Mannix, P.M., Skene, C.S. orcid.org/0000-0003-0994-2013, Auroux, D. et al. (1 more author) (2024) A robust, discrete-gradient descent procedure for optimisation with time-dependent PDE and norm constraints. The SMAI Journal of computational mathematics, 10. pp. 1-28. ISSN 2426-8399
Abstract
Many physical questions in fluid dynamics can be recast in terms of norm constrained optimisation problems; which in-turn, can be further recast as unconstrained problems on spherical manifolds. Due to the nonlinearities of the governing PDEs, and the computational cost of performing optimal control on such systems, improving the numerical convergence of the optimisation procedure is crucial. Borrowing tools from the optimisation on manifolds community we outline a numerically consistent, discrete formulation of the direct-adjoint looping method accompanied by gradient descent and line-search algorithms with global convergence guarantees. We numerically demonstrate the robustness of this formulation on three example problems of relevance in fluid dynamics and provide an accompanying library SphereManOpt.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The authors, 2024. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | optimal control, adjoint-based methods, optimisation on manifolds |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Funding Information: | Funder Grant number EU - European Union 786780 |
Depositing User: | Symplectic Publications |
Date Deposited: | 07 Feb 2024 14:34 |
Last Modified: | 09 Feb 2024 12:44 |
Status: | Published |
Publisher: | Société de Mathématiques Appliquées et Industrielles |
Identification Number: | 10.5802/smai-jcm.104 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:208799 |