Real-world multi-agent systems are often dynamic and continuous, where the
agents co-evolve and undergo changes in their trajectories and interactions
over time. For example, the COVID-19 transmission in the U.S. can be viewed as
a multi-agent system, where states act as agents and daily population movements
between them are interactions. Estimating the counterfactual outcomes in such
systems enables accurate future predictions and effective decision-making, such
as formulating COVID-19 policies. However, existing methods fail to model the
continuous dynamic effects of treatments on the outcome, especially when
multiple treatments (e.g., "stay-at-home" and "get-vaccine" policies) are
applied simultaneously. To tackle this challenge, we propose Causal Graph
Ordinary Differential Equations (CAG-ODE), a novel model that captures the
continuous interaction among agents using a Graph Neural Network (GNN) as the
ODE function. The key innovation of our model is to learn time-dependent
representations of treatments and incorporate them into the ODE function,
enabling precise predictions of potential outcomes. To mitigate confounding
bias, we further propose two domain adversarial learning-based objectives,
which enable our model to learn balanced continuous representations that are
not affected by treatments or interference. Experiments on two datasets (i.e.,
COVID-19 and tumor growth) demonstrate the superior performance of our proposed
model.

通过使用图神经网络 (GNN) 作为普通微分方程 (ODE) 函数，我们提出了因果图普通微分方程 (CAG-ODE) 模型，该模型能够捕捉多个代理间的连续交互，并学习时间相关的处理表示，从而实现对潜在结果的准确预测。通过引入两个域对抗学习目标以减少混淆偏差，我们的模型能够学习到平衡且不受处理或干扰影响的连续表示。在两个数据集（COVID-19 和肿瘤生长）上的实验证明了我们提出模型的出色表现。