Kan: Kolmogorov-arnold networks
Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold
Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs …
Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs …
A unified framework for multiscale spectral generalized FEMs and low-rank approximations to multiscale PDEs
C Ma - arxiv preprint arxiv:2311.08761, 2023 - arxiv.org
This work presents an abstract framework for the design, implementation, and analysis of the
multiscale spectral generalized finite element method (MS-GFEM), a particular numerical …
multiscale spectral generalized finite element method (MS-GFEM), a particular numerical …
Wavelet-based Edge Multiscale Finite Element Methods for Singularly Perturbed Convection-Diffusion Equations
We propose a novel efficient and robust Wavelet-based Edge Multiscale Finite Element
Method (WEMsFEM) motivated by\cite {MR3980476, GL18} to solve the singularly perturbed …
Method (WEMsFEM) motivated by\cite {MR3980476, GL18} to solve the singularly perturbed …
On optimal bases for multiscale PDEs and Bayesian homogenization
PDE solutions are numerically represented by basis functions. Classical methods employ
pre-defined bases that encode minimum desired PDE properties, which naturally cause …
pre-defined bases that encode minimum desired PDE properties, which naturally cause …
[BOOK][B] On Multiscale and Statistical Numerical Methods for PDEs and Inverse Problems
Y Chen - 2023 - search.proquest.com
This thesis is about numerical methods for scientific computing and scientific machine
learning, with a focus on solving partial differential equations (PDEs) and inverse problems …
learning, with a focus on solving partial differential equations (PDEs) and inverse problems …