@article {2022,
	title = {A comparison of reduced-order modeling approaches using artificial neural networks for PDEs with bifurcating solutions},
	journal = {ETNA - Electronic Transactions on Numerical Analysis},
	volume = {56},
	year = {2022},
	pages = {52{\textendash}65},
	doi = {10.1553/etna_vol56s52},
	author = {Martin W. Hess and Annalisa Quaini and Gianluigi Rozza}
}
@article {2017,
	title = {Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology},
	journal = {Journal of Computational Physics},
	volume = {344},
	year = {2017},
	month = {09/2017},
	pages = {557},
	chapter = {534},
	abstract = {<div class="abstract svAbstract " style="border: 0px; font-size: 16px; margin: 0px; padding: 0px; vertical-align: baseline; font-family: Arial, Helvetica, {\textquoteright}Lucida Sans Unicode{\textquoteright}, {\textquoteright}Microsoft Sans Serif{\textquoteright}, {\textquoteright}Segoe UI Symbol{\textquoteright}, STIXGeneral, {\textquoteright}Cambria Math{\textquoteright}, {\textquoteright}Arial Unicode MS{\textquoteright}, sans-serif; color: $\#$2e2e2e;" data-etype="ab"><p id="sp0250" style="border: 0px; margin: 0px 0px 9px; padding: 0px; vertical-align: baseline; word-spacing: -0.15ex;">We focus on reducing the computational costs associated with the hydrodynamic stability of solutions of the incompressible Navier{\textendash}Stokes equations for a Newtonian and viscous fluid in contraction{\textendash}expansion channels. In particular, we are interested in studying steady bifurcations, occurring when non-unique stable solutions appear as physical and/or geometric control parameters are varied. The formulation of the stability problem requires solving an eigenvalue problem for a partial differential operator. An alternative to this approach is the direct simulation of the flow to characterize the asymptotic behavior of the solution. Both approaches can be extremely expensive in terms of computational time. We propose to apply Reduced Order Modeling (ROM) techniques to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics. The application that motivated the present study is the onset of asymmetries (i.e., symmetry breaking bifurcation) in blood flow through a regurgitant mitral valve, depending on the Reynolds number and the regurgitant mitral valve orifice shape.</p></div>},
	keywords = {Parametrized Navier{\textendash}Stokes equations, Reduced basis method, Stability of flows, Symmetry breaking bifurcation},
	doi = {https://doi.org/10.1016/j.jcp.2017.05.010},
	author = {Giuseppe Pitton and Annalisa Quaini and Gianluigi Rozza}
}
