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JuliaReach

Sergiy Bogomolov, Marcelo Forets, Goran Frehse, Kostiantyn Potomkin, Christian Schilling
2019 Proceedings of the 22nd ACM International Conference on Hybrid Systems Computation and Control - HSCC '19  
We present JuliaReach, a toolbox for set-based reachability analysis of dynamical systems.  ...  JuliaReach consists of two main packages: Reachability, containing implementations of reachability algorithms for continuous and hybrid systems, and LazySets, a standalone library that implements state-of-the-art  ...  ACKNOWLEDGMENTS This work was partially supported by the Air Force Office of Scientific Research under award number FA2386-17-1-4065, by the ARC project DP140104219 (Robust AI Planning for Hybrid Systems  ... 
doi:10.1145/3302504.3311804 dblp:conf/hybrid/BogomolovFFPS19 fatcat:iutewqbt5jhxvb6fl7etwdvseq

ARCH-COMP20 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics

Luca Geretti, Julien Alexandre Dit Sandretto, Matthias Althoff, Luis Benet, Alexandre Chapoutot, Xin Chen, Pieter Collins, Marcelo Forets, Daniel Freire, Fabian Immler, Niklas Kochdumper, David P. Sanders (+1 others)
2020 International Workshop on Applied Verification of Continuous and Hybrid Systems  
We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics.  ...  This year, 6 tools Ariadne, CORA, DynIbex, Flow*, Isabelle/HOL, and JuliaReach (in alphabetic order) participated.  ...  Settings for JuliaReach.  ... 
doi:10.29007/zkf6 dblp:conf/arch/GerettiSABCCCFF20 fatcat:x6h55rud3rcxbjrq6ivkr4d32i

Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopes [article]

Christian Schilling, Marcelo Forets, Sebastian Guadalupe
2022 arXiv   pre-print
We present an algorithm to chain approaches based on Taylor models and zonotopes, yielding a precise reachability algorithm for NNCS.  ...  We study the verification problem for closed-loop dynamical systems with neural-network controllers (NNCS). This problem is commonly reduced to computing the set of reachable states.  ...  Acknowledgments We thank Luis Benet for fruitful discussions about the Taylor-model implementation. We also thank the anonymous reviewers at AAAI 2022 for their feedback.  ... 
arXiv:2112.09197v2 fatcat:n5syezrt2zfw7pagquarvz7hj4

Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopes

Christian Schilling, Marcelo Forets, Sebastián Guadalupe
2022 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
We present an algorithm to chain approaches based on Taylor models and zonotopes, yielding a precise reachability algorithm for NNCS.  ...  We study the verification problem for closed-loop dynamical systems with neural-network controllers (NNCS). This problem is commonly reduced to computing the set of reachable states.  ...  Acknowledgments We thank Luis Benet for fruitful discussions about the Taylor-model implementation. We also thank the anonymous reviewers for their feedback.  ... 
doi:10.1609/aaai.v36i7.20790 fatcat:fu6z5vdqsbfknadukcjes33wjy

LazySets.jl: Scalable Symbolic-Numeric Set Computations [article]

Marcelo Forets, Christian Schilling
2021 arXiv   pre-print
LazySets is the core library of JuliaReach, a cutting-edge software addressing the fundamental problem of reachability analysis: computing the set of states that are reachable by a dynamical system from  ...  LazySets provides methods to apply common set operations, convert between different set representations, and efficiently compute with sets in high dimensions using specialized algorithms based on the set  ...  Finally, we thank the people behind Julia Seasons of Contributions and Google Summer of Code programs for their financial support of several students to further develop LazySets.  ... 
arXiv:2110.01711v1 fatcat:g6grvdiayrg3hefym5cfl3wuaa

Reachability analysis of linear hybrid systems via block decomposition [article]

Sergiy Bogomolov, Marcelo Forets, Goran Frehse, Kostiantyn Potomkin, Christian Schilling
2020 arXiv   pre-print
Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems.  ...  In particular, we improve the continuous-post operator by performing computations in high-dimensional state space only for time intervals relevant for the subsequent application of the discrete-post operator  ...  We implemented the algorithm in JuliaReach, a toolbox for reachability analysis [3] , [4] , and we evaluate the algorithm on several benchmark problems, including a 1024-dimensional hybrid system (cf  ... 
arXiv:1905.02458v3 fatcat:yvcr72wkabg5vbhmkjqvsfq2mm

LazySets.jl: Scalable Symbolic-Numeric Set Computations$^*$

2021 JuliaCon Proceedings  
LazySets is the core library of JuliaReach, a cutting-edge software addressing the fundamental problem of reachability analysis: computing the set of states that are reachable by a dynamical system from  ...  LazySets provides methods to apply common set operations, convert between different set representations, and efficiently compute with sets in high dimensions using specialized algorithms based on the set  ...  Finally, we greatly appreciate Benoît Legat and Guillaume Dalle for their work in revising this paper.  ... 
doi:10.21105/jcon.00097 fatcat:ezb5jf5dt5gqlbbno5yh2wucru

Learning Provably Robust Motion Planners Using Funnel Libraries [article]

Ali Ekin Gurgen, Anirudha Majumdar, Sushant Veer
2021 arXiv   pre-print
First, we curate a library of motion primitives where the robustness of each primitive is characterized by an over-approximation of the forward reachable set, i.e., a "funnel".  ...  within an admissible set.  ...  We perform offline reachability analysis computations using the JuliaReach toolbox [51] to generate the funnels around the nominal motion primitive trajectories (Fig. 5(a) ).  ... 
arXiv:2111.08733v1 fatcat:ars47f5afja5ronc2lpfxeizna

