approximation theory 1graph neural networks 1message passing 1permutation equivariance 1random features 1universality 1
From the 1 of 21 linked papers with an AI index.
Showing math.NAShow all
3 papers · 1 filter
math.NA2026
Random Neural Network Expressivity for Non-Linear Partial Differential Equations
Muhammed Ali Mehmood, Lukas Gonon
Neural networks with randomly generated hidden weights (RaNNs) have been extensively studied, both as a standalone learning method and as an initialization for fully trainable deep…
math.NA2025
Error analysis for the deep Kolmogorov method
Iulian Cîmpean, Thang Do, Lukas Gonon +2
The deep Kolmogorov method is a simple and popular deep learning based method for approximating solutions of partial differential equations (PDEs) of the Kolmogorov type. In this w…
math.NA2024
An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning
Lukas Gonon, Arnulf Jentzen, Benno Kuckuck +3
The approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of meth…