@inbook{10283d24d2454fd0ab24bff359de4497,

title = "Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs",

abstract = "In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method. A numerical example on a parametrized elasticity problem is shown.",

keywords = "weighted reduced order models, uncertainty quantification, weighted reduced order models, uncertainty quantification",

author = "Francesco Ballarin and Luca Venturi and Davide Torlo and Gianluigi Rozza",

year = "2019",

doi = "10.1007/978-3-030-04870-9_2",

language = "English",

isbn = "978-3-030-04869-3",

series = "POLITO SPRINGER SERIES",

pages = "27--40",

booktitle = "Uncertainty modeling for engineering applications",

}