01267nas a2200145   4500008004100000245010200041210006900143300001000212520067900222100001600901700001400917700001700931700002100948856015200969       2019                        eng d00aWeighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs0 aWeighted Reduced Order Methods for Parametrized Partial Differen  a27-403 a<p>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.</p>1 aVenturi, L.1 aTorlo, D.1 aBallarin, F.1 aRozza, Gianluigi  uhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85084009379&doi=10.1007%2f978-3-030-04870-9_2&partnerID=40&md5=446bcc1f331167bbba67bc00fb170150