@article {2020,
	title = {A reduced order modeling technique to study bifurcating phenomena: Application to the gross-pitaevskii equation},
	journal = {SIAM Journal on Scientific Computing},
	year = {2020},
	abstract = {<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{\textquoteright}s method with a reduced order modeling (ROM) technique, suitably supplemented with a hyperreduction method. To demonstrate the effectiveness of our ROM approach, we trace the steady solution branches of a nonlinear Schr{\"o}dinger equation, called the 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>},
	doi = {10.1137/20M1313106},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85096768803\&doi=10.1137\%2f20M1313106\&partnerID=40\&md5=47d6012d10854c2f9a04b9737f870592},
	author = {Federico Pichi and Annalisa Quaini and Gianluigi Rozza}
}
