Related papers: Implicit parametrizations in shape optimization: b…
In this paper we present an algorithm for computing a matrix representation for a surface in P^3 parametrized over a 2-dimensional toric variety T. This algorithm follows the ideas of [Botbol-Dickenstein-Dohm-09] and it was implemented in…
We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the…
Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for…
We provide an abstract framework for optimal goal-oriented adaptivity for finite element methods and boundary element methods in the spirit of [Carstensen et al., Comput. Math. Appl. 67 (2014)]. We prove that this framework covers standard…
We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…
A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of the design that require underlying support structures during…
Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks. Many of these methods, however, learn only closed surfaces and are…
This paper continues earlier work and is concerned with the inverse problem of parameter identification in variational inequalities of the second kind that does not only treat the parameter linked to a bilinear form, but importantly also…
Adaptive structures are characterized by their ability to adjust their geometrical and other properties to changing loads or requirements during service. This contribution deals with a method for the design of quasi-static motions of…
Multi-material structural topology and shape optimization problems are formulated within a phase field approach. First-order conditions are stated and the relation of the necessary conditions to classical shape derivatives are discussed. An…
This paper is dedicated to the investigation of a new numerical method to approximate the optimal stopping problem for a discrete-time continuous state space Markov chain under partial observations. It is based on a two-step discretization…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…
Statistical Shape Modeling (SSM) is a quantitative method for analyzing morphological variations in anatomical structures. These analyses often necessitate building models on targeted anatomical regions of interest to focus on specific…
When combining the numerical concept of variational discretization and semi-smooth Newton methods for the numerical solution of pde constrained optimization with control constraints, special emphasis has to be taken on the implementation,…
We introduce a novel method for the implementation of shape optimziation in fluid dynamics applications, where we propose to use the shape derivative to determine deformation fields with the help of the $p-$ Laplacian for $p > 2$. This…
A parameterized surface can be represented as a projection from a certain toric surface. This generalizes the classical homogeneous and bihomogeneous parameterizations. We extend to the toric case two methods for computing the implicit…
In structured prediction problems where we have indirect supervision of the output, maximum marginal likelihood faces two computational obstacles: non-convexity of the objective and intractability of even a single gradient computation. In…
A practical method is developed to deal with the second quantization of the many-body system containing the composite particles. In our treatment, the modes associated with composite particles are regarded approximately as independent ones…
We present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces…