related fields.

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.

Figures (6)

• Figure 1: Problem setup and Model Illustration. a, Ground truth nodal ODE $\frac{d\boldsymbol{x}_i}{dt}$ and topology that govern the network states. In the ODE, $f_i, g$ denote the self-dynamics and interaction term respectively and adjacency matrix $\boldsymbol{A}$ describes the network structure. Nodes with a higher degree have a more intense colors. b, The model takes an initial period of time-series data for each node as input, with the edges assumed to be unknown. c, The encoder maps each nodal trajectory to a corresponding hidden vector and infers network interactions based on the nodal embeddings. d, The neural ODE drives the latent state evolution. e, The hidden representation at each timestamp is decoded to the input space. f, The model forecasts nodal trajectories beyond the observation window.
• Figure 2: State inference error versus time for SIS and population dynamics on ER and SF network types. The error at each timestamp is averaged across 20 graphs and all their nodes.
• Figure 3: OOD test cases
• Figure 4: Hyperparameter study: condition length and latent dimension.
• Figure 5: Effect of observation noise on the condition window.