# Statistical Verification of Autonomous Systems using Surrogate Models and Conformal Inference

arXiv: https://arxiv.org/abs/2004.00279 · HTML: https://mlsanity.com/paper/2004.00279/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Apr 2020.

## Built on by (most cited first, 8 of 8)

- [Distributionally Robust Statistical Verification with Imprecise Neural Networks](https://mlsanity.com/paper/2308.14815/) (2023)
- [How Safe Am I Given What I See? Calibrated Prediction of Safety Chances for Image-Controlled Autonomy](https://mlsanity.com/paper/2308.12252/) (2023)
- [Testing Rare Downstream Safety Violations via Upstream Adaptive Sampling of Perception Error Models](https://mlsanity.com/paper/2209.09674/) (2022)
- [Recursively Feasible Shrinking-Horizon MPC in Dynamic Environments with Conformal Prediction Guarantees](https://mlsanity.com/paper/2405.10875/) (2024)
- [Learning Spatio-Temporal Specifications for Dynamical Systems](https://mlsanity.com/paper/2112.10714/) (2021)
- [Tolerance of Reinforcement Learning Controllers against Deviations in Cyber Physical Systems](https://mlsanity.com/paper/2406.17066/) (2024)
- [How Safe Will I Be Given What I Saw? Calibrated Prediction of Safety Chances for Image-Controlled Autonomy](https://mlsanity.com/paper/2508.09346/) (2025)
- [Conformal Signal Temporal Logic for Robust Reinforcement Learning Control: A Case Study](https://mlsanity.com/paper/2602.14322/) (2026)

## Abstract (arXiv)

In this paper, we propose conformal inference based approach for statistical verification of CPS models. Cyber-physical systems (CPS) such as autonomous vehicles, avionic systems, and medical devices operate in highly uncertain environments. This uncertainty is typically modeled using a finite number of parameters or input signals. Given a system specification in Signal Temporal Logic (STL), we would like to verify that for all (infinite) values of the model parameters/input signals, the system satisfies its specification. Unfortunately, this problem is undecidable in general. em Statistical model checking (SMC) offers a solution by providing guarantees on the correctness of CPS models by statistically reasoning on model simulations. We propose a new approach for statistical verification of CPS models for user-provided distribution on the model parameters. Our technique uses model simulations to learn em surrogate models, and uses em conformal inference to provide probabilistic guarantees on the satisfaction of a given STL property. Additionally, we can provide prediction intervals containing the quantitative satisfaction values of the given STL property for any user-specified confidence level. We also propose a refinement procedure based on Gaussian Process (GP)-based surrogate models for obtaining fine-grained probabilistic guarantees over sub-regions in the parameter space. This in turn enables the CPS designer to choose assured validity domains in the parameter space for safety-critical applications. Finally, we demonstrate the efficacy of our technique on several CPS models.