Feedforward neural nets as discretization schemes for ODEs and DAEs
type: Item
instance of: scholarly article
title: Feedforward neural nets as discretization schemes for ODEs and DAEs
zbMATH Open document ID: 0889.65072
DOI: 10.1016/S0377-0427(97)00085-X
author: R. Gerstberger
author: Peter Rentrop
published in: Journal of Computational and Applied Mathematics
publication date: 1998-06-18T00:00:00Z
review text: Because of their neurophysical origin neural nets can be studied for classification tasks, approximation properties or iterative algorithms. They can be interpreted as a distributed or massively parallel computer, where each unit accumulates a scalar product and computes a one-dimensional nonlinear activation function. A supervised learning strategy defines a nonlinear least squares problem, which is solved by gradient techniques such as backpropagation. Interpreting the weights in a net as state variable feedforward neural nets can be designed as numerical discretization schemes for ordinary differential equations (ODEs) and differential-algebraic equations (DAEs). The net architecture for the implicit Euler scheme is presented here and some experiments are given. The net approach is of interest for the overdetermined index-3 approach of DAEs from multibody system dynamics. More generally, these nets determine a parallel shooting-type algorithm.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 68T05
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34A09
zbMATH DE Number: 1084093
zbMATH Keywords: parallel computation
zbMATH Keywords: neural nets
zbMATH Keywords: iterative algorithms
zbMATH Keywords: learning strategy
zbMATH Keywords: nonlinear least squares problem
zbMATH Keywords: feedforward neural nets
zbMATH Keywords: index-3
zbMATH Keywords: multibody system dynamics
zbMATH Keywords: parallel shooting-type algorithm
reviewed by: Michael Sever
describes a project that uses: RODAS
MaRDI profile type: Publication
cites work: Q4000061
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full work available at URL: s0377-0427(97)00085-x
OpenAlex ID: W2087262774
description: scientific article; zbMATH DE number 1084093