@article {42756,
	title = {Investigating molecular transport in the human brain from MRI with physics-informed neural networks},
	journal = {Scientific Reports},
	volume = {12},
	year = {2022},
	month = {Jan-12-2022},
	pages = {15475},
	publisher = {Springer Nature},
	doi = {10.1038/s41598-022-19157-w},
	url = {https://www.nature.com/articles/s41598-022-19157-w},
	author = {Zapf, Bastian and Haubner, Johannes and Kuchta, Miroslav and Ringstad, Geir and Per Kristian {Eide} and Mardal, Kent-Andre}
}
@article {28237,
	title = {A Continuous Perspective on Shape Optimization via Domain Transformations},
	journal = {SIAM Journal of Scientific Computing},
	volume = {43},
	year = {2021},
	pages = {A1997{\textendash}A2018},
	publisher = {Society for Industrial and Applied Mathematics},
	abstract = {In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes, a reference domain is introduced, and it is optimized over a set of admissible transformations. The focus is on the choice of the set of transformations, which we motivate from a continuous perspective. In order to guarantee local injectivity of the admissible transformations, we enrich the optimization problem by a nonlinear constraint. Numerical results for drag minimization of Stokes flow are presented.},
	doi = {10.1137/20M1332050},
	author = {Haubner, Johannes and Siebenborn, Martin and Ulbrich, Michael}
}
@article {28236,
	title = {Topology optimization of Stokes flow via density based approaches},
	journal = {SIAM Journal on Scientific Computing},
	year = {2021},
	publisher = {Society for Industrial and Applied Mathematics},
	abstract = {A new method for performing density-based topology optimization for Stokes flow is presented. It differs from previous approaches in the way the underlying mixed integer problem is relaxed. We extend\&nbsp;the\&nbsp;existing theory for the generalized Stokes equations, which allows us to choose BV or fractional order Sobolev spaces for the density. We investigate the arising optimization problems concerning existence of solutions, differentiability, and convergence of relaxed solutions towards solutions of the original problem. We motivate a localized fractional order Sobolev norm as an approximation of the\&nbsp;BV\&nbsp;-norm for\&nbsp;{\textpm}1-valued functions and discuss its discretization for piecewise constant finite elements. Building on these theoretical findings, we present our numerical realization and show computational results.},
	author = {Haubner, Johannes and Neumann, Franziska and Ulbrich, Michael}
}
@article {28235,
	title = {Analysis of shape optimization problems for unsteady fluid-structure interaction},
	journal = {Inverse Problems},
	volume = {36},
	number = {3},
	year = {2020},
	month = {02/2020},
	pages = {034001},
	publisher = {IOP Publishing},
	abstract = {Shape optimization via the method of mappings is investigated for unsteady fluid-structure interaction (FSI) problems that couple the Navier{\textendash}Stokes equations and the Lam{\'e} system. Building on recent existence and regularity theory we prove Fr{\'e}chet differentiability results for the state with respect to domain variations. These results form an analytical foundation for optimization und inverse problems governed by FSI systems. Our analysis develops a general framework for deriving local-in-time continuity and differentiability results for parameter dependent nonlinear systems of partial differential equations. The main part of the paper is devoted to conducting this analysis for the FSI problem, transformed to a shape reference domain. The underlying shape transformation{\textemdash}actually we work with the corresponding shape displacement instead{\textemdash}represents the shape and the main result proves the Fr{\'e}chet differentiability of the solution of the FSI system with respect to the shape transformation.},
	doi = {10.1088/1361-6420/ab5a11},
	author = {Haubner, Johannes and Ulbrich, Michael and Ulbrich, Stefan}
}
@phdthesis {28238,
	title = {Shape Optimization for Fluid-Structure Interaction},
	year = {2020},
	abstract = {In this thesis, shape optimization for unsteady fluid-structure interaction problems via the method of mappings is investigated theoretically and numerically. New existence and regularity results are proven. A framework for deriving differentiability for the solution of nonlinear, unsteady, parameter-dependent partial differential equations is developed and applied to show differentiability of the states with respect to domain variations.},
	url = {https://mediatum.ub.tum.de/doc/1520895/file.pdf},
	author = {Haubner, Johannes}
}
@article {haubner2022learning,
	title = {Learning a Mesh Motion Technique with Application to Fluid-Structure Interaction and Shape Optimization},
	journal = {arXiv preprint arXiv:2206.02217},
	publisher = {Arxiv},
	author = {Haubner, Johannes and Kuchta, Miroslav}
}
