{"ID":2826452,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.18548","arxiv_id":"2512.18548","title":"An adaptive adjoint-oriented neural network for solving parametric optimal control problems with singularities","abstract":"In this work, we present an adaptive adjoint-oriented neural network (adaptive AONN) for solving parametric optimal control problems governed by partial differential equations. The proposed method integrates deep adaptive sampling techniques with the adjoint-oriented neural network (AONN) framework. It alleviates the limitations of AONN in handling low-regularity solutions and enhances the generalizability of deep adaptive sampling for surrogate modeling without labeled data ($\\text{DAS}^2$). The effectiveness of the adaptive AONN is demonstrated through numerical examples involving singularities.","short_abstract":"In this work, we present an adaptive adjoint-oriented neural network (adaptive AONN) for solving parametric optimal control problems governed by partial differential equations. The proposed method integrates deep adaptive sampling techniques with the adjoint-oriented neural network (AONN) framework. It alleviates the l...","url_abs":"https://arxiv.org/abs/2512.18548","url_pdf":"https://arxiv.org/pdf/2512.18548v1","authors":"[\"Zikang Yuan\",\"Guanjie Wang\",\"Qifeng Liao\"]","published":"2025-12-21T00:21:04Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}