{"ID":2856316,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.11325","arxiv_id":"2510.11325","title":"A model reduction method based on nonlinear optimization for multiscale stochastic optimal control problems","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2510.11325","url_pdf":"https://arxiv.org/pdf/2510.11325v2","authors":"[\"Lingling Ma\",\"Jingyi Zhang\",\"Qiuqi Li\"]","published":"2025-10-13T12:22:01Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[\"Diffusion Model\"]","has_code":false}