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Optimization with learning-informed differential equation constraints and its applications

Guozhi Dong(guozhi.dong***at***hu-berlin.de)
Michael Hintermueller(michael.hintermueller***at***wias-berlin.de)
Kostas Papafitsoros(kostas.papafitsoros***at***wias-berlin.de)

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.

Keywords: Artificial neural network; optimal control; semilinear PDEs; integrated physics-based imaging; learning-informed model; quantitative MRI; semi-smooth Newton SQP algorithm

Category 1: Infinite Dimensional Optimization

Category 2: Nonlinear Optimization

Category 3: Applications -- Science and Engineering (Biomedical Applications )

Citation: WIAS preprint: DOI 10.20347/WIAS.PREPRINT.2754, Weierstrass Institute, Mohrenstraße 39 10117 Berlin, Germnay, 2020

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Entry Submitted: 01/01/2021
Entry Accepted: 01/01/2021
Entry Last Modified: 01/01/2021

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