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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2512.19291 |
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| _version_ | 1866917163627970560 |
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| author | Romagnoli, Raffaele Kar, Soummya |
| author_facet | Romagnoli, Raffaele Kar, Soummya |
| contents | This paper investigates the stability properties of neural operators through the structured representation offered by the Hybrid B-spline Deep Neural Operator (HBDNO). While existing stability-aware architectures typically enforce restrictive constraints that limit universality, HBDNO preserves full expressive power by representing outputs via B-spline control points. We show that these control points form a natural observable for post-training stability analysis. By applying Dynamic Mode Decomposition and connecting the resulting discrete dynamics to the Koopman operator framework, we provide a principled approach to spectral characterization of learned operators. Numerical results demonstrate the ability to assess stability and reveal future directions for safety-critical applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19291 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability Analysis of a B-Spline Deep Neural Operator for Nonlinear Systems Romagnoli, Raffaele Kar, Soummya Systems and Control This paper investigates the stability properties of neural operators through the structured representation offered by the Hybrid B-spline Deep Neural Operator (HBDNO). While existing stability-aware architectures typically enforce restrictive constraints that limit universality, HBDNO preserves full expressive power by representing outputs via B-spline control points. We show that these control points form a natural observable for post-training stability analysis. By applying Dynamic Mode Decomposition and connecting the resulting discrete dynamics to the Koopman operator framework, we provide a principled approach to spectral characterization of learned operators. Numerical results demonstrate the ability to assess stability and reveal future directions for safety-critical applications. |
| title | Stability Analysis of a B-Spline Deep Neural Operator for Nonlinear Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2512.19291 |