Dynamic Multi-Target Spatio-Temporal Prediction Based on Improved Neural Ordinary Differential Equations Network

WANG Yimeng; CHENG Yue; XING Weiwei; LIU Weibin; KANG Xiao

doi:10.12382/bgxb.2025.0576

您当前的位置：

首页 >

文章列表页 >

Dynamic Multi-Target Spatio-Temporal Prediction Based on Improved Neural Ordinary Differential Equations Network

更新时间：2026-05-06

- Dynamic Multi-Target Spatio-Temporal Prediction Based on Improved Neural Ordinary Differential Equations Network
- Acta Armamentarii (2026)
- 作者机构：
  
  1. 中国地质大学（北京）数理学院,北京,100083
  2. 北京交通大学视觉智能交叉创新教育部国际合作联合实验室,北京,100044
  3. 北京交通大学软件学院,北京,100044
  4. 北京交通大学计算机科学与技术学院,北京,100044
  5. 中兵智能创新研究院有限公司,北京,100072
- 作者简介：
- 基金信息：
- DOI：10.12382/bgxb.2025.0576
  CLC： TP391
- Received：29 June 2025，
  
  Online First：06 May 2026，
- 稿件说明：
移动端阅览
王艺萌，程岳，邢薇薇，等. 基于改进神经常微分方程网络的动态多目标时空预测王艺萌1,2，程岳3，邢薇薇3*，刘渭滨2,4**，康晓5[J/OL]. 兵工学报, 2026(2026-05-06). https://doi.org/10.12382/bgxb.2025.0576.

WANG Y M, CHENG Y, XING W W, et al. Dynamic multi-target spatio-temporal prediction based on improved neural ordinary differential equations network[J/OL]. Acta Armamentarii, 2026(2026-05-06). https://doi.org/10.12382/bgxb.2025.0576. (in Chinese)
王艺萌，程岳，邢薇薇，等. 基于改进神经常微分方程网络的动态多目标时空预测王艺萌1,2，程岳3，邢薇薇3*，刘渭滨2,4**，康晓5[J/OL]. 兵工学报, 2026(2026-05-06). https://doi.org/10.12382/bgxb.2025.0576. DOI：

WANG Y M, CHENG Y, XING W W, et al. Dynamic multi-target spatio-temporal prediction based on improved neural ordinary differential equations network[J/OL]. Acta Armamentarii, 2026(2026-05-06). https://doi.org/10.12382/bgxb.2025.0576. (in Chinese) DOI：

摘要

多目标时空预测是动态场景中目标演化与决策的关键。传统静态方法难以捕捉动态环境下多目标间的动态时空演变过程。而神经常微分方程网络虽适配动态系统，但在多目标时空关联方面仍存局限。为此提出一种基于改进神经常微分方程网络的动态多目标时空预测算法，将神经常微分方程与稀疏图卷积网络相结合，建立动态多目标时空预测架构。首先利用稀疏图卷积网络从历史观测轨迹中提取多目标之间的稀疏时空交互特征，实现对多目标时空关联间的建模；然后利用神经常微分方程灵活高效的时序建模能力对目标的高维隐藏状态进行时序建模，最终得到多目标的时空预测轨迹。实验结果表明，所建模型在ETH/UCY数据集上的平均位移误差和最终位移误差分别为0.36和0.56，相比于基准模型神经常微分方程分别降低了3%和10%，预测结果准确度更高。

