Related papers: Shape optimization for interface identification in…

We present an optimization-based coupling method for local and nonlocal continuum models. Our approach couches the coupling of the models into a control problem where the states are the solutions of the nonlocal and local equations, the…

Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a…

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…

Matching deformable objects using their shapes is an important problem in computer vision since shape is perhaps the most distinguishable characteristic of an object. The problem is difficult due to many factors such as intra-class…

In this paper we discuss a level set approach for the identification of an unknown boundary in a computational domain. The problem takes the form of a Bernoulli problem where only the Dirichlet datum is known on the boundary that is to be…

This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…

We introduce a novel mesh-free and direct method for computing the shape derivative in PDE-constrained shape optimization problems. Our approach is based on a probabilistic representation of the shape derivative and is applicable for…

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 non-magnetic bulk dielectric. The shape…

The computation of correspondences between shapes is a principal task in shape analysis. To this end, methods based on partial differential equations (PDEs) have been established, encompassing e.g. the classic heat kernel signature as well…

Many high-dimensional optimisation problems exhibit rich geometric structures in their set of minimisers, often forming smooth manifolds due to over-parametrisation or symmetries. When this structure is known, at least locally, it can be…

We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…

3D shape editing is widely used in a range of applications such as movie production, computer games and computer aided design. It is also a popular research topic in computer graphics and computer vision. In past decades, researchers have…

This paper is concerned with a shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations with nonhomogeneous boundary condition. The structure of shape gradient with respect to the shape of the variable domain…

It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the…

The use of machine learning techniques to improve the performance of branch-and-bound optimization algorithms is a very active area in the context of mixed integer linear problems, but little has been done for non-linear optimization. To…

We implement a shape optimization algorithm for body-assisted light-matter interactions described by the formalism of macroscopic quantum electrodynamics. The approach uses the level-set method to represent and incrementally evolve…

We propose the combination of forward shape derivatives and the use of an iterative inversion scheme for Bayesian optimization to find optimal designs of nanophotonic devices. This approach widens the range of applicability of Bayesian…

We extend thresholding methods for numerical realization of mean curvature flow on obstacles to the anisotropic setting where interfacial energy depends on the orientation of the interface. This type of schemes treats the interface…

This paper develops and analyses numerical approximation for linear-quadratic optimal control problem governed by elliptic interface equations. We adopt variational discretization concept to discretize optimal control problem, and apply an…

Nonlinear optimization-based control policies, such as those those arising in nonlinear Model Predictive Control, have seen remarkable success in recent years. These policies require solving computationally demanding nonlinear optimization…