{"ID":2868788,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.15889","arxiv_id":"2509.15889","title":"An optimal-control framework for reaction diffusion systems with application to synthetic developmental biology","abstract":"Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of optimal control for a class of coupled reaction-diffusion systems. The couplings are justified by the shared regulatory mechanisms encountered in synthetic biology. Furthermore, we introduce inputs and polynomial input-gain functions to guarantee well-posedness of the control system while maintaining biological relevance. As a result, we formulate an optimal control problem and derive necessary optimality conditions. We demonstrate our framework on an instance of such equations modeling the Nodal-Lefty interactions in mammalian cells. Numerical simulations showcase the effectiveness in directing pattern towards diverse targeted ones.","short_abstract":"Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of optimal control for a class of coupled reaction-diffusion systems. The couplings are...","url_abs":"https://arxiv.org/abs/2509.15889","url_pdf":"https://arxiv.org/pdf/2509.15889v2","authors":"[\"Mohamed Amine Ouchdiri\",\"Hamza Faquir\",\"Saad Benjelloun\",\"Mohamed Adlene Maghenem\",\"Irene Otero-Muras\",\"Adnane Saoud\"]","published":"2025-09-19T11:36:02Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[\"Diffusion Model\",\"Generative Adversarial Network\"]","has_code":false}