Related papers: Shape optimization for interface identification in…
In this paper, we consider the algorithms and convergence for a general optimization problem, which has a wide range of applications in image segmentation, topology optimization, flow network formulation, and surface reconstruction. In…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…
This article presents a new and efficient alternative to well established algorithms for molecular geometry optimization. The new approach exploits the approximate decoupling of molecular energetics in a curvilinear internal coordinate…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
We propose a general framework for differentiating shapes represented in binary images with respect to their parameters. This framework functions as an automatic differentiation tool for shape parameters, generating both binary density maps…
Shape optimization with constraints given by partial differential equations (PDE) is a highly developed field of optimization theory. The elegant adjoint formalism allows to compute shape gradients at the computational cost of a further PDE…
In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…
The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry,…
In this paper, we propose a novel shape optimization approach for the source identification of elliptic equations. This identification problem arises from two application backgrounds: actuator placement in PDE-constrained optimal controls…
Spaces where each element describes a shape, so-called shape spaces, are of particular interest in shape optimization and its applications. Theory and algorithms in shape optimization are often based on techniques from differential…
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…
In the present work, a new computational framework for structural topology optimization based on the concept of moving deformable components is proposed. Compared with the traditional pixel or node point-based solution framework, the…
Shape optimization based on shape calculus has received a lot of attention in recent years, particularly regarding the development, analysis, and modification of efficient optimization algorithms. In this paper we propose and investigate…
The alternating direction method of multipliers within a shape optimization framework is developed for solving geometric inverse problems, focusing on a cavity identification problem from the perspective of non-destructive testing and…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
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 introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…
In this research, we investigate a general shape optimization problem in which the state equation is expressed using a nonlocal and nonlinear operator. We prove the existence of a minimum point for a functional $F$ defined on the family of…