# Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods

arXiv: https://arxiv.org/abs/1910.02500 · HTML: https://mlsanity.com/paper/1910.02500/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2019.

## Built on by (most cited first, 14 of 14)

- [Data-Driven Reachability Analysis from Noisy Data](https://mlsanity.com/paper/2105.07229/) (2021)
- [Learning Density Distribution of Reachable States for Autonomous Systems](https://mlsanity.com/paper/2109.06728/) (2021)
- [Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference](https://mlsanity.com/paper/2309.09187/) (2023)
- [Symbolic Abstractions From Data: A PAC Learning Approach](https://mlsanity.com/paper/2104.13901/) (2021)
- [Pick-to-Learn for Systems and Control: Data-driven Synthesis with State-of-the-art Safety Guarantees](https://mlsanity.com/paper/2512.04781/) (2025)
- [Statistical Reachability Analysis of Stochastic Cyber-Physical Systems under Distribution Shift](https://mlsanity.com/paper/2407.11609/) (2024)
- [Data-Driven Reachability analysis and Support set Estimation with Christoffel Functions](https://mlsanity.com/paper/2112.09995/) (2021)
- [GenCtrl -- A Formal Controllability Toolkit for Generative Models](https://mlsanity.com/paper/2601.05637/) (2026)
- [Learning to Reach, Swim, Walk and Fly in One Trial: Data-Driven Control with Scarce Data and Side Information](https://mlsanity.com/paper/2106.10533/) (2021)
- [Case Studies for Computing Density of Reachable States for Safe Autonomous Motion Planning](https://mlsanity.com/paper/2209.08073/) (2022)
- [A GP-based Robust Motion Planning Framework for Agile Autonomous Robot Navigation and Recovery in Unknown Environments](https://mlsanity.com/paper/2402.01617/) (2024)
- [Data-Driven Safety Verification using Barrier Certificates and Matrix Zonotopes](https://mlsanity.com/paper/2504.01007/) (2025)
- [Safe and Nonconservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barriers](https://mlsanity.com/paper/2509.07464/) (2025)
- [Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees](https://mlsanity.com/paper/2604.00283/) (2026)

## Abstract (arXiv)

We present two data-driven methods for estimating reachable sets with probabilistic guarantees. Both methods make use of a probabilistic formulation allowing for a formal definition of a data-driven reachable set approximation that is correct in a probabilistic sense. The first method recasts the reachability problem as a binary classification problem, using a Gaussian process classifier to represent the reachable set. The quantified uncertainty of the Gaussian process model allows for an adaptive approach to the selection of new sample points. The second method uses a Monte Carlo sampling approach to compute an interval-based approximation of the reachable set. This method comes with a guarantee of probabilistic correctness, and an explicit bound on the number of sample points needed to achieve a desired accuracy and confidence. Each method is illustrated with a numerical example.