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ISSN Печать: 2152-5080
ISSN Онлайн: 2152-5099
Indexed in
POLYNOMIAL CHAOS FOR SEMIEXPLICIT DIFFERENTIAL ALGEBRAIC EQUATIONS OF INDEX 1
Краткое описание
Mathematical modeling of technical applications often yields systems of differential algebraic equations. Uncertainties of physical parameters can be considered by the introduction of random variables. A corresponding uncertainty quantification requires one to solve the stochastic model. We focus on semiexplicit systems of nonlinear differential algebraic equations with index 1. The stochastic model is solved using the expansion of the generalised polynomial chaos. We investigate both the stochastic collocation technique and the stochastic Galerkin method to determine the unknown coefficient functions. In particular, we analyze the index of the larger coupled systems, which result from the stochastic Galerkin method. Numerical simulations of test examples are presented, where the two approaches are compared with respect to their efficiency.
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Pulch Roland, Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations, Journal of Computational and Applied Mathematics, 262, 2014. Crossref
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Pulch Roland, Stochastic Galerkin Methods for Analyzing Equilibria of Random Dynamical Systems, SIAM/ASA Journal on Uncertainty Quantification, 1, 1, 2013. Crossref
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Pulch Roland, ter Maten E. Jan W., Augustin Florian, Sensitivity analysis and model order reduction for random linear dynamical systems, Mathematics and Computers in Simulation, 111, 2015. Crossref
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Wu Kailiang, Xiu Dongbin, Numerical aspects for approximating governing equations using data, Journal of Computational Physics, 384, 2019. Crossref
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Pulch Roland, Polynomial-Chaos Based Methods for Differential Algebraic Equations with Random Parameters, in Progress in Industrial Mathematics at ECMI 2012, 19, 2014. Crossref
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Pulch Roland, Model order reduction for random nonlinear dynamical systems and low-dimensional representations for their quantities of interest, Mathematics and Computers in Simulation, 166, 2019. Crossref
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Chen Zhen, Xiu Dongbin, On generalized residual network for deep learning of unknown dynamical systems, Journal of Computational Physics, 438, 2021. Crossref
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Saha Premjit, Singh Tarunraj, Dargush Gary, Uncertainty Quantification of Differential Algebraic Equations Using Polynomial Chaos, Journal of Computational and Nonlinear Dynamics, 16, 10, 2021. Crossref
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Churchill Victor, Xiu Dongbin, LEARNING FINE SCALE DYNAMICS FROM COARSE OBSERVATIONS VIA INNER RECURRENCE, Journal of Machine Learning for Modeling and Computing, 3, 3, 2022. Crossref