Optimization with learning-informed differential equation constraints and its applications
Optimization and Control
2020-08-26 v1 Machine Learning
Numerical Analysis
Analysis of PDEs
Numerical Analysis
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.
Cite
@article{arxiv.2008.10893,
title = {Optimization with learning-informed differential equation constraints and its applications},
author = {Guozhi Dong and Michael Hintermueller and Kostas Papafitsoros},
journal= {arXiv preprint arXiv:2008.10893},
year = {2020}
}