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:2608.23022v1 Announce Type: cross
Abstract: The dynamics of particles in the early universe are described by Boltzmann equations, which involve high-dimensional phase-space integrals. Classical...
By Jonas Spinner, Jack Shergold
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:2512.07766v2 Announce Type: replace
Abstract: Neural networks are widely used, yet their analysis and verification remain challenging. We present a Lean~4 formalization covering both determinis...
By Matteo Cipollina, Michail Karatarakis, Freek Wiedijk