Machine Learning to Approximate Solutions of Ordinary Differential Equations: Neural Networks vs. Linear Regressors

Georg Engel*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


We discuss surrogate models based on machine learning as approximation to the solution of an ordinary differential equation. Neural networks and a multivariate linear regressor are assessed for this application. Both of them show a satisfactory performance for the considered case study of a damped perturbed harmonic oscillator. The interface of the surrogate model is designed to work similar to a solver of an ordinary differential equation, respectively a simulation unit. Computational demand and accuracy in terms of local and global error are discussed. Parameter studies are performed to discuss the sensitivity of the method and to tune the performance.

Original languageEnglish
Title of host publicationComputational Science – ICCS 2019 - 19th International Conference, Proceedings
EditorsJoão M.F. Rodrigues, Pedro J.S. Cardoso, Jânio Monteiro, Roberto Lam, Valeria V. Krzhizhanovskaya, Michael H. Lees, Peter M.A. Sloot, Jack J. Dongarra
PublisherSpringer-Verlag Italia
Number of pages9
ISBN (Print)9783030227463
Publication statusPublished - 1 Jan 2019
Event19th International Conference on Computational Science, ICCS 2019 - Faro, Portugal
Duration: 12 Jun 201914 Jun 2019

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11539 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Conference on Computational Science, ICCS 2019


  • Machine learning
  • Multivariate linear regressor
  • Neural network
  • Ordinary differential equations
  • Surrogate model

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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