Abstract

Spatio-temporal prediction of multi-targetsis keyto target evolution and decision-making in dynamic scenarios.Traditional static methods struggle to capture the dynamic spatiotemporal evolution of multiple objectives in dynamic environments. While neural networks based on stochastic differential equations are well-suited for dynamic systems

they still have limitations when it comes to modeling spatiotemporal correlations among multiple objectives.Therefore

this paper proposes a dynamic multi-targetspatio-temporal prediction algorithm based on the improved neuralordinarydifferential equation network. Itestablishes adynamicmulti-targetspatio-temporal prediction architecture by combining neuralordinarydifferential equations and sparse graph convolutional network. Firstly

the sparse graph convolutional network is used to extract the sparse spatio-temporal interaction features between multi-targets from historical observation trajectories to achieve the modelling of multi-target spatio-temporal correlations; then the flexible and efficient temporal modelling capability of theneural ordinarydifferential equations is used to carry out the temporal modelling of the high-dimensional hidden state of the targets

and finally

the spatio-temporal prediction trajectories of the multipletargetsare obtained. Experiments show that the average displacement error (ADE) and final displacement error (FDE) of thismodelon the ETH/UCY dataset are0.36and0.56

which are decreased by 3% and 10%

respectively

compared withtheordinary differential equationsnetwork model

resulting in higher prediction accuracy.

关键词

Keywords

references

CHEN X B, ZHANG H J, ZHAO F, et al. Intention-aware vehicle trajectory prediction based on spatial-temporal dynamic attention network for internet of vehicles[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(10): 19471-19483.DOI: 10.1109/TITS.2022.3170551.

MO X Y, HUANG Z Y, XING Y, et al. Multi-agent trajectory prediction with heterogeneous edge-enhanced graph attention network[J]. IEEE Transactions on Intelligent Transportation Systems, 2022, 23(7): 9554-9567. DOI: 10.1109/TITS.2022.3146300.

ZHAI L B, ZHU X M, CHENG C. Energy efficient data evacuation path for multi-UAV system based on multi-objective optimization method[J]. IEEE Transactions on Vehicular Technology, 2025, 74(5): 7364-7377.

FENG Z K, WU D, HUANG M X, et al. Graph-attention-based reinforcement learning for trajectory design and resource assignment in multi-UAV-assisted communication[J]. IEEE Internet of Things Journal, 2024, 11(16): 27421-27434.

WANG Z H, XUE L, LUO X P, et al. Driving state-aware anomaly detection for autonomous vehicles[J]. IEEE Transactions on Information Forensics and Security, 2025, 20:3788-3803.

崔皓,叶洪涛,罗文广,等. 车辆纵向队列分布式多目标模型预测控制[J]. 控制工程, 2025, 32(12): 2126-2134.

Cui H, Ye H T, Luo W G, et al. Distributed multi-objective model predictive control of vehicle longitudinal queues[J]. Control Engineering, 2025,32(12): 2126-2134. (in Chinese)

ZHANG B, LIU X, ZHENG H F, et al. Hidden Markov model based cyberattack prediction in power systems[J]. IEEE Transactions on Smart Grid, 2024, 16(2): 1694-1705.

BECKERS T, HIRCHE S. Prediction with approximated Gaussian process dynamical models[J]. IEEE Transactions on Automatic Control, 2021, 67(12): 6460-6473.

LAI G K, CHANG W C, YANG Y M, et al. Modeling long-and short-term temporal patterns with deep neural networks[C]//Proceedings of the 41st international ACM SIGIR Conference on Research & Development in Information Retrieval. Ann Arbor, MI, US: ACM, 2018: 95-104.

LEA C, FLYNN M D, VIDAL R, et al. Temporal convolutional networks for action segmentation and detection[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Honolulu, HI, US: IEEE, 2017: 156-165.

WU H X, XU J H, WANG J M, et al. Autoformer: Decomposition transformers with auto-correlation for long-term series forecasting[C]//Proceedings of the 35th International Conference on Neural Information Processing Systems. Virtual: Curran Associates, 2021: 22419-22430.

DONG M. Pedestrian cross forecasting with hybrid feature fusion[C]//Proceedings of the 15th Asian Conference on Machine Learning. Wuhan, China: PMLR, 2024: 327-342.

GUPTA A, JOHNSON J, LI F F, et al. Social GAN: socially acceptable trajectories with generative adversarial networks[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Salt Lake City, UT, US: IEEE, 2018: 2255-2264.

