# Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference

arXiv: https://arxiv.org/abs/2309.09187 · HTML: https://mlsanity.com/paper/2309.09187/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 40 references that are in the map.
- First posted on arXiv 17 Sep 2023.

## Builds on (most cited first, 20 of 20)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [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)
- [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)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [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 for STL Runtime Verification](https://mlsanity.com/paper/2211.01539/) (2022)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [ReachNN: Reachability Analysis of Neural-Network Controlled Systems](https://mlsanity.com/paper/1906.10654/) (2019)
- [A Tutorial on Concentration Bounds for System Identification](https://mlsanity.com/paper/1906.11395/) (2019)
- [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)
- [Conformal Quantitative Predictive Monitoring of STL Requirements for Stochastic Processes](https://mlsanity.com/paper/2211.02375/) (2022)
- [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)
- [Stochastic reachability of a target tube: Theory and computation](https://mlsanity.com/paper/1810.05217/) (2018)

## Built on by (most cited first, 9 of 9)

- [ConformalNL2LTL: Translating Natural Language Instructions into Temporal Logic Formulas with Conformal Correctness Guarantees](https://mlsanity.com/paper/2504.21022/) (2025)
- [Pick-to-Learn for Systems and Control: Data-driven Synthesis with State-of-the-art Safety Guarantees](https://mlsanity.com/paper/2512.04781/) (2025)
- [Multi-Modal Conformal Prediction Regions with Simple Structures by Optimizing Convex Shape Templates](https://mlsanity.com/paper/2312.07434/) (2023)
- [Statistical Reachability Analysis of Stochastic Cyber-Physical Systems under Distribution Shift](https://mlsanity.com/paper/2407.11609/) (2024)
- [Probabilistic Robustness Analysis in High Dimensional Space: Application to Semantic Segmentation Network](https://mlsanity.com/paper/2509.11838/) (2025)
- [Single Trajectory Conformal Prediction](https://mlsanity.com/paper/2406.01570/) (2024)
- [Data-Driven Safety Verification using Barrier Certificates and Matrix Zonotopes](https://mlsanity.com/paper/2504.01007/) (2025)
- [TubeDAgger: Reducing the Number of Expert Interventions with Stochastic Reach-Tubes](https://mlsanity.com/paper/2510.00906/) (2025)
- [Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees](https://mlsanity.com/paper/2604.00283/) (2026)

## Abstract (arXiv)

We consider data-driven reachability analysis of discrete-time stochastic dynamical systems using conformal inference. We assume that we are not provided with a symbolic representation of the stochastic system, but instead have access to a dataset of K-step trajectories. The reachability problem is to construct a probabilistic flowpipe such that the probability that a K-step trajectory can violate the bounds of the flowpipe does not exceed a user-specified failure probability threshold. The key ideas in this paper are: (1) to learn a surrogate predictor model from data, (2) to perform reachability analysis using the surrogate model, and (3) to quantify the surrogate model's incurred error using conformal inference in order to give probabilistic reachability guarantees. We focus on learning-enabled control systems with complex closed-loop dynamics that are difficult to model symbolically, but where state transition pairs can be queried, e.g., using a simulator. We demonstrate the applicability of our method on examples from the domain of learning-enabled cyber-physical systems.