Neural Networks to Approximate Solutions of Ordinary Differential Equations

  • Georg EngelEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 997)


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.


Ordinary differential equations Machine learning Surrogate model Neural network 



The financial support by the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development is gratefully acknowledged. We further acknowledge fruitful discussions with Gerald Schweiger, Claudio Gomes and Philip Ohnewein.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Christian Doppler Laboratory for Quality Assurance Methodologies for Autonomous Cyber-Physical Systems, Institute for Software TechnologyGraz University of TechnologyGrazAustria

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