Neural Networks to Approximate Solutions of Ordinary Differential Equations

Georg Engel

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Abstract

We discuss surrogate data models based on machine learning as approximation to the solution of an ordinary differential equation. The surrogate model is designed to work like a simulation unit, i.e. it takes a few recent points of the trajectory and the input variables at the given time and calculates the next point of the trajectory as output. The Dahlquist test equation and the Van der Pol oscillator are considered as case studies. Computational demand and accuracy in terms of local and global error are discussed. Parameter studies are performed to discuss the sensitivity of the method.

Original languageEnglish
Title of host publicationIntelligent Computing - Proceedings of the 2019 Computing Conference
EditorsKohei Arai, Rahul Bhatia, Supriya Kapoor
PublisherSpringer-Verlag Italia
Pages776-784
Number of pages9
ISBN (Print)9783030228705
DOIs
Publication statusPublished - 1 Jan 2019
EventComputing Conference, 2019 - London, United Kingdom
Duration: 16 Jul 201917 Jul 2019

Publication series

NameAdvances in Intelligent Systems and Computing
Volume997
ISSN (Print)2194-5357
ISSN (Electronic)2194-5365

Conference

ConferenceComputing Conference, 2019
CountryUnited Kingdom
CityLondon
Period16/07/1917/07/19

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Keywords

  • Machine learning
  • Neural network
  • Ordinary differential equations
  • Surrogate model

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science(all)

Cite this

Engel, G. (2019). Neural Networks to Approximate Solutions of Ordinary Differential Equations. In K. Arai, R. Bhatia, & S. Kapoor (Eds.), Intelligent Computing - Proceedings of the 2019 Computing Conference (pp. 776-784). (Advances in Intelligent Systems and Computing; Vol. 997). Springer-Verlag Italia. https://doi.org/10.1007/978-3-030-22871-2_54