Formal Certification Methods for Automated Vehicle Safety Assessment [article]

Tong Zhao, Ekim Yurtsever, Joel Paulson, Giorgio Rizzoni
2022 arXiv   pre-print
We also propose a unified scenario coverage framework that can provide either a formal or sample-based estimate of safety verification for full AVs.  ...  A majority of approaches used in providing safety guarantees for AV motion control originate from formal methods, especially reachability analysis (RA), which relies on mathematical models for the dynamic  ...  He focuses “Juliareach: a toolbox for set-based reachability,” in Proceedings of the on the development of optimization, machine learning, and multi-scale 22nd ACM International Conference  ... 
arXiv:2202.02818v2 fatcat:spgyrglbwjhshl2n43kyx722fa

Interval-Based Simulation of Zélus IVPs using DynIbex

Jason Brown, François Pessaux
2020 Acta Cybernetica  
Interval-based guaranteed integration methods provide a solution to this problem.  ...  This makes it necessary to run multiple simulations to check that the system fulfills particular requirements (safety for instance) for all the values in the uncertainty ranges.  ...  Julia library performing set-based reachability analysis on both linear and non-linear systems.  ... 
doi:10.14232/actacyb.285246 fatcat:jgcg37pkaffgvhlluoqr626vse

ARCH-COMP21 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics

Luca Geretti, Julien Alexandre Dit Sandretto, Matthias Althoff, Luis Benet, Alexandre Chapoutot, Pieter Collins, Parasara Sridhar Duggirala, Marcelo Forets, Edward Kim, Uziel Linares, David P. Sanders, Christian Schilling (+1 others)
unpublished
We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics.  ...  This year, 5 tools Ariadne, CORA, DynIbex, JuliaReach and Kaa (in alphabetic order) participated.  ...  JuliaReach: a toolbox for set-based reachability. In HSCC, 2019. doi:10.1145/3302504.3311804. [18] N. Chan and S. Mitra. Verifying safety of an autonomous spacecraft rendezvous mission.  ... 
doi:10.29007/2jw8 fatcat:xlmbgk46qzc2vd2m4j6hcbqbke

ARCH-COMP19 Category Report: Continuous and Hybrid Systems with Nonlinear Dynamics

Fabian Immler, Matthias Althoff, Luis Benet, Alexandre Chapoutot, Xin Chen, Marcelo Forets, Luca Geretti, Niklas Kochdumper, David P. Sanders, Christian Schilling
unpublished
We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics.  ...  In this year, 6 tools Ariadne, CORA, DynIbex, Flow*, Isabelle/HOL, and JuliaReach (in alphabetic order) participated.  ...  JuliaReach. (Marcelo Forets, Christian Schilling, David P. Sanders, Luis Benet) Ju-liaReach [15] is a toolbox for reachability computations of dynamical systems, available at http://juliareach.org.  ... 
doi:10.29007/m75b fatcat:qkyvij4hbrhtxnicg34d3td4ny

ARCH-COMP21 Category Report: Artificial Intelligence and Neural Network Control Systems (AINNCS) for Continuous and Hybrid Systems Plants

Taylor T. Johnson, Diego Manzanas Lopez, Luis Benet, Marcelo Forets, Sebastián Guadalupe, Christian Schilling, Radoslav Ivanov, Taylor J. Carpenter, James Weimer, Insup Lee
unpublished
JuliaReach is a new participant in this category, Verisig participated previously in 2019 and NNV has participated in all previous competitions.  ...  This report is a snapshot of the current landscape of tools and the types of benchmarks for which these tools are suited.  ...  Reachable sets are shown for those methods that are able to construct them. JuliaReach This subsection presents the results of JuliaReach.  ... 
doi:10.29007/kfk9 fatcat:bpr7k4nv5vcv5ngmniq32tjx24

Algorithms for Verifying Deep Neural Networks [article]

Changliu Liu, Tomer Arnon, Christopher Lazarus, Clark Barrett, Mykel J. Kochenderfer
2020 arXiv   pre-print
In addition, we provide pedagogical implementations of existing methods and compare them on a set of benchmark problems.  ...  This article surveys methods that have emerged recently for soundly verifying such properties. These methods borrow insights from reachability analysis, optimization, and search.  ...  implementation; and Amelia Hardy and Zongzhang Zhang for their comments.  ... 
arXiv:1903.06758v2 fatcat:25pqxtxpfzfz7phnnsx53q3j5y

ARCH-COMP18 Category Report: Continuous and Hybrid Systems with Linear Continuous Dynamics

Matthias Althoff, Stanley Bak, Xin Chen, Chuchu Fan, Marcelo Forets, Goran Frehse, Niklas Kochdumper, Yangge Li, Sayan Mitra, Rajarshi Ray, Christian Schilling, Stefan Schupp
unpublished
, Hylaa-Continuous, JuliaReach, SpaceEx, and XSpeed.  ...  This report is a snapshot of the current landscape of tools and the types of benchmarks they are particularly suited for.  ...  JuliaReach JuliaReach is a software framework for reachability computations of dynamical systems, available at http://juliareach.org.  ... 
doi:10.29007/73mb fatcat:tb5j6xp6wzhebh5dm6kumiash4
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