# Statistical Reachability Analysis of Stochastic Cyber-Physical Systems under Distribution Shift arXiv: https://arxiv.org/abs/2407.11609 · HTML: https://mlsanity.com/paper/2407.11609/ ## Key facts - Cited by 4 papers in the map (data through 14 Oct 2026). - Builds on 28 of its 54 references that are in the map. - First posted on arXiv 16 Jul 2024. ## Builds on (most cited first, 28 of 28) - [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021) - [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017) - [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016) - [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019) - [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018) - [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018) - [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016) - [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017) - [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017) - [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020) - [Distributionally Robust Logistic Regression](https://mlsanity.com/paper/1509.09259/) (2015) - [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020) - [Sample-Efficient Safety Assurances using Conformal Prediction](https://mlsanity.com/paper/2109.14082/) (2021) - [POLAR: A Polynomial Arithmetic Framework for Verifying Neural-Network Controlled Systems](https://mlsanity.com/paper/2106.13867/) (2021) - [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023) - [Robust Conformal Prediction for STL Runtime Verification under Distribution Shift](https://mlsanity.com/paper/2311.09482/) (2023) - [DRYVR:Data-driven verification and compositional reasoning for automotive systems](https://mlsanity.com/paper/1702.06902/) (2017) - [Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods](https://mlsanity.com/paper/1910.02500/) (2019) - [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021) - [Data-Driven Reachability Analysis with Christoffel Functions](https://mlsanity.com/paper/2104.13902/) (2021) - [Generating Formal Safety Assurances for High-Dimensional Reachability](https://mlsanity.com/paper/2209.12336/) (2022) - [Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference](https://mlsanity.com/paper/2309.09187/) (2023) - [Stochastic reachability of a target tube: Theory and computation](https://mlsanity.com/paper/1810.05217/) (2018) - [Data-driven Reachability using Christoffel Functions and Conformal Prediction](https://mlsanity.com/paper/2309.08976/) (2023) - [Model-Free Stochastic Reachability Using Kernel Distribution Embeddings](https://mlsanity.com/paper/1908.00697/) (2019) - [Efficient Backward Reachability Using the Minkowski Difference of Constrained Zonotopes](https://mlsanity.com/paper/2207.04272/) (2022) - [Probabilistic reachable and invariant sets for linear systems with correlated disturbance](https://mlsanity.com/paper/2004.06960/) (2020) - [Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms](https://mlsanity.com/paper/1610.04550/) (2016) ## Built on by (most cited first, 4 of 4) - [Probabilistic Robustness Analysis in High Dimensional Space: Application to Semantic Segmentation Network](https://mlsanity.com/paper/2509.11838/) (2025) - [Scalable Data-Driven Reachability Analysis and Control via Koopman Operators with Conformal Coverage Guarantees](https://mlsanity.com/paper/2601.01076/) (2026) - [Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees](https://mlsanity.com/paper/2604.00283/) (2026) - [Data-driven Reachable Set Estimation with Tunable Adversarial and Wasserstein Distributional Guarantees](https://mlsanity.com/paper/2604.12654/) (2026) ## Abstract (arXiv) Reachability analysis is a popular method to give safety guarantees for stochastic cyber-physical systems (SCPSs) that takes in a symbolic description of the system dynamics and uses set-propagation methods to compute an overapproximation of the set of reachable states over a bounded time horizon. In this paper, we investigate the problem of performing reachability analysis for an SCPS that does not have a symbolic description of the dynamics, but instead is described using a digital twin model that can be simulated to generate system trajectories. An important challenge is that the simulator implicitly models a probability distribution over the set of trajectories of the SCPS; however, it is typical to have a sim2real gap, i.e., the actual distribution of the trajectories in a deployment setting may be shifted from the distribution assumed by the simulator. We thus propose a statistical reachability analysis technique that, given a user-provided threshold 1-ε, provides a set that guarantees that any reachable state during deployment lies in this set with probability not smaller than this threshold. Our method is based on three main steps: (1) learning a deterministic surrogate model from sampled trajectories, (2) conducting reachability analysis over the surrogate model, and (3) employing em robust conformal inference using an additional set of sampled trajectories to quantify the surrogate model's distribution shift with respect to the deployed SCPS. To counter conservatism in reachable sets, we propose a novel method to train surrogate models that minimizes a quantile loss term (instead of the usual mean squared loss), and a new method that provides tighter guarantees using conformal inference using a normalized surrogate error. We demonstrate the effectiveness of our technique on various case studies.