Towards a set-based IVP solver for ODEs on the GPU

Autor/innen

Ekaterina Auer
University of Applied Sciences Wismar
https://orcid.org/0000-0003-4059-3982
Lorenz Gillner
University of Applied Sciences Wismar
https://orcid.org/0009-0007-8244-5810
Julien Alexandre dit Sandretto
ENSTA, Institut Polytechnique de Paris
DOI: https://doi.org/10.17877/tudobooks-11.197

Über dieses Buch

Reachability analysis is a key component of (formal) verification techniques for cyber-physical systems subject to uncertainty, as it enables the computation of sets of states that the system can reach over time. However, such methods are often computationally expensive, making algorithmic and implementation-level optimizations essential. In this paper, we propose a verified interval-based ODE solver for reachability analysis, based on the classical fourth-order Runge–Kutta scheme and designed to execute entirely within a single GPU kernel. This enables efficient subdivision strategies to mitigate overestimation while supporting the parallel propagation of a large number of subboxes. Using the Van der Pol oscillator as a benchmark, we demonstrate the applicability of the proposed approach and compare its performance with non-verified GPU-based uncertainty propagation techniques derived from Müller-type theorems, as well as with the CPU-based reference tool DynIbex.

REC 2026 Reliability Computations in a Data and Model-Driven World

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REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World

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516-531

Veröffentlicht

21.08.2026
Copyright (c) 2026 Matthias Faes, Michael Beer, Julian Behrend, Marco Broccardo, Guohai Chen, Hanshu Chen, Jieyu Chen, Fang Cong, Henrik Ebel, Peter Eberhard, Andrea Franchini, Zhuojia Fu, Yanzhao Gu, Michael Hanss, Hui Huang, Md Maidul Islam, Jafar Jafari-Asl, Balsa Jovanovic, Tom Könecke, Olga Kosheleva, Vladik Kreinovich, Hao-Ming Li, Pei-Pei Li, Qinghe Li, Ruikun Li, Stefano Marelli, Rafi L. Muhanna, Robert L. Mullen, Chiara Nardin, Lukáš Novák, Shenghao Piao, Mario Rosenfelder, Styfen Schär, Jan Schneider, Wei Shi, Panagiotis Spyridis, Bruno Sudret, Ruben Van Coile, Bo-Yu Wang, Dixiong Yang, Xuan-Yi Zhang, Zi-Xin Zhang, Bo-Qi Zhao, Yan-Gang Zhao, Zhibao Zheng, Baihong Zhong, Zhaowei Zhou, Marcos A. Valdebenito, Chao Dang, Lan-Xin Li, Marius Bittner, Parth Tambat, Marco Behrendt, Zhao Liu, Ping Zhu, Zlatan Dimitrov, Petar O. Hristov, Meng-Ze Lyu, Yang-Yi Liu, Jian-Bing Chen, Qitian Lu, Miroslav Vořechovský, Ekaterina Auer, Lorenz Gillner, Julien Alexandre dit Sandretto, Binod K. Yadav, Ghifari Adam Faza, Hans Hallez, David Moens, Reza Naeimaei, Steffen Schön, Elisabeth Ötsch, Hans Neuner, Zhanhua Liang, Jingwen Song, Michael Desch, Mehdi Modares, Valentin Nikolov, Paulo Lucas Figueiredo, José Torres Farinha, Hugo Raposo, António J. Marques Cardoso, Alice do Carmo Duarte Rodrigues, Paula Gonçalves, Peihan Chen, Xinyu Zhu, Pengfei Wei, Kaiwen Li, Mansoureh Shahabi, Y. F. Cui, Johannes O. Royset, Salvatore Russotto, Mario Di Paola, Antonina Pirrotta, Til Lux, Johannes Sundheim, Tania Feiri, Udo Wiens, Marcus Ricker, F. Niklas Schietzold, Felix Harazin, Yoshi Diepelt, Wolfgang Graf, Michael Kaliske, Rongyao Song, Changcong Zhou, Xuanyi Zhao, Weiping Zhang, Juntao Hu, Yu Chen, Edoardo Patelli, Tingting Sun, Jianbing Chen, Bouwe Verkens, L. Bogaerts, Patrick Van Rymenant, Maximilian Schweizer, Marc Fina, Werner Wagner, Steffen Freitag, George Stefanou, Dimitros Savvas, Panagiotis Gavalas, Luigi Schiano, Razhan S. Ahmed, Oleksandr Al-Shboul, David Ringeloth, Vladislav Gudžulić, Stefanie Schoen, Jelena Bijeljić, Ernst Niederleithinger, Iurie Curoşu, Gerrit E. Neu, Jia-Hui Fu, Yi Luo, De-Cheng Feng, Xiao-Qiu Ai, Luyi Li, Hao Wang, Tairan Wang, Sifeng Bi, Emily Zeller (Kapitelautor/in)

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Creative Commons License

Dieses Werk steht unter der Lizenz Creative Commons Namensnennung 4.0 International.

Zitationsvorschlag

Towards a set-based IVP solver for ODEs on the GPU. (2026). In REC 2026 - 11th International Workshop on Reliable Engineering Computing: Reliability Computations in a Data and Model-Driven World (pp. 516-531). TUDObooks. https://doi.org/10.17877/tudobooks-11.197