arXiv:2605. 19178v2 Announce Type: replace-cross Abstract: The great success of neural networks primarily arises from the presence of the large number of weight parameters combined with nonlinearities in the input-output relationship of single neurons.
By Giovanni di Sarra, Yasser Roudi
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. 10389v1 Announce Type: cross Abstract: In recent years, neural networks have significantly advanced numerical solutions of partial differential equations (PDEs).
By Qi Gao, Kuang Huang, Xuan Di
arXiv:2608. 16475v1 Announce Type: cross Abstract: The Porous Medium Equation (PME), given by $u_t = \Delta(u^m)$ for $m > 1$, is a degenerate nonlinear parabolic partial differential equation that arises in various physical applications such as fluid flow in porous media, heat transfer in plasmas, and population dynamics.
By Noura Al Helwani, Sophie Moufawad, Nabil Nassif
arXiv:2607. 23349v1 Announce Type: new Abstract: We study the generative capabilities of Boltzmann machines to recover systems governed by the majority rule under critical conditions.
By Mauricio A. Valle, Gonzalo A. Ruz
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