# Estimating Inconsistency Response Surfaces under Uncertainty in Cyber-Physical System Development

arXiv: https://arxiv.org/abs/2609.11331 · HTML: https://mlsanity.com/paper/2609.11331/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 42 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 7 of 7)

- [Counterfactual Explanations without Opening the Black Box: Automated Decisions and the GDPR](https://mlsanity.com/paper/1711.00399/) (2017)
- [Actionable Recourse in Linear Classification](https://mlsanity.com/paper/1809.06514/) (2018)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Surrogate Modeling and Explainable Artificial Intelligence for Complex Systems: A Workflow for Automated Simulation Exploration](https://mlsanity.com/paper/2510.16742/) (2025)
- [Parameterized Hardness of Zonotope Containment and Neural Network Verification](https://mlsanity.com/paper/2509.22849/) (2025)
- [Cyber-Physical Specification Mismatches](https://mlsanity.com/paper/1806.09224/) (2018)

## Abstract (arXiv)

Cyber-Physical Systems (CPS) are commonly represented through multiple interconnected models. During development, CPS consistency requires that shared model elements remain compatible across these models. Uncertainty, for example, due to sensor noise or model abstraction, changes the admissible values of model elements and can introduce inconsistencies, i.e., situations in which models can no longer be jointly satisfied. While existing approaches can determine consistency for a given uncertainty configuration, they provide limited support for systematically exploring, analyzing, and explaining inconsistency across large uncertainty spaces. We address this challenge by reformulating inconsistency as an intervention response modeling problem. Using Saltelli sampling and multi-fidelity Monte Carlo estimation, we generate intervention-response datasets and train a surrogate model that directly predicts inconsistency from the propagated uncertainty geometry. Experiments on 48 scenarios and 10 CPS domains show that the surrogate matches Monte Carlo estimates while reducing evaluation time from milliseconds to microseconds, enabling orders-of-magnitude more response-surface evaluations within fixed computational budgets. Building on the learned response surfaces, we perform sensitivity analysis to identify dominant uncertainty drivers and introduce a gradient-based consistency recourse method to determine minimal uncertainty interventions that restore consistency. The results show that inconsistency under uncertainty can be effectively learned, analyzed, and repaired through response-surface modeling, providing a scalable foundation for uncertainty-aware consistency management in CPS development.