# Learning Approximate Forward Reachable Sets Using Separating Kernels

arXiv: https://arxiv.org/abs/2011.09678 · HTML: https://mlsanity.com/paper/2011.09678/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2020.

## Built on by (most cited first, 4 of 4)

- [A Simple and Efficient Sampling-based Algorithm for General Reachability Analysis](https://mlsanity.com/paper/2112.05745/) (2021)
- [SOCKS: A Stochastic Optimal Control and Reachability Toolbox Using Kernel Methods](https://mlsanity.com/paper/2203.06290/) (2022)
- [Convex and Nonconvex Sublinear Regression with Application to Data-driven Learning of Reach Sets](https://mlsanity.com/paper/2210.01919/) (2022)
- [Convex Hulls of Reachable Sets](https://mlsanity.com/paper/2303.17674/) (2023)

## Abstract (arXiv)

We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as an element in a reproducing kernel Hilbert space using a data-driven approach. Kernel methods provide a computationally efficient representation for the classifier that is the solution to a regularized least squares problem. The solution converges almost surely as the sample size increases, and admits known finite sample bounds. This approach is applicable to stochastic systems with arbitrary disturbances and neural network verification problems by treating the network as a dynamical system, or by considering neural network controllers as part of a closed-loop system. We present our technique on several examples, including a spacecraft rendezvous and docking problem, and two nonlinear system benchmarks with neural network controllers.