arXiv:2607. 10200v1 Announce Type: new Abstract: The Neural Tangent Kernel (NTK) is one powerful tool for analyzing the training dynamics of neural networks in the over-parameterized regime.
By Bangti Jin, Longjun Wu
arXiv:2510. 09685v2 Announce Type: replace-cross Abstract: Deep learning has become a pivotal technology in fields such as computer vision, scientific computing, and dynamical systems, significantly advancing these disciplines.
By Yongshuai Liu, Lianfang Wang, Kuilin Qin, Qinghua Zhang, Faqiang Wang, Li Cui, Jun Liu, Yuping Duan, Tieyong Zeng
arXiv:2505. 12430v2 Announce Type: replace Abstract: Recently, innovative adaptations of the Ritz method incorporating deep learning have been developed, known as the Deep Ritz Method.
By Rafael Florencio, Julio Guerrero
arXiv:2607. 24726v1 Announce Type: new Abstract: The Deep Galerkin Method (DGM) and Physics Informed Neural Networks (PINNs) have become widely-used methods for solving partial differential equations (PDEs) in the rapidly growing field of scientific machine learning.
By Justin Sirignano, Konstantinos Spiliopoulos, Samuel Cohen
arXiv:2608. 14733v1 Announce Type: cross Abstract: Building on the foundation of single-hidden-layer neural networks, Fourier Feature Networks (FENs) are proposed, which incorporate Fourier features using $\cos$, $\sin$, or a combination of both.
By Qihong Yang, Zhijie Su, Yangtao Deng, Qiaolin He
arXiv:2309. 07401v2 Announce Type: replace-cross Abstract: Deep neural networks (DNNs) show great promise for solving partial differential equations (PDEs), but their deep architectures introduce complex, large-scale, non-convex optimization challenges.
By Yuesheng Xu, Taishan Zeng