Kan: Kolmogorov-arnold networks

Z Liu, Y Wang, S Vaidya, F Ruehle, J Halverson… - arxiv preprint arxiv …, 2024 - arxiv.org
Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold
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 …

Wavelet-Based Edge Multiscale Finite Element Methods for Singularly Perturbed Convection-Diffusion Equations

S Fu, E Chung, G Li - Multiscale Modeling & Simulation, 2025 - SIAM
We propose a novel efficient and robust wavelet-based edge multiscale finite element
method (WEMsFEM) motivated by [S. Fu, E. Chung, and G. Li, J. Comput. Phys., 396 (2019) …

On optimal bases for multiscale PDEs and Bayesian homogenization

S Chen, Z Ding, Q Li, SJ Wright - arxiv preprint arxiv:2305.12303, 2023 - arxiv.org
PDE solutions are numerically represented by basis functions. Classical methods employ
pre-defined bases that encode minimum desired PDE properties, which naturally cause …

[Књига][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 …