Related papers: Radial basis function approach in nuclear mass pre…

Flux reconstruction provides a framework for solving partial differential equations in which functions are discontinuously approximated within elements. Typically, this is done by using polynomials. Here, the use of radial basis functions…

We use the Relativistic Mean Field (RMF) method to calculate properties of neutron rich, usually deformed nuclei, important for equation of state calculations and which have significant abundance in the early stages of stellar collapse. We…

A recent proposed method for $\alpha$-decay energies ($Q_\alpha$) [J.M. Dong, W. Zuo, and W. Scheid, Phys. Rev. Lett. \textbf{107}, 012501 (2011)] can reproduce experimental data of superheavy nuclei (SHN) with an $rms$-value of less than…

Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…

Multi-modal problems can be effectively addressed using multiple hypothesis frameworks, but integrating these frameworks into learning models poses significant challenges. This paper introduces a Structured Radial Basis Function Network…

A covariant energy density functional is calibrated using a principled Bayesian statistical framework informed by experimental binding energies and charge radii of several magic and semi-magic nuclei. The Bayesian sampling required for the…

Global optimization of expensive functions has important applications in physical and computer experiments. It is a challenging problem to develop efficient optimization scheme, because each function evaluation can be costly and the…

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…

This study is devoted to the inference problem of extracting the nuclear matter properties directly from a set of mass-radius observations. We employ Bayesian neural networks (BNNs), which is a probabilistic model capable of estimating the…

Conventionally, piecewise polynomials have been used in the boundary elements method (BEM) to approximate unknown boundary values. Since infinitely smooth radial basis functions (RBFs) are more stable and accurate than the polynomials for…

Recently the first laser spectroscopy measurement of the radioactive RaF molecule has been reported by Ruiz \textit{et al.} [Nature \textbf{581}, 396 (2020)]. This and similar molecules are considered to search for the New Physics effects.…

Nuclear masses are machine-learned as a function of proton and neutron numbers. The neural network with additive Gaussian process regression-optimized activation functions (GPR-NN) method is employed for the first time for this purpose.…

Support Vector Machines (SVMs) are still one of the most popular and precise classifiers. The Radial Basis Function (RBF) kernel has been used in SVMs to separate among classes with considerable success. However, there is an intrinsic…

The method of "random Fourier features (RFF)" has become a popular tool for approximating the "radial basis function (RBF)" kernel. The variance of RFF is actually large. Interestingly, the variance can be substantially reduced by a simple…

We explore three different classes of relativistic approaches applied to the description of dense nuclear matter: a Walecka-type relativistic mean field model (RMF), an extension including an effective chiral potential (RMF-C) and a further…

Given the importance of nuclear mass predictions, numerous models have been developed to extrapolate the measured data into unknown regions. While neural networks -- the core of modern artificial intelligence -- have been recently suggested…

Uncertainties in nuclear models have a major impact on simulations that aim at understanding the origin of heavy elements in the universe through the rapid neutron capture process ($r$ process) of nucleosynthesis. Within the framework of…

The variances of the fission fragment mass distributions for symmetric fission over a wide range of the fissility of the compound nucleus have been investigated within the frame work of Random Neck Rupture Model (RNRM) proposed by Brosa et.…

Machine learning offers a powerful framework for validating and predicting atomic mass. We compare three improved neural network methods for representation and extrapolation for atomic mass prediction. The powerful method, adopting a…

We derive stability estimates for three commonly used radial basis function (RBF) methods to solve hyperbolic time-dependent PDEs: the RBF generated finite difference (RBF-FD) method, the RBF partition of unity method (RBF-PUM) and Kansa's…