# Predicting Time Series of Networked Dynamical Systems without Knowing Topology

arXiv: https://arxiv.org/abs/2412.18734 · HTML: https://mlsanity.com/paper/2412.18734/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 54 references that are in the map.
- First posted on arXiv 25 Dec 2024.

## Builds on (most cited first, 7 of 7)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations](https://mlsanity.com/paper/2011.03880/) (2020)
- [LEADS: Learning Dynamical Systems that Generalize Across Environments](https://mlsanity.com/paper/2106.04546/) (2021)
- [Physics-Informed Regularization for Domain-Agnostic Dynamical System Modeling](https://mlsanity.com/paper/2410.06366/) (2024)
- [Learning the Topology and Behavior of Discrete Dynamical Systems](https://mlsanity.com/paper/2402.11686/) (2024)

## Built on by (most cited first, 1 of 1)

- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)

## Abstract (arXiv)

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.