Related papers: Sloppy nuclear energy density functionals: effecti…
A study of parameter sensitivity of nuclear energy density functionals, initiated in the first part of this work \cite{NV.16}, is extended by the inclusion of data on ground-state properties of finite nuclei in the application of the…
In this paper, we consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. We calculate the sensitivity of model behavior to variations in parameters. In most cases,…
The framework of nuclear energy density functionals has been employed to describe nuclear structure phenomena for a wide range of nuclei. Recently, statistical properties of a given nuclear model, such as parameter confidence intervals and…
Complex models in physics, biology, economics, and engineering are often sloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades…
Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are `sloppy', i.e., exhibit behavior controlled by a relatively small number of parameter…
This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This novel approach identifies stiff parameter combinations…
Parameter estimation by nonlinear least squares minimization is a common problem with an elegant geometric interpretation: the possible parameter values of a model induce a manifold in the space of data predictions. The minimization problem…
We study a particular class of relativistic nuclear energy density functionals in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance (high-momentum) correlations, as…
Relativistic energy density functionals (EDF) have become a standard tool for nuclear structure calculations, providing a complete and accurate, global description of nuclear ground states and collective excitations. Guided by the medium…
In recent years impressive progress has been made in the development of highly accurate energy density functionals, which allow to treat medium-heavy nuclei. In this approach one tries to describe not only the ground state but also the…
Scientists use mathematical modelling to understand and predict the properties of complex physical systems. In highly parameterised models there often exist relationships between parameters over which model predictions are identical, or…
Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring…
Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single- or…
We explore the relationship among model fidelity, experimental design, and parameter estimation in sloppy models. We show that the approximate nature of mathematical models poses challenges for experimental design in sloppy models. In many…
New energy-density functionals (EDFs) inspired by effective-field theories (EFTs) have been recently proposed. The present work focuses on three of such functionals which were developed to produce satisfactory equations of state for nuclear…
In this article, we study approximation properties of the variation spaces corresponding to shallow neural networks with a variety of activation functions. We introduce two main tools for estimating the metric entropy, approximation rates,…
Predictions of nuclear properties far from measured data are inherently imprecise because of uncertainties in our knowledge of nuclear forces and in our treatment of quantum many-body effects in strongly-interacting systems. While the model…
We present the basic concepts and recent developments in the time-dependent density functional theory (TDDFT) for describing nuclear dynamics at low energy. The symmetry breaking is inherent in nuclear energy density functionals (EDFs),…
We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the…
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…