Molecular Sparse Representation by 3D Ellipsoid Radial Basis Function Neural Networks via $L_1$ Regularization

基于正则单纯集几何的椭球信任区域的径向基函数优化算法

A Radial Basis Function based Optimization Algorithm with Regular Simplex set geometry in Ellipsoidal Trust-Regions

本文提出一种无导数插值优化算法，通过通用克里金方法构建插值框架，改进点分布并保证曲率，将球形信任区域扩展为椭球形以适应局部各向异性。

径向基函数生成的有限差分法结合贝塞尔权重用于二维亥姆霍兹方程

Radial basis function-generated finite differences with Bessel weights for the 2D Helmholtz equation

本文利用径向基函数生成的有限差分法（RBF-FD）结合贝塞尔函数定义的振荡径向基函数，对二维亥姆霍兹方程进行近似数值求解，通过正则化插值矩阵来解决局部插值获得权重时的病态问题，并通过不同数值测试验证了色散和污染效应的缓解。

使用稀疏径向基函数神经网络求解多尺度椭圆问题

Solving multiscale elliptic problems by sparse radial basis function neural networks

提出一种稀疏径向基函数神经网络方法，通过将二阶椭圆型偏微分方程重写为一阶系统并引入 $\ell_1$ 正则化与特定优化算法，实现了在三维多尺度问题上的高精度、高鲁棒求解，且显著减少了所需基函数数量。

Sparse Representation of Gaussian Molecular Surface

In this paper, we propose a model and algorithm for sparse representing Gaussian molecular surface. The original Gaussian molecular surface is approximated by a relatively small number of radial basis functions (RBFs) with rotational ellipsoid feature. The sparsity of the RBF representation is achieved by solving a nonlinear $L_1$ optimization problem. Experimental results demonstrate that the original Gaussian molecular surface is able to be represented with good accuracy by much fewer RBFs using our $L_1$ model and algorithm. The sparse representation of Gaussian molecular surface is useful …

反问题中的全局优化：克里金法与径向基函数的比较

Global optimization in inverse problems: A comparison of Kriging and radial basis functions

针对具有唯一解的非线性反问题，比较了基于径向基函数和克里金法的全局优化方法，并指出径向基函数算法的改进版本更具前景。