Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866910091383406592 |
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| author | Huang, Yanliang Xie, Peng Wu, Wenyuan Zeng, Zhuoqi Alanwar, Amr |
| author_facet | Huang, Yanliang Xie, Peng Wu, Wenyuan Zeng, Zhuoqi Alanwar, Amr |
| contents | We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from trajectory data alone. The predicted reachable set takes the form of a sublevel set of a nonconformity score derived from the reconstruction error, with the threshold calibrated via the Learn Then Test procedure so that the probability of excluding a reachable state is bounded with high probability. Experiments on three nonlinear systems, a forced Duffing oscillator, a planar quadrotor, and a high-dimensional reaction-diffusion system, confirm that the empirical miss rate remains below the Probably Approximately Correct (PAC) bound while scaling to state dimensions beyond the reach of classical grid-based and polynomial methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00283 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees Huang, Yanliang Xie, Peng Wu, Wenyuan Zeng, Zhuoqi Alanwar, Amr Systems and Control Machine Learning We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from trajectory data alone. The predicted reachable set takes the form of a sublevel set of a nonconformity score derived from the reconstruction error, with the threshold calibrated via the Learn Then Test procedure so that the probability of excluding a reachable state is bounded with high probability. Experiments on three nonlinear systems, a forced Duffing oscillator, a planar quadrotor, and a high-dimensional reaction-diffusion system, confirm that the empirical miss rate remains below the Probably Approximately Correct (PAC) bound while scaling to state dimensions beyond the reach of classical grid-based and polynomial methods. |
| title | Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees |
| topic | Systems and Control Machine Learning |
| url | https://arxiv.org/abs/2604.00283 |