An artificial neural network approach to bifurcating phenomena in computational fluid dynamics

This work deals with the investigation of bifurcating fluid phenomena using a reduced order modelling setting aided by artificial neural networks. We discuss the POD-NN approach dealing with non-smooth solutions set of nonlinear parametrized PDEs. Thus, we study the Navier-Stokes equations describing: (i) the Coanda effect in a channel, and (ii) the lid driven triangular cavity flow, in a physical/geometrical multi-parametrized setting, considering the effects of the domain's configuration on the position of the bifurcation points. Finally, we propose a reduced manifold-based bifurcation diagram for a non-intrusive recovery of the critical points evolution. Exploiting such detection tool, we are able to efficiently obtain information about the pattern flow behaviour, from symmetry breaking profiles to attaching/spreading vortices, even in the advection-dominated regime.

Automated summary

This study investigates bifurcating fluid phenomena using a reduced order modelling approach with the help of artificial neural networks. The authors discuss a POD-NN approach for dealing with non-smooth solutions of nonlinear parametrized PDEs. They apply this approach to study the Coanda effect in a channel and the lid-driven triangular cavity flow, considering the effects of domain configuration on bifurcation points. Additionally, they propose a reduced manifold-based bifurcation diagram for efficiently recovering critical points evolution and analyzing pattern flow behavior.