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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
Journal of Machine Learning for Modeling and Computing

ISSN Печать: 2689-3967
ISSN Онлайн: 2689-3975

Journal of Machine Learning for Modeling and Computing

DOI: 10.1615/.2020034093
pages 75-95

MACHINE LEARNING FOR TRAJECTORIES OF PARAMETRIC NONLINEAR DYNAMICAL SYSTEMS

Roland Pulch
Institute for Mathematics and Computer Science, University of Greifswald, Walther-Rathenau-Str. 47, D-17489 Greifswald, Germany
Maha Youssef
Institute for Mathematics and Computer Science, University of Greifswald, Walther-Rathenau-Str. 47, D-17489 Greifswald, Germany

Краткое описание

We investigate parameter-dependent nonlinear dynamical systems consisting of ordinary differential equations or differential-algebraic equations. A single quantity of interest is observed, which depends on the solution of a system. Our aim is to determine efficient approximations of the trajectories belonging to the quantity of interest in the time domain. We arrange a set of samples including trajectories of this quantity. A proper orthogonal decomposition of this data yields a reduced basis. Consequently, the mapping from the parameter domain to the basis coefficients is approximated. We apply machine learning with artificial neural networks for this approximation, where the degrees of freedom are fitted to the data of the sample trajectories in a nonlinear optimization. Alternatively, we consider a polynomial approximation, which is identified by regression, for comparison. Furthermore, concepts of sensitivity analysis are examined to characterize the impact of an input parameter on the output of the exact mapping or the approximations from the neural networks. We present results of numerical computations for examples of nonlinear dynamical systems.

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