基于神经常微分方程的自适应图时空同步交通流预测方法

史昕; 胡欣倩; 赵祥模; 马峻岩; 王建

doi:10.19818/j.cnki.1671-1637.2025.02.011

基于神经常微分方程的自适应图时空同步交通流预测方法

doi: 10.19818/j.cnki.1671-1637.2025.02.011

史昕^{1, 2, ,},
胡欣倩^{1, 2},
赵祥模^{1, 2},
马峻岩^{1, 2},
王建³

1.
长安大学信息工程学院，陕西西安 710064
2.
长安大学陕西省车联网与智能交通国际科技合作基地，陕西西安 710064
3.
东南大学交通学院，江苏南京 211189

基金项目:

国家自然科学基金项目 52472340

国家自然科学基金项目 52131204

详细信息

作者简介:
史昕(1987-)，男，河南南阳人，长安大学副教授，工学博士，从事交通大数据分析研究

中图分类号: U491.14
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出版历程
- 收稿日期: 2024-08-31
- 刊出日期: 2025-04-28

Adaptive graph spatio-temporal synchronization for traffic flow prediction based on NODEs

SHI Xin^{1, 2
, ,},
HU Xin-qian^{1, 2},
ZHAO Xiang-mo^{1, 2},
MA Jun-yan^{1, 2},
WANG Jian³

1.
School of Information Engineering, Chang'an University, Xi'an 710064, Shaanxi, China
2.
International Science and Technology Cooperation Base for Connected Vehicles and Intelligent Transportation Systems in Shaanxi Province, Chang'an University, Xi'an 710064, Shaanxi, China
3.
School of Transportation, Southeast University, Nanjing 211189, Jiangsu, China

Funds:

National Natural Science Foundation of China 52472340

National Natural Science Foundation of China 52131204

More Information

Corresponding author: SHI Xin (1987-), male, associate professor, PhD, alu_steven@qq.com

Article Text (Baidu Translation)

摘要

摘要: 针对现有交通流预测中时空特征获取的连续性与同步性问题，提出了一种基于神经常微分方程的自适应图(AGNODE)时空同步交通流预测模型；基于历史交通流量数据的语义和距离相关性构建了双路先验邻接矩阵，利用动态滤波和节点嵌入设计了权重可自动调整的自适应邻接矩阵；结合先验和自适应邻接矩阵，利用线性加权融合建立了静动态图融合层，通过虚拟连接层内顶点特征构建了包含时间和空间2个维度的自适应时空同步结构图；引入神经常微分方程(NODE)求解图卷积网络(GCN)形成了图卷积神经常微分方程(GCNODE)，利用求解步长时间对齐和GCNODE双层堆叠构建了AGNODE模型；利用加州高速公路公开交通数据集(PeMS04和PeMS08)，结合平均绝对误差(MAE)、均方根误差(RMSE)以及训练和推理时间等指标，测试验证了AGNODE模型。分析结果表明：相比最优基线模型STGODE，AGNODE的单步预测(5 min)在PeMS04上MAE和RMSE分别降低了3.6%和2.8%，在PeMS08上MAE和RMSE分别降低了2.2%和1.7%；AGNODE的多步预测(15、30、60 min)在PeMS04上MAE和RMSE分别平均降低了3.0%和2.4%，在PeMS08上MAE和RMSE分别平均降低了3.6%和1.2%；随着模型网络层数增大，AGNODE的MAE和RMSE分别降低了5.3%和2.6%，STGODE的MAE和RMSE分别降低了0.7%和0.6%；AGNODE的训练和推理时间相比ASTGCN，在PeMS04和PeMS08上分别减少了11.4%和7.5%，相比STGODE以增加不超过7.7%的时间成本得到更好预测精度。可见，AGNODE模型具有较强的时空建模和参数适应能力，可以准确预测短时交通流量，能够为交通参与者提供可靠的流量信息与决策依据。
- 智能交通 /
- 交通流预测 /
- 神经常微分方程 /
- 时空域联合 /
- 图卷积网络
Abstract: To tackle the continuity and synchronization in the acquisition of spatio-temporal features for traffic flow prediction, an adaptive graph based on neural ordinary differential equation (AGNODE) model for spatio-temporal synchronized traffic flow prediction was proposed. According to the correlations of semantic and distance in historical traffic flow data, a two-way prior adjacency matrix was defined. An adaptive adjacency matrix with automatically adjustable weights was designed by using dynamic filtering and node embedding. With the prior adjacency matrix and the adaptive adjacency matrix, a fusion layer of the static-dynamic map was established based on the linear weighted fusion, and an adaptive spatio-temporal synchronized graph containing both temporal and spatial dimensions was constructed via the vertex features in the virtual connection layer. The neural ordinary differential equations (NODE) were employed to solve the graph convolutional network (GCN) and then form the graph convolutional NODE (GCNODE). The AGNODE model was constructed by utilizing the time-aligned solution step and double-stacked GCNODE. Using the California freeway public traffic datasets (PeMS04 and PeMS08), combined with indicators such as the mean absolute error (MAE), root mean square error (RMSE), and training and inference time, the AGNODE model was tested and verified. Analysis results show that compared with those of the optimal baseline model of the spatio-temporal graph ordinary differential equation (STGODE), the MAE and RMSE of the AGNODE model in the single-step prediction (5 min) decrease by 3.6% and 2.8% on PeMS04, and by 2.2% and 1.7% on PeMS08, respectively. In the multistep predictions (15, 30, and 60 min), the MAE and RMSE of the AGNODE model decrease by an average of 3.0% and 2.4% on PeMS04, and by an average of 3.6% and 1.2% on PeMS08, respectively. As the network layer increases, the MAE and RMSE of the AGNODE model decrease by 5.3% and 2.6%, while those of the STGODE model decrease by 0.7% and 0.6%, respectively. The training and inference time of the AGNODE model on PeMS04 and PeMS08 decrease by 11.4% and 7.5%, respectively, compared with those of the attention-based spatial-temporal graph convolutional network (ASTGCN). Moreover, the AGNODE model can achieve better prediction accuracy with an additional time of no more than 7.7% compared to STGODE. Therefore, the AGNODE model can exhibit strong capabilities in spatio-temporal modelling and parameter adaptation, accurately predict the short-term traffic flow, and provide reliable flow information and decision basis for traffic participants.
- intelligent transportation /
- traffic flow prediction /
- neural ordinary differential equation /
- joint spatio-temporal domain /
- graph convolution network

