Veröffentlichungen

@article{0e15842ca5e14ca4ada25e4e4994e2c1,

title = "Isoperimetric conditions, lower semicontinuity, and existence results for perimeter functionals with measure data",

abstract = "We establish lower semicontinuity results for perimeter functionals with measure data on Rn and deduce the existence of minimizers to these functionals with Dirichlet boundary conditions, obstacles, or volume-constraints. In other words, we lay foundations of a perimeter-based variational approach to mean curvature measures on Rn capable of proving existence in various prescribed-mean-curvature problems with measure data. As crucial and essentially optimal assumption on the measure data we identify a new condition, called small-volume isoperimetric condition, which sharply captures cancellation effects and comes with surprisingly many properties and reformulations in itself. In particular, we show that the small-volume isoperimetric condition is satisfied for a wide class of (n−1)-dimensional measures, which are thus admissible in our theory. Our analysis includes infinite measures and semicontinuity results on very general domains. ",

author = "Thomas Schmidt",

year = "2025",

month = apr,

doi = "10.1007/s00208-024-03025-1",

language = "English",

volume = "391",

pages = "5729--5807",

journal = "Mathematische Annalen",

issn = "0025-5831",

publisher = "Springer New York",

number = "4",

@article{07914d02d5a34ebba61601f8af258a2e,

title = "A Trust‐Region Method for p‐Harmonic Shape Optimization",

abstract = "The appropriate scaling of deformation fields has a significant impact on the performance of shape optimization algorithms. We introduce a pointwise gradient constraint to an efficient algorithm for -Laplace problems, while the complexity of the algorithm remains polynomial. Using this algorithm, we compute descent directions for shape optimization using -harmonic approach that fulfill a trust-region type constraint. Numerical experiments show the advantages of deformations computed with this approach when compared to deformations that are scaled after computation. This considers, in particular, the approximation of the limit setting and the preservation of mesh quality during an optimization with a fixed step size.",

author = "Henrik Wyschka and Winnifried Wollner",

year = "2025",

month = feb,

day = "5",

doi = "10.1002/pamm.70000",

language = "English",

volume = "25",

journal = "Proceedings in applied mathematics and mechanics",

issn = "1617-7061",

publisher = "Wiley-VCH Verlag",

number = "1",

@article{d930fa6c1dc2435ab1ff03c10d10131e,

title = "Partial regularity for variational integrals with Morrey-H{\"o}lder zero-order terms, and the limit exponent in Massari{\textquoteright}s regularity theorem",

abstract = "We revisit the partial C1,α regularity theory for minimizers of non-parametric integrals with emphasis on sharp dependence of the H{\"o}lder exponent α on structural assumptions for general zero-order terms. A particular case of our conclusions carries over to the parametric setting of Massari{\textquoteright}s regularity theorem for prescribed-mean-curvature hypersurfaces and there confirms optimal regularity up to the limit exponent.",

author = "Thomas Schmidt and Sch{\"u}tt, {Jule Helena}",

year = "2025",

language = "English",

journal = "J. Lond. Math. Soc. (2)",

issn = "0024-6107",

publisher = "John Wiley and Sons Ltd",

@article{9c86c2706cce41e5a3c2d6f8d57dd758,

title = "Shape Optimization of Optical Microscale Inclusions",

abstract = "This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a nonmagnetic bulk dielectric. The shape optimization approach is based on a homogenization theory for time-harmonic Maxwell{\textquoteright}s equations that describes effective material parameters for the propagation of electromagnetic waves through the metamaterial. The control parameter of the optimization is a deformation field representing the deviation of the microscale geometry from a reference configuration of the cell problem. This allows for describing the homogenized effective permittivity tensor as a function of the deformation field. We show that the underlying deformed cell problem is well-posed and regular. This, in turn, proves that the shape optimization problem is well-posed. In addition, a numerical scheme is formulated that utilizes an adjoint formulation with either gradient descent or BFGS as optimization algorithms. The developed algorithm is tested numerically on a number of prototypical shape optimization problems with a prescribed effective permittivity tensor as the target.",

author = "Manaswinee Bezbaruah and Matthias Maier and Winnifried Wollner",

year = "2024",

month = aug,

day = "31",

doi = "10.1137/23M158262X",

language = "English",

volume = "46",

pages = "B377 -- B402",

journal = "SIAM Journal on Scientific Computing",

issn = "1064-8275",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "4",

@article{4118ee8b0a0940caaad7191abedafed6,

title = "Bathymetry reconstruction from experimental data using PDE-constrained optimisation",

