Generalizing Graph ODE for Learning Complex System Dynamics across Environments
Generalizing Graph ODE for Learning Complex System Dynamics across Environments
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DOI：
10.1145/3580305.3599362
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发表时间：
2023-07
期刊：
影响因子：
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通讯作者：
Zijie Huang;Yizhou Sun;Wei Wang
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文献类型：
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作者：
Zijie Huang;Yizhou Sun;Wei Wang
学习多智能体系统动力学已经被广泛研究用于各种现实世界的应用，例如生物学中的分子动力学，物理学中的多体系统预测以及材料科学中的粒子动力学。现有的模型大多是为了学习单个系统动力学而建立的，它们从观测到的历史数据中学习动力学并预测未来的轨迹。然而，在实践中，我们可能会观察到在不同环境中产生的多个系统，这些系统在潜在的外生因素（如温度和重力）方面存在差异。一种简单的解决方案是学习多个特定于环境的模型，但它无法利用跨环境的动态之间的潜在共性，并且在每个环境的数据稀疏或有限的情况下提供较差的预测结果。在这里，我们提出了GG-ODE（广义图常微分方程），这是一个用于跨环境学习连续多智能体系统动力学的机器学习框架。我们的模型使用由图神经网络（gnn）参数化的神经常微分方程（ODE）来学习系统动力学，以捕获智能体之间的连续交互。我们通过假设跨不同环境的动态受共同物理定律的控制来实现模型泛化，这些物理定律可以通过学习共享ODE函数来捕获。在每个环境中学习到的不同的潜在外生因素被纳入ODE函数，以解释它们的差异。为了提高模型的性能，我们还设计了两个正则化损失(1)通过互信息最小化来增强学习到的初始状态与外生因素之间的正交性；(2)通过对比学习，减少在同一系统内学习到的外生因素的时间方差。各种物理模拟实验表明，该模型可以准确地预测系统动力学，特别是在长范围内，并且可以很好地推广到很少观测值的新系统。
Learning multi-agent system dynamics have been extensively studied for various real-world applications, such as molecular dynamics in biology, multi-body system prediction 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.