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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2510.11325 |
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| _version_ | 1866916026596196352 |
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| author | Ma, Lingling Zhang, Jingyi Li, Qiuqi |
| author_facet | Ma, Lingling Zhang, Jingyi Li, Qiuqi |
| contents | This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and stochastic PDE constraints, and an L2-optimal reduced-order model is constructed to directly approximate the parameter-to-output mapping. The model is obtained by minimizing the L2 norm of the output error via gradient-based optimization, requiring only input-output data without access to the full-order system matrices or state variables. To efficiently generate high-fidelity training data for multiscale problems, the Generalized Multiscale Finite Element Method (GMsFEM) is employed as an offline solver. The proposed framework ensures accuracy in control-relevant outputs while maintaining computational complexity independent of the original PDE dimension, making it suitable for real-time applications. Numerical experiments on stochastic diffusion and advection-diffusion equations demonstrate the accuracy, efficiency, and robustness of the method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11325 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A model reduction method based on nonlinear optimization for multiscale stochastic optimal control problems Ma, Lingling Zhang, Jingyi Li, Qiuqi Optimization and Control This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and stochastic PDE constraints, and an L2-optimal reduced-order model is constructed to directly approximate the parameter-to-output mapping. The model is obtained by minimizing the L2 norm of the output error via gradient-based optimization, requiring only input-output data without access to the full-order system matrices or state variables. To efficiently generate high-fidelity training data for multiscale problems, the Generalized Multiscale Finite Element Method (GMsFEM) is employed as an offline solver. The proposed framework ensures accuracy in control-relevant outputs while maintaining computational complexity independent of the original PDE dimension, making it suitable for real-time applications. Numerical experiments on stochastic diffusion and advection-diffusion equations demonstrate the accuracy, efficiency, and robustness of the method. |
| title | A model reduction method based on nonlinear optimization for multiscale stochastic optimal control problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2510.11325 |