HOPE: High-order Graph ODE For Modeling Interacting Dynamics

Xiao Luo, Jingyang Yuan, Zijie Huang, Huiyu Jiang, Yifang Qin, Wei Ju, Ming Zhang, Yizhou Sun
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:23124-23139, 2023.

Abstract

Leading graph ordinary differential equation (ODE) models have offered generalized strategies to model interacting multi-agent dynamical systems in a data-driven approach. They typically consist of a temporal graph encoder to get the initial states and a neural ODE-based generative model to model the evolution of dynamical systems. However, existing methods have severe deficiencies in capacity and efficiency due to the failure to model high-order correlations in long-term temporal trends. To tackle this, in this paper, we propose a novel model named High-order graph ODE (HOPE) for learning from dynamic interaction data, which can be naturally represented as a graph. It first adopts a twin graph encoder to initialize the latent state representations of nodes and edges, which consists of two branches to capture spatio-temporal correlations in complementary manners. More importantly, our HOPE utilizes a second-order graph ODE function which models the dynamics for both nodes and edges in the latent space respectively, which enables efficient learning of long-term dependencies from complex dynamical systems. Experiment results on a variety of datasets demonstrate both the effectiveness and efficiency of our proposed method.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-luo23f, title = {{HOPE}: High-order Graph {ODE} For Modeling Interacting Dynamics}, author = {Luo, Xiao and Yuan, Jingyang and Huang, Zijie and Jiang, Huiyu and Qin, Yifang and Ju, Wei and Zhang, Ming and Sun, Yizhou}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {23124--23139}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/luo23f/luo23f.pdf}, url = {https://proceedings.mlr.press/v202/luo23f.html}, abstract = {Leading graph ordinary differential equation (ODE) models have offered generalized strategies to model interacting multi-agent dynamical systems in a data-driven approach. They typically consist of a temporal graph encoder to get the initial states and a neural ODE-based generative model to model the evolution of dynamical systems. However, existing methods have severe deficiencies in capacity and efficiency due to the failure to model high-order correlations in long-term temporal trends. To tackle this, in this paper, we propose a novel model named High-order graph ODE (HOPE) for learning from dynamic interaction data, which can be naturally represented as a graph. It first adopts a twin graph encoder to initialize the latent state representations of nodes and edges, which consists of two branches to capture spatio-temporal correlations in complementary manners. More importantly, our HOPE utilizes a second-order graph ODE function which models the dynamics for both nodes and edges in the latent space respectively, which enables efficient learning of long-term dependencies from complex dynamical systems. Experiment results on a variety of datasets demonstrate both the effectiveness and efficiency of our proposed method.} }
Endnote
%0 Conference Paper %T HOPE: High-order Graph ODE For Modeling Interacting Dynamics %A Xiao Luo %A Jingyang Yuan %A Zijie Huang %A Huiyu Jiang %A Yifang Qin %A Wei Ju %A Ming Zhang %A Yizhou Sun %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-luo23f %I PMLR %P 23124--23139 %U https://proceedings.mlr.press/v202/luo23f.html %V 202 %X Leading graph ordinary differential equation (ODE) models have offered generalized strategies to model interacting multi-agent dynamical systems in a data-driven approach. They typically consist of a temporal graph encoder to get the initial states and a neural ODE-based generative model to model the evolution of dynamical systems. However, existing methods have severe deficiencies in capacity and efficiency due to the failure to model high-order correlations in long-term temporal trends. To tackle this, in this paper, we propose a novel model named High-order graph ODE (HOPE) for learning from dynamic interaction data, which can be naturally represented as a graph. It first adopts a twin graph encoder to initialize the latent state representations of nodes and edges, which consists of two branches to capture spatio-temporal correlations in complementary manners. More importantly, our HOPE utilizes a second-order graph ODE function which models the dynamics for both nodes and edges in the latent space respectively, which enables efficient learning of long-term dependencies from complex dynamical systems. Experiment results on a variety of datasets demonstrate both the effectiveness and efficiency of our proposed method.
APA
Luo, X., Yuan, J., Huang, Z., Jiang, H., Qin, Y., Ju, W., Zhang, M. & Sun, Y.. (2023). HOPE: High-order Graph ODE For Modeling Interacting Dynamics. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:23124-23139 Available from https://proceedings.mlr.press/v202/luo23f.html.

Related Material