7 papers
A Practitioner's Guide to Kolmogorov-Arnold Networks
Amir Noorizadegan, Sifan Wang, Leevan Ling +1
Kolmogorov-Arnold Networks (KANs), whose design is inspired-rather than dictated-by the Kolmogorov superposition theorem, have emerged as a structured alternative to MLPs. This rev…
Making Gaussian Kolmogorov-Arnold Networks Reliable and Accurate
Amir Noorizadegan, Sifan Wang, Leevan Ling
Kolmogorov-Arnold Networks (KANs) replace fixed activations with learnable univariate edge functions whose behavior depends strongly on the chosen basis. Gaussian radial basis func…
Minimum-norm interpolation for unknown surface reconstruction
Alex Shiu Lun Chu, Leevan Ling, Ka Chun Cheung
We study algorithms to estimate geometric properties of raw point cloud data through implicit surface representations. Given that any level-set function with a constant level set c…
An Adaptive Lagrangian B-Spline Framework for Point Cloud Manifold Evolution
Muhammad Ammad, Leevan Ling
We extend our recent curve-evolution framework based on localized B-spline interpolation to present an adaptive Lagrangian framework for the geometric evolution of point-cloud data…
B-spline-Based ALE-MFS Framework for Evolving Domains
Muhammad Ammad, Leevan Ling, Shu Ma
We develop and analyze a B-spline based arbitrary Lagrangian-Eulerian method of fundamental solutions (ALE-MFS) for curvature-driven motion of two-dimensional evolving domains. Bou…
Sobolev Algorithm for Local Smoothness Analysis (SALSA) via Sharp Direct and Inverse Statements
Sara Avesani, Leevan Ling, Francesco Marchetti +1
We extend sharp direct and inverse approximation statements for kernel-based methods for finitely smooth kernels, i.e. those whose native spaces are norm-equivalent to Sobolev spac…