abstract = "Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming, expensive and inaccurate. Therefore, many approaches have been proposed how to infer the bathymetry from measurements of surface waves. Mathematically, this is an inverse problem where an unknown system state needs to be reconstructed from observations with a suitable model for the flow as constraint. In many cases, the shallow water equations can be used to describe the flow. While theoretical studies of the efficacy of such a PDE-constrained optimisation approach for bathymetry reconstruction exist, there seem to be few publications that study its application to data obtained from real-world measurements. This paper shows that the approach can, at least qualitatively, reconstruct a Gaussian-shaped bathymetry in a wave flume from measurements of the free surface level at up to three points. Achieved normalised root mean square errors (NRMSE) are in line with other approaches.",

author = "J. Angel and J. Behrens and S. G{\"o}tschel and M. Hollm and D. Ruprecht and R. Seifried",

year = "2024",

month = jun,

day = "1",

doi = "10.1016/j.compfluid.2024.106321",

language = "English",

volume = "278",

journal = "Computers and Fluids",

issn = "0045-7930",

publisher = "Elsevier Ltd",

@article{f155640b4dbe43d98ef37e9ce0778b70,

title = "Modeling and simulation of parabolic trough power plant using molten salt: Case study of NOOR i solar power station in Ouarzazate, Morocco",

abstract = "The practicality of modeling and simulating a parabolic trough power plant (PTPP) through a network-based approach is emphasized over the traditional focus on a single parabolic trough collector (PTC). Lately, molten salt has been utilized as the heat transfer fluid (HTF) in parabolic trough collectors (PTCs) to augment the performance of parabolic trough power plants (PTPP) in lieu of the conventional thermal oil. To this end, a mathematical model to describe the fluid dynamics of molten salt in the solar field of a PTPP and the associated numerical algorithm are presented in order to conduct simulations that closely mirror real-world scenarios by using data from NOOR I Power plant in Morocco.",

author = "Hamzah Bakhti and Ingenuin Gasser",

note = "Publisher Copyright: {\textcopyright} 2024 Author(s).; 9th International Conference on Modeling, Simulation and Applied Optimization, ICMSAO 2023 ; Conference date: 26-04-2023 Through 28-04-2023",

year = "2024",

month = mar,

day = "5",

doi = "10.1063/5.0195603",

language = "English",

volume = "3034",

journal = "AIP Conference Proceedings",

issn = "0094-243X",

publisher = "American Institute of Physics",

number = "1",

@article{9f233e7eba8f48f3acc9cbd3ac8b18ac,

title = "M-ENIAC: A Physics-Informed Machine Learning Recreation of the First Successful Numerical Weather Forecasts",

abstract = "In 1950 the first successful numerical weather forecast was obtained by solving the barotropic vorticity equation using the Electronic Numerical Integrator and Computer (ENIAC), which marked the beginning of the age of numerical weather prediction. Here, we ask the question of how these numerical forecasts would have turned out, if machine learning based solvers had been used instead of standard numerical discretizations. Specifically, we recreate these numerical forecasts using physics-informed neural networks. We show that physics-informed neural networks provide an easier and more accurate methodology for solving meteorological equations on the sphere, as compared to the ENIAC solver.",

keywords = "ENIAC, PINN, weather forecast",

author = "R{\"u}diger Brecht and Alex Bihlo",

year = "2024",

month = jan,

doi = "10.1029/2023GL107718",

language = "English",

volume = "51",

journal = "Geophysical Research Letters",

issn = "0094-8276",

publisher = "John Wiley and Sons Inc.",

number = "10",

@article{66a5898a5f2a49b6a3ad0e0ad657db61,

title = "Towards replacing precipitation ensemble predictions systems using machine learning",

abstract = "Forecasting precipitation accurately poses significant challenges due to various factors affecting its distribution and intensity, including but not limited to subgrid variability. Although higher resolution simulations are often considered to improve precipitation forecasts, it is crucial to note that simply increasing resolution may not suffice without appropriate adjustments to parameterization schemes or tuning. Traditionally, ensembles of simulations are used to generate uncertainty predictions associated with precipitation forecasts, but this approach can be computationally intensive. As an alternative, there is a growing trend towards leveraging neural networks for precipitation prediction, which offers potential computational advantages. We propose a new approach to generating ensemble weather predictions for high-resolution precipitation without requiring high-resolution training data. The method uses generative adversarial networks to learn the complex patterns of precipitation and produce diverse and realistic precipitation fields, allowing to generate realistic precipitation ensemble members using only the available control forecast. We demonstrate the feasibility of generating realistic precipitation ensemble members on unseen higher resolutions. We use evaluation metrics such as RMSE, CRPS, rank histogram and ROC curves to demonstrate that our generated ensemble is almost identical to the ECMWF IFS ensemble, on which our model was trained on.",

keywords = "ensemble weather prediction, machine learning, precipitation, tools and methods",

author = "R{\"u}diger Brecht and Alex Bihlo",

year = "2024",

month = jan,

doi = "10.1002/asl.1262",

language = "English",

volume = "25",

journal = "Atmospheric Science Letters",

issn = "1530-261X",

publisher = "John Wiley & Sons Inc.",

number = "11",