Related papers: Impact Study of Numerical Discretization Accuracy …
In this paper we study adaptive discretization of the iteratively regularized Gauss-Newton method IRGNM with an a posteriori (discrepancy principle) choice of the regularization parameter in each Newton step and of the stopping index. We…
Nuclear resonant x-ray diffraction in grazing incidence geometry is used to determine the lateral magnetic configuration in a one-dimensional lattice of ferromagnetic nanostripes. During magnetic reversal, strong nuclear superstructure…
Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…
We present an optimizer which uses Bayesian optimization to tune the system parameters of distributed stochastic gradient descent (SGD). Given a specific context, our goal is to quickly find efficient configurations which appropriately…
This paper investigates the simultaneous identification of a spatially dependent potential and the initial condition in a subdiffusion model based on two terminal observations. The existence, uniqueness, and conditional stability of the…
We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of…
Gravitational lens modeling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the…
In this paper, we focus on the numerical analysis of quantitative photoacoustic tomography. Our goal is to reconstruct the optical coefficients, i.e., the diffusion and absorption coefficients, using multiple internal observational data.…
Estimation of the optical properties of scattering media such as tissue is important in diagnostics as well as in the development of techniques to image deeper. As light penetrates the sample scattering events occur that alter the…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
In our work we focus on the accurate computation of light propagation in finite size photonic crystal structures with the finite element method (FEM). We discuss how we utilize numerical concepts like high-order finite elements, transparent…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
A design optimization framework for process parameters of additive manufacturing based on finite element simulation is proposed. The finite element method uses a coupled thermomechanical model developed for fused deposition modeling from…
This paper introduces a Bayesian image segmentation algorithm based on finite mixtures. An EM algorithm is developed to estimate parameters of the Gaussian mixtures. The finite mixture is a flexible and powerful probabilistic modeling tool.…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack…
We propose new strategies to handle polygonal grids refinement based on Convolutional Neural Networks (CNNs). We show that CNNs can be successfully employed to identify correctly the "shape" of a polygonal element so as to design suitable…
We present numerical simulations of the impact of laser beam wavefront aberrations in cold atom interferometers. We demonstrate that to reach accuracy at the mrad level, simulations cannot be based on a description of the retroreflection…
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…
The estimation of regression parameters in one dimensional broken stick models is a research area of statistics with an extensive literature. We are interested in extending such models by aiming to recover two or more intersecting…