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

Althoff, Matthias; Bak, Stanley; Forets, Marcelo; Frehse, Goran; Kochdumper, Niklas; Ray, Rajarshi; Schilling, Christian; Schupp, Stefan

doi:10.29007/bj1w

Cited by 7 publications

(7 citation statements)

References 24 publications

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“…We believe that this is an important enough subclass of neural networks that the results are still meaningful. Once the neural network verification community is more mature, we expect a standard input format and a set of categorized benchmarks will arise, similar to what has happened in the SMT [2], software verification [3], and hybrid systems [1] communities.…”

Section: Discussionmentioning

confidence: 99%

Improved Geometric Path Enumeration for Verifying ReLU Neural Networks

Bak

Tran

Hobbs

et al. 2020

Lecture Notes in Computer Science

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Neural networks provide quick approximations to complex functions, and have been increasingly used in perception as well as control tasks. For use in mission-critical and safety-critical applications, however, it is important to be able to analyze what a neural network can and cannot do. For feed-forward neural networks with ReLU activation functions, although exact analysis is NP-complete, recently-proposed verification methods can sometimes succeed. The main practical problem with neural network verification is excessive analysis runtime. Even on small networks, tools that are theoretically complete can sometimes run for days without producing a result. In this paper, we work to address the runtime problem by improving upon a recently-proposed geometric path enumeration method. Through a series of optimizations, several of which are new algorithmic improvements, we demonstrate significant speed improvement of exact analysis on the well-studied ACAS Xu benchmarks, sometimes hundreds of times faster than the original implementation. On more difficult benchmark instances, our optimized approach is often the fastest, even outperforming inexact methods that leverage overapproximation and refinement.

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Section: Discussionmentioning

confidence: 99%

Improved Geometric Path Enumeration for Verifying ReLU Neural Networks

Bak

Tran

Hobbs

et al. 2020

Lecture Notes in Computer Science

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“…In numerous applications it is critical to formally verify that all solutions of the system (1) always avoid certain predefined unsafe regions; see, e.g. [4,Sect. 3] and the references given therein.…”

Section: Introductionmentioning

confidence: 99%

Overapproximating Reachable Tubes of Linear Time-Varying Systems

Serry

Reißig

2022

IEEE Trans. Automat. Contr.

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We present a method to over-approximate reachable tubes over compact time-intervals, for linear continuous-time, time-varying control systems whose initial states and inputs are subject to compact convex uncertainty. The method uses numerical approximations of transition matrices, is convergent of first order, and assumes the ability to compute with compact convex sets in finite dimension. We also present a variant that applies to the case of zonotopic uncertainties, uses only linear algebraic operations, and yields zonotopic over-approximations. The performance of the latter variant is demonstrated on an example.

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“…The model describes a closed-loop system comprising a plant model as well as a controller and is representative for challenges in automotive systems. The original Simulink model has been simplified for usage in various analysis tools 10 . Here, we consider a linearized version with parameters.…”

Section: Resultsmentioning

confidence: 99%

“…For the 2020 edition, we have decided to keep all benchmarks from our 2019 friendly competition [10] and have added two further benchmarks: a high-dimensional heat transfer problem and an electro-mechanical braking system subject to many discrete transitions.…”

Section: Verification Of Benchmarksmentioning

confidence: 99%

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

Althoff¹,

Bak²,

Bao³

et al.

EPiC Series in Computing

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We present the results of the ARCH1 2020 friendly competition for formal verification of continuous and hybrid systems with linear continuous dynamics. In its fourth edition, eight tools have been applied to solve eight different benchmark problems in the category for linear continuous dynamics (in alphabetical order): CORA, C2E2, HyDRA, Hylaa, 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. Due to the diversity of problems, we are not ranking tools, yet the presented results provide one of the most complete assessments of tools for the safety verification of continuous and hybrid systems with linear continuous dynamics up to this date.

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

Cited by 7 publications

References 24 publications

Improved Geometric Path Enumeration for Verifying ReLU Neural Networks

Improved Geometric Path Enumeration for Verifying ReLU Neural Networks

Overapproximating Reachable Tubes of Linear Time-Varying Systems

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

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