9 papers
Retraction based regression methods on Riemannian manifolds
Estefanía Loayza-Romero, Benedikt Sibum, Kathrin Welker
Geodesic regression generalizes classical regression models to manifold-valued data by replacing affine models in Euclidean spaces with geodesic models on Riemannian manifolds. In…
Numerical techniques for geodesic approximation in Riemannian shape optimization
Estefania Loayza-Romero, Kathrin Welker
Shape optimization is commonly applied in engineering to optimize shapes with respect to an objective functional relying on PDE solutions. In this paper, we view shape optimization…
A Riemannian approach for PDE-constrained shape optimization over the diffeomorphism group using outer metrics
Estefania Loayza-Romero, Lidiya Pryymak, Kathrin Welker
In this paper, we study the use of outer metrics, in particular Sobolev-type metrics on the diffeomorphism group in the context of PDE-constrained shape optimization. Leveraging th…
A general formulation of reweighted least squares fitting
Carlotta Giannelli, Sofia Imperatore, Lisa Maria Kreusser +3
We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be ex…
Multi-level Optimal Control with Neural Surrogate Models
Dante Kalise, Estefanía Loayza-Romero, Kirsten A. Morris +1
Optimal actuator and control design is studied as a multi-level optimisation problem, where the actuator design is evaluated based on the performance of the associated optimal clos…
A Discretize-Then-Optimize Approach to PDE-Constrained Shape Optimization
Roland Herzog, Estefanía Loayza-Romero
We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admi…
PDE-constrained shape optimization: towards product shape spaces and stochastic models
Caroline Geiersbach, Estefania Loayza-Romero, Kathrin Welker
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional i…
A Manifold of Planar Triangular Meshes with Complete Riemannian Metric
Roland Herzog, Estefanía Loayza-Romero
Shape spaces are fundamental in a variety of applications including image registration, morphing, matching, interpolation, and shape optimization. In this work, we consider two-dim…
Stochastic approximation for optimization in shape spaces
Caroline Geiersbach, Estefania Loayza-Romero, Kathrin Welker
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-di…