Related papers: Sensitivity Analysis and Uncertainty Quantificatio…
Estimation of the intensity of a point process is considered within a nonparametric framework. The intensity measure is unknown and depends on covariates, possibly many more than the observed number of jumps. Only a single trajectory of the…
We overview some recent results in the field of uncertainty quantification for kinetic equations and related problems with random inputs. Uncertainties may be due to various reasons, such as lack of knowledge on the microscopic interaction…
In this paper we consider the rate of convergence of solutions of a scalar ordinary differential equation which is a perturbed version of an autonomous equation with a globally stable equilibrium. Under weak assumptions on the nonlinear…
Nucleosynthesis beyond Fe poses additional challenges not encountered when studying astrophysical processes involving light nuclei. Generally higher temperatures and nuclear level densities lead to stronger contributions of transitions on…
Although uncertainty quantification has been making its way into nuclear theory, these methods have yet to be explored in the context of reaction theory. For example, it is well known that different parameterizations of the optical…
Statistical parametric models are proposed to explain the values of the Planck constant obtained by comparing electrical and mechanical powers and by counting atoms in Si 28 enriched crystals. They assume that uncertainty contributions --…
We present a method for computing uncertainties in spectral models, i.e. level populations, line emissivities, and emission line ratios, based upon the propagation of uncertainties originating from atomic data. We provide analytic…
Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose additional…
Propagating uncertainties introduced by chemical reaction rate parameters to high-fidelity numerical simulations of complex combustion devices is necessary to ascertain impact on computational predictions. However, the high cost of detailed…
The use of high-dimensional regression techniques from machine learning has significantly improved the quantitative accuracy of interatomic potentials. Atomic simulations can now plausibly target quantitative predictions in a variety of…
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better…
Different approximations to describe nucleation kinetics have been analyzed. Some new approximations for solution of diffusion problem are proposed. Error of the approximation with constant radius of an embryo is clarified. The theory is…
The evolution of point defect concentrations under irradiation is controlled by their diffusion properties, and by their formation and elimination mechanisms. The latter include the mutual recombination of vacancies and interstitials, and…
The formation and subsequent growth of structural defects in an irradiated material can strongly influence the material's performance in technological and industrial applications. Predicting how the growth of defects affects material…
We consider the dynamics of pattern formation in a system of point defects under sustained irradiation within the framework of the rate theory. In our study we generalize the standard approach taking into account a production of defects by…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…
Most machine learning techniques are based upon statistical learning theory, often simplified for the sake of computing speed. This paper is focused on the uncertainty aspect of mathematical modeling in machine learning. Regression analysis…
Disorder in point patterns can be quantified by means of the complexity, rather than in terms of geometric attributes of pattern structure. A complexity-based disorder-quantifying statistic indicates the practical difficulties associated…
Charge-exchange reactions are versatile probes for nuclear structure. In particular, when populating isobaric analog states, these reactions are used to study isovector nuclear densities and neutron skins. The quality of the information…
Information about the physical properties of astrophysical objects cannot be measured directly but is inferred by interpreting spectroscopic observations in the context of atomic physics calculations. Ratios of emission lines, for example,…