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Learning multi-agent system dynamics has been extensively studied for various real-world applications, such as molecular dynamics in biology, multi-body system in physics, and particle dynamics in material science. Most of the existing models are built to learn single system dynamics, which learn the dynamics from observed historical data and predict the future trajectory. In practice, however, we might observe multiple systems that are generated across different environments, which differ in latent exogenous factors such as temperature and gravity. One simple solution is to learn multiple environment-specific models, but it fails to exploit the potential commonalities among the dynamics across environments and offers poor prediction results where per-environment data is sparse or limited. Here, we present GG-ODE (Generalized Graph Ordinary Differential Equations), a machine learning framework for learning continuous multi-agent system dynamics across environments. Our model learns system dynamics using neural ordinary differential equations (ODE) parameterized by Graph Neural Networks (GNNs) to capture the continuous interaction among agents. We achieve the model generalization by assuming the dynamics across different environments are governed by common physics laws that can be captured via learning a shared ODE function. The distinct latent exogenous factors learned for each environment are incorporated into the ODE function to account for their differences. To improve model performance, we additionally design two regularization losses to (1) enforce the orthogonality between the learned initial states and exogenous factors via mutual information minimization; and (2) reduce the temporal variance of learned exogenous factors within the same system via contrastive learning. Experiments over various physical simulations show that our model can accurately predict system dynamics, especially in the long range, and can generalize well to new systems with few observations.
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HOPE: High-order Graph ODE For Modeling Interacting Dynamics
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.
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- PAR ID:
- 10464443
- Date Published:
- Journal Name:
- Proceedings of the 40th International Conference on Machine Learning
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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