• Corpus ID: 237592730

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

  title={An artificial neural network approach to bifurcating phenomena in computational fluid dynamics},
  author={Federico Pichi and Francesco Ballarin and Gianluigi Rozza and Jan S. Hesthaven},
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 NavierStokes 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… 
Model order reduction for bifurcating phenomena in Fluid-Structure Interaction problems
This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coandă effect, in a multi-physics setting involving fluid and solid media, and provides several insights on how the introduction of an elastic structure influences the bifURcating behaviour.
Model Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier-Stokes Equations
The findings establish sparse polynomial interpolation as another instrument in the toolbox of methods for breaking the curse of dimensionality.
Fast and accurate numerical simulations for the study of coronary artery bypass grafts by artificial neural network
An artificial neural network, an empirical interpolation method, and a non-uniform rational basis spline model for orthogonal decomposition are described.
A hybrid partitioned deep learning methodology for moving interface and fluid–structure interaction
In this work, we present a hybrid partitioned deep learning framework for the reduced-order modeling of moving interfaces and predicting fluid-structure interaction. Using the discretized
Finite element based model order reduction for parametrized one-way coupled steady state linear thermomechanical problems
This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermo-mechanical problems in a finite element setting. We apply Proper Orthogonal


Computational reduction strategies for the detection of steady bifurcations in incompressible fluid-dynamics: Applications to Coanda effect in cardiology
Reduced Order Modeling techniques are proposed to apply to reduce the demanding computational costs associated with the detection of a type of steady bifurcations in fluid dynamics.
Reduced Basis Approaches for Parametrized Bifurcation Problems held by Non-linear Von Kármán Equations
This work focuses on the detection of the buckling phenomena and bifurcation analysis of the parametric Von Karm\'an plate equations based on reduced order methods and spectral analysis, and carries out anAnalysis of the linearized eigenvalue problem, that allows to better understand the physical behaviour near the bIfurcation points.
Driving bifurcating parametrized nonlinear PDEs by optimal control strategies: application to Navier-Stokes equations with model order reduction
This work deals with optimal control problems as a strategy to drive bifurcating solutions of nonlinear parametrized partial differential equations towards a desired branch, and describes how optimal control allows to change the solution profile and the stability of state solution branches.
On the use of POD-based ROMs to analyze bifurcations in some dissipative systems
Abstract This paper deals with the use of POD-based reduced order models to construct bifurcation diagrams (which requires calculating steady and time-dependent attractors) in complex bifurcation
Non-intrusive reduced order modeling of nonlinear problems using neural networks
We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial differential equations (PDEs). The method extracts a reduced basis from a collection of high-fidelity
Reduced basis model order reduction for Navier–Stokes equations in domains with walls of varying curvature
ABSTRACT We consider the Navier–Stokes equations in a channel with a narrowing and walls of varying curvature. By applying the empirical interpolation method to generate an affine parameter
On the Application of Reduced Basis Methods to Bifurcation Problems in Incompressible Fluid Dynamics
The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising and the proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams.
The lid-driven right-angled isosceles triangular cavity flow
We employ lattice Boltzmann simulation to numerically investigate the two-dimensional incompressible flow inside a right-angled isosceles triangular enclosure driven by the tangential motion of its
A localized reduced-order modeling approach for PDEs with bifurcating solutions
Abstract Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the
Non-intrusive reduced order modeling of unsteady flows using artificial neural networks with application to a combustion problem
The proposed reduced-basis method, referred as the POD-NN, fully decouples the online stage and the high-fidelity scheme, and is thus able to provide fast and reliable solutions of complex unsteady flows.