# Predicting Long-term Dynamics of Complex Networks via Identifying Skeleton in Hyperbolic Space

arXiv: https://arxiv.org/abs/2408.09845 · HTML: https://mlsanity.com/paper/2408.09845/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2024.

## Built on by (most cited first, 6 of 6)

- [Graph ODEs and Beyond: A Comprehensive Survey on Integrating Differential Equations with Graph Neural Networks](https://mlsanity.com/paper/2503.23167/) (2025)
- [UniGO: A Unified Graph Neural Network for Modeling Opinion Dynamics on Graphs](https://mlsanity.com/paper/2502.11519/) (2025)
- [Predicting the Energy Landscape of Stochastic Dynamical System via Physics-informed Self-supervised Learning](https://mlsanity.com/paper/2502.16828/) (2025)
- [Physics-Inspired Spatial Temporal Graph Neural Networks for Predicting Industrial Chain Resilience](https://mlsanity.com/paper/2508.16836/) (2025)
- [Physics-Informed High-order Graph Dynamics Identification Learning for Predicting Complex Networks Long-term Dynamics](https://mlsanity.com/paper/2510.09082/) (2025)
- [Deep Hierarchical Knowledge Loss for Fault Intensity Diagnosis](https://mlsanity.com/paper/2604.16459/) (2026)

## Abstract (arXiv)

Learning complex network dynamics is fundamental for understanding, modeling, and controlling real-world complex systems. Though great efforts have been made to predict the future states of nodes on networks, the capability of capturing long-term dynamics remains largely limited. This is because they overlook the fact that long-term dynamics in complex network are predominantly governed by their inherent low-dimensional manifolds, i.e., skeletons. Therefore, we propose the Dynamics-Invariant Skeleton Neural Network (DiskNet), which identifies skeletons of complex networks based on the renormalization group structure in hyperbolic space to preserve both topological and dynamics properties. Specifically, we first condense complex networks with various dynamics into simple skeletons through physics-informed hyperbolic embeddings. Further, we design graph neural ordinary differential equations to capture the condensed dynamics on the skeletons. Finally, we recover the skeleton networks and dynamics to the original ones using a degree-based super-resolution module. Extensive experiments across three representative dynamics as well as five real-world and two synthetic networks demonstrate the superior performances of the proposed DiskNet, which outperforms the state-of-the-art baselines by an average of 10.18% in terms of long-term prediction accuracy. Code for reproduction is available at: https://github.com/tsinghua-fib-lab/DiskNet.