01419nas a2200121   4500008004100000245010700041210006900148520098100217100002001198700002101218700002101239856003701260       2020                        eng d00aA Reduced Order technique to study bifurcating phenomena: application to the Gross-Pitaevskii equation0 aReduced Order technique to study bifurcating phenomena applicati3 a<p>We propose a computationally efficient framework to treat nonlinear partial differential equations having bifurcating solutions as one or more physical control parameters are varied. Our focus is on steady bifurcations. Plotting a bifurcation diagram entails computing multiple solutions of a parametrized, nonlinear problem, which can be extremely expensive in terms of computational time. In order to reduce these demanding computational costs, our approach combines a continuation technique and Newton's method with a Reduced Order Modeling (ROM) technique, suitably supplemented with a hyper-reduction method. To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schrödinger equation, called Gross-Pitaevskii equation, as one or two physical parameters are varied. In the two parameter study, we show that our approach is 60 times faster in constructing a bifurcation diagram than a standard Full Order Method.</p>1 aPichi, Federico1 aQuaini, Annalisa1 aRozza, Gianluigi  uhttps://arxiv.org/abs/1907.07082