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

Abstract

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 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.

Verse: A Python Library for Reasoning About Multi-agent Hybrid System Scenarios

“…Automatic hybrid verification tools typically require the input model to be written in a tool-specific language [10,[13][14][15]17,25]. Libraries like JuliaReach [7] Hylaa [5] and HyPro [8] share our motivation to reduce the usability barrier by providing reachability analysis APIs for popular programming languages.…”

“…Despite the potentially large user base, currently this technology is inaccessible without formal methods training. Automatic hybrid verification tools [10,13,17,25,31] require the input model to be written in a tool-specific language. Tools like C2E2 [15] attempt to translate models from Simulink/Stateflow, but the language-barrier goes down to the underlying math models.…”

On the Verification of Neural ODEs with Stochastic Guarantees

“…Whenever the initial set B 0 is known from the context, we simply refer to the reachset as the Reachset at time t j , or B j . (Kapela et al 2020) yes no Lohner algorithm yes Flow-star (Chen et al 2013) yes no Taylor models yes δ-reachability (Gao et al 2013) yes no approximate satisfiability yes C2E2 (Duggirala et al 2015) yes no discrepancy function yes LDFM (Fan et al 2017) yes yes simulation, matrix measures no TIRA (Meyer et al 2019) yes yes second-order sensitivity no Isabelle/HOL (Immler 2015) yes no proof-assistant yes Breach (Donzé et al 2007) yes yes simulation, sensitivity no PIRK (Devonport et al 2020) yes yes simulation, contraction bounds no HR (Li et al 2020) yes no hybridization yes ProbReach (Shmarov et al 2015a) no no δ-reachability, probability interval yes VSPODE (Enszer et al 2011) no no p-boxes yes GP (Bortolussi et al 2014) no no Gaussian process no SLR Ours no yes stochastic Lagrangian reachability no…”

On The Verification of Neural ODEs with Stochastic Guarantees

“…Formally: Definition 2. Given a set of initial states B 0 at time t 0 , and a time horizon T , we use B(B 0 , T ) to denote (Chen, Ábrahám, and Sankaranarayanan 2013) yes no Taylor models yes δ-reachability (Gao, Kong, and Clarke 2013) yes no approximate satisfiability yes C2E2 (Duggirala et al 2015) yes no discrepancy function yes LDFM (Fan et al 2017) yes yes simulation, matrix measures no TIRA (Meyer, Devonport, and Arcak 2019) yes yes second-order sensitivity no Isabelle/HOL (Immler 2015) yes no proof-assistant yes Breach (Donzé 2010;Donzé and Maler 2007) yes yes simulation, sensitivity no PIRK (Devonport et al 2020) yes yes simulation, contraction bounds no HR (Li, Bak, and Bogomolov 2020) yes no hybridization yes ProbReach (Shmarov and Zuliani 2015a) no no δ-reachability, probability interval yes VSPODE (Enszer and Stadtherr 2011) no no p-boxes yes GP (Bortolussi and Sanguinetti 2014) no no Gaussian process no SLR Ours no yes stochastic Lagrangian reachability no…”