Related papers: A general method to compute numerical dispersion e…
The method is described and tested for analysis of statistical parameters of reduced neutron widths distributions accounting for possibility of coexistence of superposition of some functions with non-zero mean values of neutron amplitude…
Explicit finite-sample statistical guarantees on model performance are an important ingredient in responsible machine learning. Previous work has focused mainly on bounding either the expected loss of a predictor or the probability that an…
A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the…
One of the important advantages of optical metasurfaces over conventional diffractive optical elements is their capability to efficiently deflect light by large angles. However, metasurfaces are conventionally designed using approaches that…
A quantitative evaluation of the influence of sampling on the numerical fractal analysis of experimental profiles is of critical importance. Although this aspect has been widely recognized, a systematic analysis of the sampling influence is…
Universal meshes have recently appeared in the literature as a compu- tationally efficient and robust paradigm for the generation of conforming simpli- cial meshes for domains with evolving boundaries. The main idea behind a univer- sal…
Error estimates on parton density distributions are presently based on the traditional method of least squares minimisation and linear error propagation in global QCD fits. We review the underlying assumptions and the various mathematical…
Nonlocal diffusion model provides an appropriate description of the diffusion process of solute in the complex medium, which cannot be described properly by classical theory of PDE. However, the operators in the nonlocal diffusion models…
In regression analysis under artificial neural networks, the prediction performance depends on determining the appropriate weights between layers. As randomly initialized weights are updated during back-propagation using the gradient…
The gradient scheme framework is based on a small number of properties and encompasses a large number of numerical methods for diffusion models. We recall these properties and develop some new generic tools associated with the gradient…
Dispersion is a fundamental concept in statistics, yet standard approaches - especially via stochastic orders - face limitations in the discrete setting. In particular, the classical dispersive order, well-established for continuous…
This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for…
Stretched Gaussian distribution is the fundamental solution of the Hausdorff derivative diffusion equation and its corresponding stretched Gaussian noise is a widely encountered non-Gaussian noise in science and engineering. The least…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…
I discuss the effects of measurement error on regression and density estimation. I review the statistical methods that have been developed to correct for measurement error that are most popular in astronomical data analysis, discussing…
In this work, we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method supports general meshes made of polygonal/polyhedral elements, which provides…
This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free…
Towards identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with high speed and high accuracy. Our numerical scheme is based on the method of fundamental…
We introduce new numerical integration operators which compose the mass and stiffness matrices of a modified spectral element method for simulation of elastic wave propagation. While these operators use the same quadrature nodes as does the…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…