Related papers: A Linear View on Shape Optimization
This paper sets up an approach for shape optimization problems constrained by variational inequalities (VI) in an appropriate shape space. In contrast to classical VI, where no explicit dependence on the domain is given, VI constrained…
An unsupervised shape analysis is proposed to learn concepts reflecting shape commonalities. Our approach is two-fold: i) a spatial topology analysis of point cloud segment constellations within objects is used in which constellations are…
This paper investigates the problem of optimal predictor design for distributed parameter systems using neural networks and shape optimization. Sensors with various shapes are placed on the domain of the distributed parameter system. Data…
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or…
This paper investigates a family of dynamical systems arising from an evolutionary re-interpretation of certain optimal control and optimization problems. We focus particularly on the application in image registration of the theory of…
We study the deformation theory of nonsigular projective curves defined over algebraic closed fields of positive characteristic. We show that under some assumptions the local deformation problem for automorphisms of powerseries can be…
The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…
We represent 3D shape by structured 2D representations of fixed length making it feasible to apply well investigated 2D convolutional neural networks (CNN) for both discriminative and geometric tasks on 3D shapes. We first provide a general…
A lot of information concerning solutions of linear differential equations can be computed directly from the equation. It is therefore natural to consider these equations as a data-structure, from which mathematical properties can be…
The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
The goal of this paper is to improve the performance of an electric motor by modifying the geometry of a specific part of the iron core of its rotor. To be more precise, the objective is to smooth the rotation pattern of the rotor. A shape…
We present a new skeletal representation along with a matching framework to address the deformable shape recognition problem. The disconnectedness arises as a result of excessive regularization that we use to describe a shape at an…
The robotic shape control of deformable linear objects has garnered increasing interest within the robotics community. Despite recent progress, the majority of shape control approaches can be classified into two main groups: open-loop…
In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
The shape control of deformable linear objects (DLOs) is challenging, since it is difficult to obtain the deformation models. Previous studies often approximate the models in purely offline or online ways. In this paper, we propose a scheme…
In this article, the shape optimization of a linear elastic body subject to frictional (Tresca) contact is investigated. Due to the projection operators involved in the formulation of the contact problem, the solution is not shape…
The novel Riemannian view on shape optimization developed in [Schulz, FoCM, 2014] is extended to a Lagrange-Newton approach for PDE constrained shape optimization problems. The extension is based on optimization on Riemannian vector space…
In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…