Semi-autonomous neural networks differential equation solver

José Delpiano, Pablo Zegers

Research output: Contribution to conferencePaper

2 Scopus citations

Abstract

The finite element method frequently needs complex grids to solve partial differential equations. This becomes more serious in highly dimensional problems and complicated geometries. In this article we present an improved gridless solver, which trains a neural network to fit the differential equation solution. The advantage of a gridless method is its easier scalability to problems with a high number of dimensions. A smart stopping criterion, based on statistical learning theory concepts, makes the method more autonomous than preceding algorithms. The proposed method uses a simple rule to include the boundary conditions in the error measure of the network. For validation, we show the results of solving some simple first and second order equations and one from a classical application problem.
Original languageAmerican English
Pages1863-1869
Number of pages7
DOIs
StatePublished - 1 Jan 2006
EventIEEE International Conference on Neural Networks - Conference Proceedings -
Duration: 1 Jan 2006 → …

Conference

ConferenceIEEE International Conference on Neural Networks - Conference Proceedings
Period1/01/06 → …

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