Learning multi-agent system dynamics has been extensively studied for various real-world applications, such as molecular dynamics in biology. Most of the existing models are built to learn single system 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.

翻译：多智能体系统动力学学习已在诸多实际应用中得到广泛研究，例如生物学中的分子动力学。现有模型大多基于观测到的历史数据学习单一系统动力学并预测未来轨迹。然而在实际应用中，我们可能观测到不同环境下生成的多个系统，这些环境在温度、重力等潜在外源因素上存在差异。一种简单的解决方案是学习多个环境特异性模型，但这未能利用跨环境动力学中潜在的共性，且在每环境数据稀疏或有限的情况下预测效果不佳。本文提出GG-ODE（泛化图常微分方程），这是一个跨环境学习连续多智能体系统动力学的机器学习框架。该模型采用图神经网络参数化的神经常微分方程学习系统动力学，以捕捉智能体间的连续交互。通过假设不同环境下的动力学受共同物理定律支配，且该定律可通过学习共享的ODE函数捕获，我们实现了模型泛化。为每个环境学习的独特潜在外源因素被纳入ODE函数以解释环境差异。为提升模型性能，我们额外设计了两项正则化损失：（1）通过互信息最小化强制学习初始状态与外源因素的正交性；（2）通过对比学习降低同一系统内学习到的外源因素的时间方差。在多种物理模拟上的实验表明，本模型能准确预测系统动力学（尤其擅长长期预测），并能基于少量观测高效泛化至新系统。