# Learning Time-Varying Graph Signals via Koopman

arXiv: https://arxiv.org/abs/2511.06493 · HTML: https://mlsanity.com/paper/2511.06493/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 65 references that are in the map.
- First posted on arXiv 9 Nov 2025.

## Builds on (most cited first, 30 of 31)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networks](https://mlsanity.com/paper/1810.02244/) (2018)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Gate-Variants of Gated Recurrent Unit (GRU) Neural Networks](https://mlsanity.com/paper/1701.05923/) (2017)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Discriminative Embeddings of Latent Variable Models for Structured Data](https://mlsanity.com/paper/1603.05629/) (2016)
- [Forecasting Sequential Data using Consistent Koopman Autoencoders](https://mlsanity.com/paper/2003.02236/) (2020)
- [Graph Representation Learning in Biomedicine](https://mlsanity.com/paper/2104.04883/) (2021)
- [Understanding graph embedding methods and their applications](https://mlsanity.com/paper/2012.08019/) (2020)
- [Graph Signal Processing: History, Development, Impact, and Outlook](https://mlsanity.com/paper/2303.12211/) (2023)
- [Graph Neural Networks for Communication Networks: Context, Use Cases and Opportunities](https://mlsanity.com/paper/2112.14792/) (2021)
- [GiGaMAE: Generalizable Graph Masked Autoencoder via Collaborative Latent Space Reconstruction](https://mlsanity.com/paper/2308.09663/) (2023)
- [Reconstruction of Time-varying Graph Signals via Sobolev Smoothness](https://mlsanity.com/paper/2207.06439/) (2022)
- [Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction](https://mlsanity.com/paper/2403.19800/) (2024)
- [Continuous Product Graph Neural Networks](https://mlsanity.com/paper/2405.18877/) (2024)
- [Robust Time-Varying Graph Signal Recovery for Dynamic Physical Sensor Network Data](https://mlsanity.com/paper/2202.06432/) (2022)
- [Time-varying Signals Recovery via Graph Neural Networks](https://mlsanity.com/paper/2302.11313/) (2023)
- [Koopman AutoEncoder via Singular Value Decomposition for Data-Driven Long-Term Prediction](https://mlsanity.com/paper/2408.11303/) (2024)

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

- [Toward Scalable SDN for LEO Mega-Constellations: A Graph Learning Approach](https://mlsanity.com/paper/2604.27478/) (2026)

## Abstract (arXiv)

A wide variety of real-world data, such as sea measurements, e.g., temperatures collected by distributed sensors and multiple unmanned aerial vehicles (UAV) trajectories, can be naturally represented as graphs, often exhibiting non-Euclidean structures. These graph representations may evolve over time, forming time-varying graphs. Effectively modeling and analyzing such dynamic graph data is critical for tasks like predicting graph evolution and reconstructing missing graph data. In this paper, we propose a framework based on the Koopman autoencoder (KAE) to handle time-varying graph data. Specifically, we assume the existence of a hidden non-linear dynamical system, where the state vector corresponds to the graph embedding of the time-varying graph signals. To capture the evolving graph structures, the graph data is first converted into a vector time series through graph embedding, representing the structural information in a finite-dimensional latent space. In this latent space, the KAE is applied to learn the underlying non-linear dynamics governing the temporal evolution of graph features, enabling both prediction and reconstruction tasks.