PIRK: Scalable Interval Reachability Analysis for High-Dimensional Nonlinear Systems Alex Devonport 1(B ) , Mahmoud Khaled 2 , Murat Arcak 1 , and Majid Zamani 3,4 1 University of California, Berkeley, Berkeley, CA, USA {alex devonport,arcak}@berkeley.edu 2 Technical University of Munich, Munich, Germany khaled.mahmoud@tum.de 3 University of Colorado, Boulder, Boulder, CO, USA majid.zamani@colorado.edu 4 Ludwig Maximilian University, Munich, Germany Abstract. Reachability analysis is a critical tool for the formal verifica- tion 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 implementa- tions, are not designed to leverage parallelism. They use algorithms that are designed to run serially within one compute unit and they can not uti- lize 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 can utilize HPC platforms for computing reachable sets for general high- dimensional non-linear systems. PIRK has been tested on several systems, with state dimensions up to 4 billion. The scalability of PIRK’s parallel implementations is found to be highly favorable. Keywords: Reachability analysis · ODE integration · Runge-Kutta method · Mixed monotonicity · Monte Carlo simulation · Parallel algorithms 1 Introduction Applications of safety-critical cyber-physical systems (CPS) are growing due to emerging IoT technologies and the increasing availability of efficient com- puting devices. These include smart buildings, traffic networks, autonomous vehicles, truck platooning, and drone swarms, which require reliable bug-free A. Devonport and M. Khaled—Contributed equally. c  The Author(s) 2020 S. K. Lahiri and C. Wang (Eds.): CAV 2020, LNCS 12224, pp. 556–568, 2020. https://doi.org/10.1007/978-3-030-53288-8_27