Related papers: Gradient-Based Eigenvalue Optimization for Electro…
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…
We consider the simultaneous optimization of the reliability and the cost of a ceramic component in a biobjective PDE constrained shape optimization problem. A probabilistic Weibull-type model is used to assess the probability of failure of…
In this paper, we discuss adaptive approximations of an elliptic eigenvalue optimization problem in a phase-field setting by a conforming finite element method. An adaptive algorithm is proposed and implemented in several two dimensional…
Probabilistic constellation shaping enables easy rate adaption and has been proven to reduce the gap to Shannon capacity. Constellation point probabilities are optimized to maximize either the mutual information or the bit-wise mutual…
This report describes the computation of gradients by algorithmic differentiation for statistically optimum beamforming operations. Especially the derivation of complex-valued functions is a key component of this approach. Therefore the…
The paper is devoted to optimization of resonances in a 1-D open optical cavity. The cavity's structure is represented by its dielectric permittivity function e(s). It is assumed that e(s) takes values in the range 1 <= e_1 <= e(s) <= e_2.…
Engineering the Hamiltonian of a quantum system is fundamental to the design of quantum systems. Automating Hamiltonian design through gradient-based optimization can dramatically accelerate this process. However, computing the gradients of…
We are interested in the optimization of convex domains under a PDE constraint. Due to the difficulties of approximating convex domains in $\mathbb{R}^3$, the restriction to rotationally symmetric domains is used to reduce shape…
We present a novel data-driven approach for enhancing gradient reconstruction in unstructured finite volume methods for hyperbolic conservation laws, specifically for the 2D Euler equations. Our approach extends previous structured-grid…
MRI systems are traditionally engineered to produce close to idealized performance, enabling a simplified pulse sequence design philosophy. An example of this is control of eddy currents produced by gradient fields; usually these are…
Parametric shape optimization aims at minimizing an objective function f(x) where x are CAD parameters. This task is difficult when f is the output of an expensive-to-evaluate numerical simulator and the number of CAD parameters is large.…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
We propose a variational method for constructing the eigenvalues and generalized eigenvalues for an arbitrary $N\times N$ complex matrix. The quantum part of our algorithm is based on encoding the matrix elements into the pure state of a…
In this paper, a spectral method based on conformal mappings is proposed to solve Steklov eigenvalue problems and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
High current storage rings, such as the Z-pole operating mode of the FCC-ee, require accelerating cavities that are optimized with respect to both the fundamental mode and the higher order modes. Furthermore, the cavity shape needs to be…
Radio frequency (RF) cavities are commonly used to accelerate charged particle beams. The shape of the RF cavity determines the resonant electromagnetic fields and frequencies, which need to satisfy a variety of requirements for a stable…
M-eigenvalues of fourth order hierarchically symmetric tensors play a significant role in nonlinear elastic material analysis and quantum entanglement problems. This paper focuses on computing extreme M-eigenvalues for such tensors. To…
Optimizing shapes and topology of physical devices is crucial for both scientific and technological advancements, given its wide-ranging implications across numerous industries and research areas. Innovations in shape and topology…
High quality mechanical resonators are critical for driving advances in quantum information technologies, precision sensing, and optomechanics. However, achieving compact resonator designs that maintain high performance is a key challenge.…