Volume 28, 2022
|Number of page(s)||44|
|Published online||11 January 2022|
Institute for Mathematics, Humboldt-Universität zu Berlin,
Unter den Linden 6,
2 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.
*** Corresponding author: email@example.com
Accepted: 9 November 2021
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through data-driven techniques are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components. For a rather general context, an error analysis is provided, and particular properties resulting from artificial neural network based approximations are addressed. Moreover, for each of the two inspiring applications analytical details are presented and numerical results are provided.
Mathematics Subject Classification: 49M15 / 65J15 / 65J20 / 65K10 / 90C30 / 35J61 / 68T07
Key words: Optimal control / semilinear PDEs / integrated physics-based imaging / learning-informed model / artificial neural network / quantitative MRI / semi-smooth Newton SQP algorithm
This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy – The Berlin Mathematics Research Center MATH+ (EXC-2046/1, project ID: 390685689). The work of MH is partially supported by the DFG SPP 1962, project-145r. The work of GD is partially supported by an NSFC grant (No. 12001194).
© The authors. Published by EDP Sciences, SMAI 2022
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