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Multi-agent dynamical systems refer to scenarios where multiple unitsinteract with each other and evolve collectively over time. To make informeddecisions in multi-agent dynamical systems, such as determining the optimalvaccine distribution plan, it is essential for decision-makers to estimate thecontinuous-time counterfactual outcomes. However, existing studies of causalinference over time rely on the assumption that units are mutually independent,which is not valid for multi-agent dynamical systems. In this paper, we aim tobridge this gap and study how to estimate counterfactual outcomes inmulti-agent dynamical systems. Causal inference in a multi-agent dynamicalsystem has unique challenges: 1) Confounders are time-varying and are presentin both individual unit covariates and those of other units; 2) Units areaffected by not only their own but also others' treatments; 3) The treatmentsare naturally dynamic, such as receiving vaccines and boosters in a seasonalmanner. We model a multi-agent dynamical system as a graph and proposeCounterFactual GraphODE (CF-GODE), a causal model that estimatescontinuous-time counterfactual outcomes in the presence of inter-dependenciesbetween units. To facilitate continuous-time estimation, we proposeTreatment-Induced GraphODE, a novel ordinary differential equation based onGNN, which incorporates dynamical treatments as additional inputs to predictpotential outcomes over time. To remove confounding bias, we propose two domainadversarial learning based objectives that learn balanced continuousrepresentation trajectories, which are not predictive of treatments andinterference. We further provide theoretical justification to prove theireffectiveness. Experiments on two semi-synthetic datasets confirm that CF-GODEoutperforms baselines on counterfactual estimation. We also provide extensiveanalyses to understand how our model works.

CF-GODE: Continuous-Time Causal Inference for Multi-Agent Dynamical Systems