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Journal of ZheJiang University (Engineering Science)  2024, Vol. 58 Issue (12): 2500-2509    DOI: 10.3785/j.issn.1008-973X.2024.12.009
    
Graph neural network model for multivariate time series forecasting
Han ZHANG()
School of Data Science and Artificial Intelligence, Dongbei University of Finance and Economics, Dalian 116025, China
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Abstract  

Most of the existing graph neural network models for forecasting multivariate time series capture the time series characteristics in a static way based on predefined graphs, and may be lack of capturing the dynamic adaptation of the system and some potential dynamic relationships between time series samples. A graph neural network model for multivariate time series prediction (MTSGNN) was proposed. In a graph learning module, the static and dynamic evolution graphs of time series data were learned in a data-driven way to capture the complex relationships between time series samples. The information interaction between the static and dynamic graphs was realized by the graph interaction module, and the convolution operation was used to extract the dependency in the interaction information. A multi-layer perceptron was used to forecast the multivariate time series. Experimental results on six real multivariate time series datasets showed that the forecasting effect of the proposed model was significantly better than those of the current state-of-the-art methods, and it had the advantages of small parameter quantity and fast operation speed.



Key wordsmultivariate time series      graph neural network      static graph      dynamic graph      graph interaction     
Received: 30 December 2023      Published: 25 November 2024
CLC:  TP 393  
Fund:  辽宁省应用基础研究计划资助项目(2023JH2/101600040);辽宁省教育厅基本科研资助项目(LJKMZ20221598).
Cite this article:

Han ZHANG. Graph neural network model for multivariate time series forecasting. Journal of ZheJiang University (Engineering Science), 2024, 58(12): 2500-2509.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2024.12.009     OR     https://www.zjujournals.com/eng/Y2024/V58/I12/2500


用于多元时间序列预测的图神经网络模型

现有用于多元时序预测的图神经网络模型大多基于预定义图以静态的方式捕捉时序特征,缺少对于系统动态适应和对时序样本之间潜在动态关系的捕捉. 提出用于多元时序预测的图神经网络模型 (MTSGNN). 该模型在一个图学习模块中,采用数据驱动的方式学习时间序列数据的静态图和动态演化图,以捕捉时序样本之间的复杂关系. 通过图交互模块实现静态图和动态图之间的信息交互,并使用卷积运算提取交互信息中的依赖关系. 利用多层感知机对多元时序进行预测. 实验结果表明,所提模型在6个真实的多元时间序列数据集上的预测效果显著优于当前最先进的方法,并且具有参数量较小、运算速度较快的优点.


关键词: 多元时间序列,  图神经网络,  静态图,  动态图,  图交互 
Fig.1 Overall framework of proposed model MTSGNN
任务数据集$ N $$ U $$ I $$ L $$ H $
多步预测METR-LA342722075 min1212
PEMS-BAY521163255 min1212
单步预测Traffic175448621 h1681
Solar-Energy5256013710 min1681
Electricity263043211 h1681
Exchange-Rate758881 d1681
Tab.1 Statistics of benchmark datasets
模型MAEMAPE/%RMSE
METR-LAPEMS-BAYMETR-LAPEMS-BAYMETR-LAPEMS-BAY
VAR3.602.074.9010.504.7427.60
DSANet4.592.494.9012.705.6929.40
DCRNN3.531.955.7910.014.5227.37
STGCN3.592.204.6310.635.0627.11
ASTGCN3.491.915.4510.014.4628.07
STSGCN3.401.954.6010.054.4926.88
AGCRN3.491.944.539.874.4725.24
MTSGNN-S3.101.894.389.254.3721.85
MTSGNN-D3.151.914.459.254.4222.12
MTSGNN-GL3.091.883.379.173.3821.81
MTSGNN3.051.754.018.724.0220.72
Tab.2 Experimental results of models for multi-step forecasting
模型lRSECORR
Exchange-RateTrafficElectricitySolar-EnergyExchange-RateTrafficElectricitySolar-Energy
AR30.0230.6060.0910.2440.9760.7850.8870.971
60.0280.6280.1010.3790.9650.7630.8640.926
120.0350.6280.1120.5910.9540.7630.8530.811
240.0450.6390.1230.8700.9420.7520.8750.531
VAR-MLP30.0270.5610.1450.1920.8530.8210.8750.983
60.0390.6630.1670.2680.8750.7750.8420.966
120.0400.6060.1560.4240.8310.7970.8210.906
240.0570.6280.1340.6840.7770.7850.8620.715
GP30.0240.6070.1560.2260.8750.7850.8760.975
60.0270.6850.1890.3290.8210.7410.8310.945
120.0390.6410.1670.5200.8530.7740.8420.852
240.0580.6070.1320.7970.8310.7960.8860.597
RNN-GRU30.0190.5490.1120.1930.9860.8530.8640.982
60.0260.5510.1230.2630.9760.8530.8750.968
120.0410.5610.1340.4160.9530.8420.8530.915
240.0630.5720.1450.4850.9250.8310.8750.882
LSTNet30.0230.4820.0860.1840.9760.8750.9320.984
60.0280.5160.0930.2560.9650.8640.9110.969
120.0360.4930.1120.3250.9540.8530.9010.947
240.0440.5050.1010.4640.9430.8420.9210.887
TPA-LSTM30.0190.4590.0820.1800.9870.8860.9430.985
60.0260.4610.0920.2350.9760.8750.9320.974
120.0360.4710.0960.3230.9650.8860.9210.949
240.0460.4820.1120.4390.9420.8640.9110.908
MTGNN30.0190.4260.0880.1780.9870.9090.9450.985
60.0260.4710.0910.2350.9770.8750.9430.973
120.0350.4590.1010.3110.9760.8970.9320.951
240.0460.4610.1120.4270.9540.8860.9430.903
SDGL30.0180.4140.0700.0180.9810.9010.9530.981
60.0250.4480.0810.0250.9730.8830.9450.973
120.0340.4580.0890.0340.9580.8760.9350.958
240.0460.4570.0940.0460.9400.8770.930.940
MTSGNN30.0160.3650.0750.0160.9860.9210.9720.986
60.0230.4150.0790.0230.9820.9420.9610.982
120.0320.4050.0890.0320.9870.9570.9520.987
240.0410.4150.0890.0410.9650.9430.9630.965
Tab.3 Experimental results of models for single-step forecasting
模型$ {n}_{\mathrm{p}} $$ {T}_{{\mathrm{e}}}/{\mathrm{s}} $$ {T}_{{\mathrm{t}}}/{\mathrm{h}} $
LSTNet7161334.110.94
TPA-LSTM379051313.418.71
MTGNN337345349.574.86
MTSGNN163325111.891.55
Tab.4 Training time per epoch for four models on dataset Exchange-Rate
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