The Deep Ritz Method for Parametric $p$-Dirichlet Problems

Autor:	Kaltenbach, Alex, Zeinhofer, Marius
Rok vydání:	2022
Předmět:	Mathematics - Numerical Analysis Computer Science - Machine Learning Computer Science - Neural and Evolutionary Computing Mathematics - Analysis of PDEs 68T07 35A35 65N15
Druh dokumentu:	Working Paper
Popis:	We establish error estimates for the approximation of parametric $p$-Dirichlet problems deploying the Deep Ritz Method. Parametric dependencies include, e.g., varying geometries and exponents $p\in (1,\infty)$. Combining the derived error estimates with quantitative approximation theorems yields error decay rates and establishes that the Deep Ritz Method retains the favorable approximation capabilities of neural networks in the approximation of high dimensional functions which makes the method attractive for parametric problems. Finally, we present numerical examples to illustrate potential applications. Comment: 30 pages, 11 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2207.01894 Zobrazit plný text záznamu View this record from Arxiv