Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.11325 |
| Tags: |
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Sommario:
- 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.