# Learning the Evolutionary and Multi-scale Graph Structure for Multivariate Time Series Forecasting

arXiv: https://arxiv.org/abs/2206.13816 · HTML: https://mlsanity.com/paper/2206.13816/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 28 Jun 2022.

## Builds on (most cited first, 21 of 21)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Discrete Graph Structure Learning for Forecasting Multiple Time Series](https://mlsanity.com/paper/2101.06861/) (2021)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [Temporal Pattern Attention for Multivariate Time Series Forecasting](https://mlsanity.com/paper/1809.04206/) (2018)
- [STG2Seq: Spatial-temporal Graph to Sequence Model for Multi-step Passenger Demand Forecasting](https://mlsanity.com/paper/1905.10069/) (2019)
- [Coupled Layer-wise Graph Convolution for Transportation Demand Prediction](https://mlsanity.com/paper/2012.08080/) (2020)
- [Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecasting](https://mlsanity.com/paper/2101.10460/) (2021)

## Built on by (most cited first, 30 of 36)

- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [LargeST: A Benchmark Dataset for Large-Scale Traffic Forecasting](https://mlsanity.com/paper/2306.08259/) (2023)
- [Self-Supervised Learning for Time Series Analysis: Taxonomy, Progress, and Prospects](https://mlsanity.com/paper/2306.10125/) (2023)
- [A Comprehensive Survey of Deep Learning for Multivariate Time Series Forecasting: A Channel Strategy Perspective](https://mlsanity.com/paper/2502.10721/) (2025)
- [Disentangling Structured Components: Towards Adaptive, Interpretable and Scalable Time Series Forecasting](https://mlsanity.com/paper/2305.13036/) (2023)
- [A Shapelet-based Framework for Unsupervised Multivariate Time Series Representation Learning](https://mlsanity.com/paper/2305.18888/) (2023)
- [A Systematic Literature Review of Spatio-Temporal Graph Neural Network Models for Time Series Forecasting and Classification](https://mlsanity.com/paper/2410.22377/) (2024)
- [STG4Traffic: A Survey and Benchmark of Spatial-Temporal Graph Neural Networks for Traffic Prediction](https://mlsanity.com/paper/2307.00495/) (2023)
- [A Co-training Approach for Noisy Time Series Learning](https://mlsanity.com/paper/2308.12551/) (2023)
- [Learning Time-aware Graph Structures for Spatially Correlated Time Series Forecasting](https://mlsanity.com/paper/2312.16403/) (2023)
- [Graph Learning and Its Advancements on Large Language Models: A Holistic Survey](https://mlsanity.com/paper/2212.08966/) (2022)
- [Nearest Neighbor Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.11625/) (2025)
- [RATSF: Empowering Customer Service Volume Management through Retrieval-Augmented Time-Series Forecasting](https://mlsanity.com/paper/2403.04180/) (2024)
- [MARLP: Time-series Forecasting Control for Agricultural Managed Aquifer Recharge](https://mlsanity.com/paper/2407.01005/) (2024)
- [Scalable Transformer for High Dimensional Multivariate Time Series Forecasting](https://mlsanity.com/paper/2408.04245/) (2024)
- [PGT-I: Scaling Spatiotemporal GNNs with Memory-Efficient Distributed Training](https://mlsanity.com/paper/2507.11683/) (2025)
- [Unified Data Management and Comprehensive Performance Evaluation for Urban Spatial-Temporal Prediction [Experiment, Analysis & Benchmark]](https://mlsanity.com/paper/2308.12899/) (2023)
- [Multimodal joint prediction of traffic spatial-temporal data with graph sparse attention mechanism and bidirectional temporal convolutional network](https://mlsanity.com/paper/2412.19842/) (2024)
- [Leveraging Multivariate Long-Term History Representation for Time Series Forecasting](https://mlsanity.com/paper/2505.14737/) (2025)
- [Beyond Pairwise Connections: Extracting High-Order Functional Brain Network Structures under Global Constraints](https://mlsanity.com/paper/2510.09175/) (2025)
- [Empowering Power Outage Prediction with Spatially Aware Hybrid Graph Neural Networks and Contrastive Learning](https://mlsanity.com/paper/2604.04916/) (2026)
- [Time Series Forecasting via Semi-Asymmetric Convolutional Architecture with Global Atrous Sliding Window](https://mlsanity.com/paper/2301.13691/) (2023)
- [A Simple Framework for Multi-mode Spatial-Temporal Data Modeling](https://mlsanity.com/paper/2308.11204/) (2023)
- [Multi-Scale Spatial-Temporal Recurrent Networks for Traffic Flow Prediction](https://mlsanity.com/paper/2310.08138/) (2023)
- [Backbone-based Dynamic Graph Spatio-Temporal Network for Epidemic Forecasting](https://mlsanity.com/paper/2312.00485/) (2023)
- [FCDNet: Frequency-Guided Complementary Dependency Modeling for Multivariate Time-Series Forecasting](https://mlsanity.com/paper/2312.16450/) (2023)
- [From Chaos to Clarity: Time Series Anomaly Detection in Astronomical Observations](https://mlsanity.com/paper/2403.10220/) (2024)
- [Tel2Veh: Fusion of Telecom Data and Vehicle Flow to Predict Camera-Free Traffic via a Spatio-Temporal Framework](https://mlsanity.com/paper/2403.12991/) (2024)
- [Enhancing Sustainable Urban Mobility Prediction with Telecom Data: A Spatio-Temporal Framework Approach](https://mlsanity.com/paper/2405.17507/) (2024)
- [STAHGNet: Modeling Hybrid-grained Heterogenous Dependency Efficiently for Traffic Prediction](https://mlsanity.com/paper/2412.17524/) (2024)

## Abstract (arXiv)

Recent studies have shown great promise in applying graph neural networks for multivariate time series forecasting, where the interactions of time series are described as a graph structure and the variables are represented as the graph nodes. Along this line, existing methods usually assume that the graph structure (or the adjacency matrix), which determines the aggregation manner of graph neural network, is fixed either by definition or self-learning. However, the interactions of variables can be dynamic and evolutionary in real-world scenarios. Furthermore, the interactions of time series are quite different if they are observed at different time scales. To equip the graph neural network with a flexible and practical graph structure, in this paper, we investigate how to model the evolutionary and multi-scale interactions of time series. In particular, we first provide a hierarchical graph structure cooperated with the dilated convolution to capture the scale-specific correlations among time series. Then, a series of adjacency matrices are constructed under a recurrent manner to represent the evolving correlations at each layer. Moreover, a unified neural network is provided to integrate the components above to get the final prediction. In this way, we can capture the pair-wise correlations and temporal dependency simultaneously. Finally, experiments on both single-step and multi-step forecasting tasks demonstrate the superiority of our method over the state-of-the-art approaches.