| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 3 | |
| Number of page(s) | 44 | |
| DOI | https://doi.org/10.1051/cocv/2021100 | |
| Published online | 11 January 2022 | |
Optimization with learning-informed differential equation constraints and its applications★,★★
1
Institute for Mathematics, Humboldt-Universität zu Berlin,
Unter den Linden 6,
10099
Berlin, Germany.
2
Weierstrass Institute for Applied Analysis and Stochastics,
Mohrenstrasse 39,
10117
Berlin, Germany.
*** Corresponding author: michael.hintermueller@wias-berlin.de
Received:
26
November
2020
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
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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