Nuclear mass predictions with radial basis function approach

With the help of radial basis function (RBF) and the Garvey-Kelson relation, the accuracy and predictive power of some global nuclear mass models are significantly improved. The rms deviation between predictions from four models and 2149 known masses falls to about 200 keV. The AME95-03 and AME03-Border tests show that the RBF approach is a very useful tool for further improving the reliability of mass models. Simultaneously, the differences from different model predictions for unknown masses are remarkably reduced and the isospin symmetry is better represented when the RBF extrapolation is combined.Comment: 4 figures, 4 tables; accepted for publication as a Rapid Communication in Physical Review

Anisotropic Radial Basis Function Methods for Continental Size Ice Sheet Simulations

In this paper we develop and implement anisotropic radial basis function methods for simulating the dynamics of ice sheets and glaciers. We test the methods on two problems: the well-known benchmark ISMIP-HOM B that corresponds to a glacier size ice and a synthetic ice sheet whose geometry is inspired by the EISMINT benchmark that corresponds to a continental size ice sheet. We illustrate the advantages of the radial basis function methods over a standard finite element method. We also show how the use of anisotropic radial basis functions allows for accurate simulation of the velocities on a large ice sheet, which was not possible with standard isotropic radial basis function methods due to a large aspect ratio between the ice length and the ice thickness. Additionally, we implement a partition of unity method in order to improve the computational efficiency of the radial basis function methods.Comment: The authors contributed equally to this wor

A Discrete Adapted Hierarchical Basis Solver For Radial Basis Function Interpolation

In this paper we develop a discrete Hierarchical Basis (HB) to efficiently solve the Radial Basis Function (RBF) interpolation problem with variable polynomial order. The HB forms an orthogonal set and is adapted to the kernel seed function and the placement of the interpolation nodes. Moreover, this basis is orthogonal to a set of polynomials up to a given order defined on the interpolating nodes. We are thus able to decouple the RBF interpolation problem for any order of the polynomial interpolation and solve it in two steps: (1) The polynomial orthogonal RBF interpolation problem is efficiently solved in the transformed HB basis with a GMRES iteration and a diagonal, or block SSOR preconditioner. (2) The residual is then projected onto an orthonormal polynomial basis. We apply our approach on several test cases to study its effectiveness, including an application to the Best Linear Unbiased Estimator regression problem

Radial basis function approach in nuclear mass predictions

The radial basis function (RBF) approach is applied in predicting nuclear masses for 8 widely used nuclear mass models, ranging from macroscopic-microscopic to microscopic types. A significantly improved accuracy in computing nuclear masses is obtained, and the corresponding rms deviations with respect to the known masses is reduced by up to 78%. Moreover, strong correlations are found between a target nucleus and the reference nuclei within about three unit in distance, which play critical roles in improving nuclear mass predictions. Based on the latest Weizs\"{a}cker-Skyrme mass model, the RBF approach can achieve an accuracy comparable with the extrapolation method used in atomic mass evaluation. In addition, the necessity of new high-precision experimental data to improve the mass predictions with the RBF approach is emphasized as well.Comment: 18 pages, 8 figure

Error estimates for interpolation of rough data using the scattered shifts of a radial basis function

The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a natural function space dictated by the choice of radial basis function -- the native space. The native space contains functions possessing a certain amount of smoothness. This paper establishes error estimates when the function being interpolated is conspicuously rough.Comment: 12 page

Theoretical Interpretations and Applications of Radial Basis Function Networks

Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains