Sparse Polynomial Zonotopes: A Novel Set Representation for Reachability Analysis
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Abstract (arXiv)
We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models. Operations like Minkowski sum, quadratic mapping, and reduction of the representation size can be computed with polynomial complexity w.r.t. the dimension of the system. In particular, for reachability analysis of nonlinear systems, the wrapping effect is substantially reduced using sparse polynomial zonotopes, as demonstrated by numerical examples. In addition, we can significantly reduce the computation time compared to zonotopes when dealing with nonlinear dynamics.
Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Jan 2019.
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Citing papers per year: 2021: 3; 2022: 3; 2023: 1; 2024: 3; 2025: 0; 2026: 4.
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- 2021Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopescited by 26
- 2022Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopescited by 24
- 2022Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopescited by 23
- 2021Data-Driven Reachability Analysis from Noisy Datacited by 14
- 2024Formal Verification of Graph Convolutional Networks with Uncertain Node Features and Uncertain Graph Structurecited by 8
- 2023Fully Automatic Neural Network Reduction for Formal Verificationcited by 6
- 2024RAIL: Reachability-Aided Imitation Learning for Safe Policy Executioncited by 5
- 2021Robust Data-Driven Predictive Control using Reachability Analysiscited by 3
- 2026The FABRIC Strategy for Verifying Neural Feedback Systemscited by 1
- 2022Towards Global Neural Network Abstractions with Locally-Exact Reconstructioncited by 0
- 2024Learning from Uncertain Data: From Possible Worlds to Possible Modelscited by 0
- 2026Perception with Guarantees: Certified Pose Estimation via Reachability Analysiscited by 0
- 2026Safe Multi-Robot Coordination via VLM-LLM Reasoning and Reachability Analysis18 Aug 2026
- 2026Formally Verifying Analog Neural Networks Under Process Variations Using Polynomial Zonotopes11 May 2026
- 2026The FABRIC Strategy for Verifying Neural Feedback Systems9 Mar 2026
- 2026Perception with Guarantees: Certified Pose Estimation via Reachability Analysis10 Feb 2026
- 2024RAIL: Reachability-Aided Imitation Learning for Safe Policy Execution28 Sep 2024
- 2024Learning from Uncertain Data: From Possible Worlds to Possible Models28 May 2024
- 2024Formal Verification of Graph Convolutional Networks with Uncertain Node Features and Uncertain Graph Structure23 Apr 2024
- 2023Fully Automatic Neural Network Reduction for Formal Verification3 May 2023
- 2022Towards Global Neural Network Abstractions with Locally-Exact Reconstruction21 Oct 2022
- 2022Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopes19 Oct 2022
- 2022Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopes6 Jul 2022
- 2021Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopes16 Dec 2021
2 more
- 2021Data-Driven Reachability Analysis from Noisy Data15 May 2021
- 2021Robust Data-Driven Predictive Control using Reachability Analysis25 Mar 2021
- 2021Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopescited by 26
- 2022Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopescited by 24
- 2022Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopescited by 23
- 2021Data-Driven Reachability Analysis from Noisy Datacited by 14
- 2024Formal Verification of Graph Convolutional Networks with Uncertain Node Features and Uncertain Graph Structurecited by 8
- 2023Fully Automatic Neural Network Reduction for Formal Verificationcited by 6
- 2021Robust Data-Driven Predictive Control using Reachability Analysiscited by 3
- 2026The FABRIC Strategy for Verifying Neural Feedback Systemscited by 1
- 2022Towards Global Neural Network Abstractions with Locally-Exact Reconstructioncited by 0
- 2024Learning from Uncertain Data: From Possible Worlds to Possible Modelscited by 0
- 2026Perception with Guarantees: Certified Pose Estimation via Reachability Analysiscited by 0
- 2026Formally Verifying Analog Neural Networks Under Process Variations Using Polynomial Zonotopescited by 0
12 most cited of 13 All 13 (JSON)
- 2026Safe Multi-Robot Coordination via VLM-LLM Reasoning and Reachability Analysis18 Aug 2026
- 2026Formally Verifying Analog Neural Networks Under Process Variations Using Polynomial Zonotopes11 May 2026
- 2026The FABRIC Strategy for Verifying Neural Feedback Systems9 Mar 2026
- 2026Perception with Guarantees: Certified Pose Estimation via Reachability Analysis10 Feb 2026
- 2024Learning from Uncertain Data: From Possible Worlds to Possible Models28 May 2024
- 2024Formal Verification of Graph Convolutional Networks with Uncertain Node Features and Uncertain Graph Structure23 Apr 2024
- 2023Fully Automatic Neural Network Reduction for Formal Verification3 May 2023
- 2022Towards Global Neural Network Abstractions with Locally-Exact Reconstruction21 Oct 2022
- 2022Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopes19 Oct 2022
- 2022Open- and Closed-Loop Neural Network Verification using Polynomial Zonotopes6 Jul 2022
- 2021Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopes16 Dec 2021
- 2021Data-Driven Reachability Analysis from Noisy Data15 May 2021
12 newest of 13 All 13 (JSON)