Equilibrium Causal Digital Twins: Validation, Transport, and Identification Limits
Digital twins are often used to predict how a system would respond to an intervention. In systems with feedback, a twin must reproduce an equilibrium counterfactual, and a twin developed in one domain may fail after mechanisms change. We study when these predictions can be validated and transported. For equilibrium causal games, we give conditions on the mechanisms, equilibrium selection, and intervention design under which agreement with experimental distributions identifies the counterfactual of interest. We show why agreement of means and covariances is insufficient for distributional queries. We then introduce cyclic selection diagrams and derive criteria for direct reuse and for hybrid models that combine invariant source mechanisms with target information. An impossibility result constructs systems that agree under every experiment in a finite design but disagree on the target counterfactual, showing that validation requires structural assumptions. For linear models, we derive intervention requirements that depend on the mechanisms that changed, the observation model, and graph support. When point identification fails, we characterize the remaining range of query values. We also provide statistical tests for reconstructed means and covariances and illustrate the theory in synthetic feedback systems.