Three ways to solve partial differential equations with neural networks—A review

J Blechschmidt, OG Ernst - GAMM‐Mitteilungen, 2021 - Wiley Online Library
Neural networks are increasingly used to construct numerical solution methods for partial
differential equations. In this expository review, we introduce and contrast three important …

Overview frequency principle/spectral bias in deep learning

ZQJ Xu, Y Zhang, T Luo - Communications on Applied Mathematics and …, 2024 - Springer
Understanding deep learning is increasingly emergent as it penetrates more and more into
industry and science. In recent years, a research line from Fourier analysis sheds light on …

Deep nitsche method: Deep ritz method with essential boundary conditions

Y Liao, P Ming - ar** between infinite-
dimensional parameter and solution spaces of partial differential equations (PDEs). In this …

A deep domain decomposition method based on Fourier features

S Li, Y ** by Fourier neural network with transfer learning
X Ye, YQ Ni, WK Ao, L Yuan - Mechanical Systems and Signal Processing, 2024 - Elsevier
The particle damper (PD) filled with granular material exhibits hysteretic behavior under
dynamic excitation, meaning that its response depends not only on the current excitation but …