@inproceedings{dfc406a0456f4016afce7ca20df16bef,

title = "Neural Networks to Approximate Solutions of Ordinary Differential Equations",

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.",

keywords = "Machine learning, Neural network, Ordinary differential equations, Surrogate model",

author = "Georg Engel",

year = "2019",

month = "1",

day = "1",

doi = "10.1007/978-3-030-22871-2_54",

language = "English",

isbn = "9783030228705",

series = "Advances in Intelligent Systems and Computing",

publisher = "Springer-Verlag Italia",

pages = "776--784",

editor = "Kohei Arai and Rahul Bhatia and Supriya Kapoor",

booktitle = "Intelligent Computing - Proceedings of the 2019 Computing Conference",

address = "Italy",

}