SALZMANN T, IVANOVIC B, CHAKRAVARTY P, et al. Trajectron++: dynamically-feasible trajectory forecasting with heterogeneous data[C]//Proceedings of the European Conference on Computer Vision. Glasgow, UK: Springer, 2020: 683-700.

WANG X C, YANG X, ZHOU D K. Goal-CurveNet: a pedestrian trajectory prediction network using heterogeneous graph attention goal prediction and curve fitting[J]. Engineering Applications of Artificial Intelligence, 2024, 133: 108323.

MOHAMED A, QIAN K, ELHOSEINY M, et al. Social-STGCNN: a social spatio-temporal graph convolutional neural network for human trajectory prediction[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Seattle, WA, US: IEEE, 2020: 14424-14432.

CHEN R T Q, RUBANOVA Y, BETTENCOURT J, et al. Neural ordinary differential equations[C]//Proceedings of the 32nd International Conference on Neural Information Processing Systems. Montréal, Canada: Curran Associates, 2018: 6572- 6583.

LIANG Y X, OUYANG K, YAN H S, et al. Modeling trajectories with neural ordinary differential equations[C]//Proceedings of the 30th International Joint Conference on Artificial Intelligence. Montréal, Canada: IJCAI, 2021: 1498-1504.

XIONG N, YANG Y, JIANG Y Q, et al. Diffusion graph neural ordinary differential equation network for traffic prediction[C]//Proceedings of the 2023 International Joint Conference on Neural Networks. Gold Coast, QLD, Australia: IEEE, 2023: 1-8.

WEN S, WANG H, LIU D, et al. Second-order graph odes for multi-agent trajectory forecasting[C]//Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision. Waikoloa, HI, US: IEEE, 2024: 5101-5110.

SHI L S, WANG L, LONG C J, et al. SGCN: Sparse graph convolution network for pedestrian trajectory prediction[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Nashville, TN, US: IEEE, 2021: 8994-9003.

RANGAPURAM S S, SEEGER M, GASTHAUS J, et al. Deep state space models for time series forecasting[C]//Proceedings of the 32nd International Conference on Neural Information Processing Systems. Montréal, Canada: Curran Associates, 2018: 7796–7805.

LUO D H, WANG X. ModernTCN: a modern pure convolution structure for general time series analysis[C]//Proceedings of the Twelfth International Conference on Learning Representations. Vienna, Austria: ICLR, 2024: 1-43.

PELLEGRINI S, ESS A, SCHINDLER K, et al. You’ll never walk alone: modeling social behavior for multi-target tracking[C]//Proceedings of the IEEE 12th International Conference on Computer Vision. Kyoto, Japan: IEEE, 2009: 261-268.

LERNER A, CHRYSANTHOU Y, LISCHINSKI D. Crowds by example[C]//Computer Graphics Forum. Oxford, UK: Blackwell Publishing Ltd. 2007, 26(3): 655-664.

ALAHI A, GOEL K, RAMANATHAN V, et al. Social LSTM: human trajectory prediction in crowded spaces[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Las Vegas, NV, US: IEEE, 2016: 961-971.

SUN J H, JIANG Q H, LU C W. Recursive social behavior graph for trajectory prediction[C]//Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. Seattle, WA, US: IEEE, 2020: 660-669.

KOSARAJU V, SADEGHIAN A, MARTÍN-MARTÍN R, et al. Social-bigat: Multimodal trajectory forecasting using bicycle-gan and graph attention networks[C]//Proceedings of the 33rd International Conference on Neural Information Processing Systems. Vancouver, BC, Canada: Curran Associates, 2019, 32: 137-146

Views

下载量

CNKI被引量

Alert me when the article has been cited

提交

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

Postal code：100089
Tel：010-68963060/68962718 Fax：010-68963025 Email：bgxb@cos.org.cn
Technical support is provided by Beijing Founder electronics co., LTD 京ICP备05059581号-4 京公网安备11010802024360号
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.
Total Visits：145286 Visits Today：1374

⁰