HTML全文

图 1 交通流预测基于图的时空问题表述

Figure 1. Graph based representation of spatio-temporal problems in traffic flow prediction

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图 2 交通流时空相关性

Figure 2. Spatio-temporal correlation in traffic flow

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图 3 时空特征连续性分析

Figure 3. Analysis of spatio-temporal feature continuity

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图 4 AGNODE及前端核心模块结构

Figure 4. Structure of AGNODE and its front core modules

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图 5 自适应邻接矩阵计算流程

Figure 5. Computational process of adaptive adjacency matrix

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图 6 时空同步图NODE卷积层模块

Figure 6. NODE convolution layer module in spatio-temporal synchronization diagram

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图 7 PeMS采集数据的路网结构和部分传感器部署位置

Figure 7. Road network structure and selected sensor deployment locations in PeMS data collection

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图 8 PeMS04上不同模型不同预测时长的性能比较

Figure 8. Performance comparison of different models with different prediction durations in PeMS04

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图 9 PeMS08上不同模型不同预测时长的性能比较

Figure 9. Performance comparison of different models with different prediction durations in PeMS08

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图 10 PeMS04消融试验结果

Figure 10. Ablation experiment results in PeMS04

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图 11 PeMS08消融试验结果

Figure 11. Ablation experiment results in PeMS08

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图 12 PeMS04数据集(一周/一天)预测可视化结果

Figure 12. Visualization results for one week/one day prediction in PeMS04

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图 13 PeMS08数据集(一周/一天)预测可视化结果

Figure 13. Visualization results for one week/one day prediction in PeMS08

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图 14 网络深度增加性能对比

Figure 14. Performance comparison based on increasing network depth

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图 15 PeMS04邻接矩阵对比

Figure 15. Comparison of adjacency matrices in PeMS04

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图 16 PeMS08邻接矩阵对比

Figure 16. Comparison of adjacency matrices in PeMS08

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图 17 PeMS04、PeMS08数据集训练时间及平均误差值

Figure 17. Training time and average errors for PeMS04 and PeMS08 datasets

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表 1 交通流预测模型的性能对比

Table 1. Performance comparison of traffic flow prediction models

数据集	模型	5 min		15 min		30 min		60 min
数据集	模型	MAE/veh	RMSE/veh	MAE/veh	RMSE/veh	MAE/veh	RMSE/veh	MAE/veh	RMSE/veh
PeMS04	HA	26.49	38.14	30.12	44.27	37.13	54.11	50.99	72.23
	VAR	19.79	33.05	24.03	43.59	30.34	63.76	44.36	110.33
	ARIMA	29.69	45.74	32.50	49.81	33.96	51.88	36.86	55.89
	FC-LSTM	18.45	29.10	22.86	37.00	25.11	38.58	32.98	49.77
	STGCN	19.25	28.73	20.53	31.29	21.67	35.41	24.34	41.57
	ASTGCN	19.25	30.06	20.60	32.92	21.67	33.82	24.04	37.03
	STSGCN	18.13	29.12	19.80	31.58	21.31	33.84	24.47	38.46
	STGODE	17.95	28.49	19.54	30.82	21.37	33.21	24.85	37.72
	AGNODE	17.31	27.70	18.71	29.12	20.39	32.75	23.89	36.93
PeMS08	HA	21.54	31.74	24.95	37.36	30.14	43.71	38.62	57.00
	VAR	14.80	22.92	19.87	32.70	24.82	42.98	33.94	59.44
	ARIMA	15.33	22.53	19.51	28.70	22.30	32.62	25.78	37.22
	FC-LSTM	21.44	34.28	24.55	38.52	31.69	46.63	39.45	56.33
	STGCN	16.40	24.55	17.48	26.46	18.40	27.92	19.90	29.94
	ASTGCN	14.79	22.92	16.46	25.66	17.87	28.09	19.99	31.89
	STSGCN	14.52	22.39	16.10	25.08	17.41	27.26	19.52	30.37
	STGODE	14.71	22.02	15.96	24.21	16.80	25.62	18.34	27.98
	AGNODE	14.20	21.65	15.23	23.54	16.09	25.29	17.95	28.13

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表 2 交通流预测模型效率对比

Table 2. Efficiency comparison of traffic flow prediction models

数据集	模型	每次迭代训练时间/s	推理时间/s
PeMS04	STGCN	15.12	3.46
	FC-LSTM	13.55	1.82
	ASTGCN	47.78	8.68
	STSGCN	80.43	27.32
	STGODE	40.38	6.27
	AGNODE	42.46	7.79
PeMS08	STGCN	8.28	2.05
	FC-LSTM	13.37	0.98
	ASTGCN	28.78	6.89
	STSGCN	50.57	12.54
	STGODE	26.74	5.23
	AGNODE	27.35	5.84

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