The effect of time discretization on the solution of parabolic PDEs with ANNs

Autor:	Calabrò, Francesco, Cuomo, Salvatore, di Serafino, Daniela, Izzo, Giuseppe, Messina, Eleonora
Rok vydání:	2022
Předmět:	Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	We investigate the resolution of parabolic PDEs via Extreme Learning Machine (ELMs) Neural Networks, which have a single hidden layer and can be trained at a modest computational cost as compared with Deep Learning Neural Networks. Our approach addresses the time evolution by applying classical ODEs techniques and uses ELM-based collocation for solving the resulting stationary elliptic problems. In this framework, the $\theta$-method and Backward Difference Formulae (BDF) techniques are investigated on some linear parabolic PDEs that are challeging problems for the stability and accuracy properties of the methods. The results of numerical experiments confirm that ELM-based solution techniques combined with BDF methods can provide high-accuracy solutions of parabolic PDEs. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.00452 Zobrazit plný text záznamu View this record from Arxiv