A Conceptual Framework for Refining Influence Knowledge from Simulation Evidence in Cyber-Physical Systems

Cyber-physical systems (CPS) are typically developed by multiple stakeholders who produce artefacts tailored to their specific domains of expertise. The behaviour of these systems emerges from the interaction between those artefacts and their operational environment. Simulation and co-simulation have become essential approaches for analysing CPS behaviour and, through simulation campaigns, developers can explore system responses under changing conditions, including interactions with the environment. However, the lack of details and understanding of some environmentmediated interactions (typically the ones beyond direct sensing and actuation), which remain unmodelled due to their complexity, a lack of time, or a lack of domain experience, hinders the proper comprehension and exploitation of simulation results. To address these limitations, we propose a conceptual framework leveraging the novel concept of Influences to support the iterative and incremental refinement of simulation campaigns and deepen the understanding of the system behaviour. We demonstrate the proposed approach through a case study involving a mobile robot implemented using Simulink/Gazebo co-simulation.

Finding Most Influential Sets

Identifying most influential sets (MIS) - size-$k$ subsets whose removal maximally changes a target estimand - is typically infeasible because it requires searching over $\binom{n}{k}$ subsets. For estimands with linear-fractional leave-set-out effects, we show that MIS selection reduces to a one-parameter sequence of top-$k$ problems. Dinkelbach's method yields an algorithm with $\mathcal{O}(n)$ cost per iteration and finite termination. For fixed residualized inputs, the algorithm returns a globally optimal set for the univariate ratio objective, including the oracle-residualized partial linear model. With estimated nuisance functions, uniform denominator and generated-score stability imply approximation to the first-order oracle orthogonal-score objective; exact set recovery follows under a separation condition. Simulations and applications show that the method recovers exact MIS that were previously computationally inaccessible.