2 citations · 4 across the 7 of their papers we have counts for
7 papers
KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics
Juan Diego Toscano, Li-Lian Wang, George Em Karniadakis
Inspired by the Kolmogorov-Arnold representation theorem and Kurkova's principle of using approximate representations, we propose the Kurkova-Kolmogorov-Arnold Network (KKAN), a ne…
FEM on nonuniform meshes for nonlocal Laplacian: Semi-analytic Implementation in One Dimension
Hongbin Chen, Changtao Sheng, Li-Lian Wang
In this paper, we compute stiffness matrix of the nonlocal Laplacian discretized by the piecewise linear finite element on nonuniform meshes, and implement the FEM in the Fourier t…
A Novel PML-type Technique for Acoustic Scattering Problems based on A Real Coordinate Transformation
Jiangxing Wang, Lilian Wang, Bo Wang
It is known that any {\em real coordinate transformation} (RCT) to compress waves in an unbounded domain into a bounded domain results in infinite oscillations that cannot be resol…
Low regularity estimates of the Lie-Totter time-splitting Fourier spectral method for the logarithmic Schrödinger equation
Xiaolong Zhang, Li-Lian Wang
In this paper, we conduct rigorous error analysis of the Lie-Totter time-splitting Fourier spectral scheme for the nonlinear Schrödinger equation with a logarithmic nonlinear term…
Müntz ball polynomials and Müntz spectral-Galerkin methods for singular eigenvalue problems
Xiu Yang, Li-Lian Wang, Huiyuan Li +1
In this paper, we introduce a new family of orthogonal systems, termed as the Müntz ball polynomials (MBPs), which are orthogonal with respect to the weight function: $\|x\|^{2θ+2μ…
Pointwise error estimates and local superconvergence of Jacobi expansions
Shuhuang Xiang, Desong Kong, Guidong Liu +1
As one myth of polynomial interpolation and quadrature, Trefethen [30] revealed that the Chebyshev interpolation of (with ) at the Clenshaw-Curtis points exhibited…