Transformer-Accelerated Interpolated Data-Driven Reachability Analysis from Noisy Data
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866914440330346496 |
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| author | Zhang, Zhen Hafez, Ahmad Xie, Peng Huang, Yanliang Wu, Wenyuan Alanwar, Amr |
| author_facet | Zhang, Zhen Hafez, Ahmad Xie, Peng Huang, Yanliang Wu, Wenyuan Alanwar, Amr |
| contents | Data-driven reachability analysis provides guaranteed outer approximations of reachable sets from input-state measurements, yet each propagation step requires a matrix-zonotope multiplication whose cost grows with the horizon length, limiting scalability. We observe that data-driven propagation is inherently step-size sensitive, in the sense that set-valued operators at different discretization resolutions yield non-equivalent reachable sets at the same physical time, a property absent in model-based propagation. Exploiting this multi-resolution structure, we propose Interpolated Reachability Analysis (IRA), which computes a sparse chain of coarse anchor sets sequentially and reconstructs fine-resolution intermediate sets in parallel across coarse intervals. We derive a fully data-driven coarse-noise over-approximation that removes the need for continuous-time system knowledge, prove deterministic outer-approximation guarantees for all interpolated sets, and establish conditional tightness relative to the fine-resolution chain. To replace the remaining matrix-zonotope multiplications in the fine phase, we further develop Transformer-Accelerated IRA (TA-IRA), where an encoder-decoder Transformer is calibrated via split conformal prediction to provide finite-sample pointwise and path-wise coverage certificates. Numerical experiments on a five-dimensional linear system confirm the theoretical guarantees and demonstrate significant computational savings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02157 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transformer-Accelerated Interpolated Data-Driven Reachability Analysis from Noisy Data Zhang, Zhen Hafez, Ahmad Xie, Peng Huang, Yanliang Wu, Wenyuan Alanwar, Amr Systems and Control Data-driven reachability analysis provides guaranteed outer approximations of reachable sets from input-state measurements, yet each propagation step requires a matrix-zonotope multiplication whose cost grows with the horizon length, limiting scalability. We observe that data-driven propagation is inherently step-size sensitive, in the sense that set-valued operators at different discretization resolutions yield non-equivalent reachable sets at the same physical time, a property absent in model-based propagation. Exploiting this multi-resolution structure, we propose Interpolated Reachability Analysis (IRA), which computes a sparse chain of coarse anchor sets sequentially and reconstructs fine-resolution intermediate sets in parallel across coarse intervals. We derive a fully data-driven coarse-noise over-approximation that removes the need for continuous-time system knowledge, prove deterministic outer-approximation guarantees for all interpolated sets, and establish conditional tightness relative to the fine-resolution chain. To replace the remaining matrix-zonotope multiplications in the fine phase, we further develop Transformer-Accelerated IRA (TA-IRA), where an encoder-decoder Transformer is calibrated via split conformal prediction to provide finite-sample pointwise and path-wise coverage certificates. Numerical experiments on a five-dimensional linear system confirm the theoretical guarantees and demonstrate significant computational savings. |
| title | Transformer-Accelerated Interpolated Data-Driven Reachability Analysis from Noisy Data |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2604.02157 |