相关论文: Analysis of two-phase shape optimization problems …

In the context of the optimization of rotating electric machines, many different objective functions are of interest and considering this during the optimization is of crucial importance. While evolutionary algorithms can provide a Pareto…

Recent developments in Deep Learning (DL) suggest a vast potential for Topology Optimization (TO). However, while there are some promising attempts, the subfield still lacks a firm footing regarding basic methods and datasets. We aim to…

While topological derivatives have proven useful in applications of topology optimisation and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, in particular in the context of nonlinear partial…

In component shape optimization, the component properties are often evaluated by computationally expensive simulations. Such optimization becomes unfeasible when it is focused on a global search requiring thousands of simulations to be…

Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…

In this paper we analyze a shape optimization problem, with Stokes equations as the state problem, defined on a domain with a part of the boundary that is described as the graph of the control function. The state problem formulation is…

This work constructs and analyzes new efficient high-order two-derivative diagonally implicit Runge--Kutta (TDDIRK) schemes with optimized phase errors. Specifically, we present a convergence result for TDDIRK methods and investigate their…

We answer a question of Serre from the 1980s on rational points of bounded height on projective thin sets, in degree at least $4$. For degrees $2$ and $3$ we improve the known bounds in general. The focus is on thin sets of type II, namely…

Higher order derivative theories, generally suffer from instabilities, known as Ostrogradsky instabilities. This issue can be resolved by removing any existing degeneracy present in such theories. We consider a model involving at most…

In this thesis I develop a variety of techniques to train, evaluate, and sample from intractable and high dimensional probabilistic models. Abstract exceeds arXiv space limitations -- see PDF.

We use high-precision spectroscopy and detailed theoretical modelling to determine the form of the coupling between a superconducting phase qubit and a two-level defect. Fitting the experimental data with our theoretical model allows us to…

The present article is dedicated to proving convergence of the stochastic gradient method in case of random shape optimization problems. To that end, we consider Bernoulli's exterior free boundary problem with a random interior boundary. We…

Within this work, we present a novel approach to fracture simulations based on shape optimization techniques. Contrary to widely-used phase-field approaches in literature the proposed method does not require a specified 'length-scale'…

We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…

This article is devoted to the shape optimization of the internal structure of an electric motor, and more precisely of the arrangement of air and ferromagnetic material inside the rotor part with the aim to increase the torque of the…

We introduce and study the problem of optimizing arbitrary functions over degree sequences of hypergraphs and multihypergraphs. We show that over multihypergraphs the problem can be solved in polynomial time. For hypergraphs, we show that…

This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overdetermined problems with potentially degenerate ellipticity…

Numerical evaluation of performance measures in heavy-tailed risk models is an important and challenging problem. In this paper, we construct very accurate approximations of such performance measures that provide small absolute and relative…

In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial discretization of the discontinuous Galerkin spectral element method to solve (non-)linear PDEs. The resulting…

The main theme of this thesis is the development of computational methods for classes of infinite-dimensional optimization problems arising in optimal control and information theory. The first part of the thesis is concerned with the…