# PIRK: Scalable Interval Reachability Analysis for High-Dimensional Nonlinear Systems

arXiv: https://arxiv.org/abs/2001.10635 · HTML: https://mlsanity.com/paper/2001.10635/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2020.

## Built on by (most cited first, 2 of 2)

- [GoTube: Scalable Stochastic Verification of Continuous-Depth Models](https://mlsanity.com/paper/2107.08467/) (2021)
- [Robustness Analysis of Continuous-Depth Models with Lagrangian Techniques](https://mlsanity.com/paper/2308.12192/) (2023)

## Abstract (arXiv)

Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with relatively small dimensions. One significant reason for such limitation is that those approaches, and their implementations, are not designed to leverage parallelism. They use algorithms that are designed to run serially within one compute unit and they can not utilize widely-available high-performance computing (HPC) platforms such as many-core CPUs, GPUs and Cloud-computing services. This paper presents PIRK, a tool to efficiently compute reachable sets for general nonlinear systems of extremely high dimensions. PIRK has been tested on several systems, with state dimensions ranging from ten up to 4 billion. The scalability of PIRK's parallel implementations is found to be highly favorable.