An artificial neural network approach to bifurcating phenomena in computational fluid dynamics
arXiv:2109.10765 · doi:10.1016/j.compfluid.2023.105813
Abstract
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 at high Reynolds numbers.
28 pages, 22 figures
References in corpus (6)
- PyTorch: An Imperative Style, High-Performance Deep Learning Library
- Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEs
- Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier-Stokes equations with model order reduction
- Model order reduction for bifurcating phenomena in Fluid-Structure Interaction problems
- Learning normal form autoencoders for data-driven discovery of universal,parameter-dependent governing equations
- Reduced order models for the buckling of hyperelastic beams
Cited by in corpus (5)
- Model order reduction for bifurcating phenomena in Fluid-Structure Interaction problems
- Compatible finite element interpolated neural networks
- Geometrically Parametrised Reduced Order Models for the Study of Hysteresis of the Coanda Effect in Finite Element-based Incompressible Fluid Dynamics
- Sparse Identification for bifurcating phenomena in Computational Fluid Dynamics
- Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEs