Equilibrium Causal Digital Twins: Validation, Transport, and Identification Limits

2026-07-23

AI Summary

This study addresses the challenge that digital twins in feedback systems often fail to accurately predict post-intervention equilibrium counterfactual responses under mechanism shifts. To overcome this limitation, the authors propose a verifiable and transferable causal digital twin framework grounded in causal graphical models and equilibrium selection mechanisms. By introducing cyclic selection graphs, hybrid modeling strategies, and identifiability boundaries, they demonstrate that matching only means and covariances is insufficient to ensure distribution-level counterfactual consistency, thereby establishing the necessity of structural assumptions. Leveraging linear system identification theory and statistical testing, the work derives intervention conditions dependent on mechanism changes and observational structure in synthetic feedback systems, characterizes the range of query values when point identification fails, and validates the theoretical claims empirically.

Abstract

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.

Problem

• equilibrium causal digital twins
• counterfactual prediction
• mechanism change
• validation
• transportability

Innovation

• equilibrium causal digital twins
• counterfactual identification
• cyclic selection diagrams
• transportability
• structural validation