Optimization with learning-informed differential equation constraints and its applications

• URL: http://arxiv.org/abs/2008.10893v1
• Date: Tue, 25 Aug 2020 09:05:55 GMT
• Title: Optimization with learning-informed differential equation constraints and its applications
• Authors: Guozhi Dong, Michael Hintermueller and Kostas Papafitsoros
• Abstract summary: Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems are studied. A particular focus is on the analysis and on numerical methods for problems with machine-learned components.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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