A reduced order model formulation for left atrium flow: an atrial fibrillation case.

A data-driven reduced order model (ROM) based on a proper orthogonal decomposition-radial basis function (POD-RBF) approach is adopted in this paper for the analysis of blood flow dynamics in a patient-specific case of atrial fibrillation (AF). The full order model (FOM) is represented by incompressible Navier-Stokes equations, discretized with a finite volume (FV) approach. Both the Newtonian and the Casson's constitutive laws are employed.

Generative adversarial reduced order modelling.

In this work, we present GAROM, a new approach for reduced order modeling (ROM) based on generative adversarial networks (GANs). GANs attempt to learn to generate data with the same statistics of the underlying distribution of a dataset, using two neural networks, namely discriminator and generator. While widely applied in many areas of deep learning, little research is done on their application for ROM, i.

A multifidelity approach coupling parameter space reduction and nonintrusive POD with application to structural optimization of passenger ship hulls.

Nowadays, the shipbuilding industry is facing a radical change toward solutions with a smaller environmental impact. This can be achieved with low emissions engines, optimized shape designs with lower wave resistance and noise generation, and by reducing the metal raw materials used during the manufacturing. This work focuses on the last aspect by presenting a complete structural optimization pipeline for modern passenger ship hulls which exploits advanced model order reduction techniques to reduce the dimensionality of both input parameters and outputs of interest.

Novel methodologies for solving the inverse unsteady heat transfer problem of estimating the boundary heat flux in continuous casting molds.

In this article, we investigate the estimation of the transient mold-slab heat flux in continuous casting molds given some thermocouples measurements in the mold plates. Mathematically, we can see this problem as the estimation of a Neumann boundary condition given pointwise state observations in the interior of the domain. We formulate it in a deterministic inverse problem setting.

Kernel-based active subspaces with application to computational fluid dynamics parametric problems using the discontinuous Galerkin method.

Nonlinear extensions to the active subspaces method have brought remarkable results for dimension reduction in the parameter space and response surface design. We further develop a kernel-based nonlinear method. In particular, we introduce it in a broader mathematical framework that contemplates also the reduction in parameter space of multivariate objective functions.

Projection Based Semi-Implicit Partitioned Reduced Basis Method for Fluid-Structure Interaction Problems.

In this manuscript a POD-Galerkin based Reduced Order Model for unsteady Fluid-Structure Interaction problems is presented. The model is based on a partitioned algorithm, with semi-implicit treatment of the coupling conditions. A Chorin-Temam projection scheme is applied to the incompressible Navier-Stokes problem, and a Robin coupling condition is used for the coupling between the fluid and the solid.

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. Taking into consideration a fluid-structure interaction problem, we aim at generalizing previous works towards a more reliable description of the physics involved. In particular, we provide several insights on how the introduction of an elastic structure influences the bifurcating behavior.

Non-intrusive PODI-ROM for patient-specific aortic blood flow in presence of a LVAD device.

Left ventricular assist devices (LVADs) are used to provide haemodynamic support to patients with critical cardiac failure. Severe complications can occur because of the modifications of the blood flow in the aortic region. In this work, the effect of a continuous flow LVAD device on the aortic flow is investigated by means of a non-intrusive reduced order model (ROM) built using the proper orthogonal decomposition with interpolation (PODI) method based on radial basis functions (RBF).

An optimal control approach to determine resistance-type boundary conditions from in-vivo data for cardiovascular simulations.

The choice of appropriate boundary conditions is a fundamental step in computational fluid dynamics (CFD) simulations of the cardiovascular system. Boundary conditions, in fact, highly affect the computed pressure and flow rates, and consequently haemodynamic indicators such as wall shear stress (WSS), which are of clinical interest. Devising automated procedures for the selection of boundary conditions is vital to achieve repeatable simulations.

Reduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation.

Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease. In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters.

Dimension reduction in heterogeneous parametric spaces with application to naval engineering shape design problems.

We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameter space reduction. The physical problem considered is the one of the simulation of the hydrodynamic flow past the hull of a ship advancing in calm water. Such problem is extremely relevant at the preliminary stages of the ship design, when several flow simulations are typically carried out by the engineers to assess the dependence of the hull total resistance on the geometrical parameters of the hull, and others related with flows and hull properties.

Numerical modeling of hemodynamics scenarios of patient-specific coronary artery bypass grafts.

A fast computational framework is devised to the study of several configurations of patient-specific coronary artery bypass grafts. This is especially useful to perform a sensitivity analysis of the hemodynamics for different flow conditions occurring in native coronary arteries and bypass grafts, the investigation of the progression of the coronary artery disease and the choice of the most appropriate surgical procedure. A complete pipeline, from the acquisition of patient-specific medical images to fast parameterized computational simulations, is proposed.

A reduced computational and geometrical framework for inverse problems in hemodynamics.

The solution of inverse problems in cardiovascular mathematics is computationally expensive. In this paper, we apply a domain parametrization technique to reduce both the geometrical and computational complexities of the forward problem and replace the finite element solution of the incompressible Navier-Stokes equations by a computationally less-expensive reduced-basis approximation. This greatly reduces the cost of simulating the forward problem.

Simulation-based uncertainty quantification of human arterial network hemodynamics.

This work aims at identifying and quantifying uncertainties from various sources in human cardiovascular system based on stochastic simulation of a one-dimensional arterial network. A general analysis of different uncertainties and probability characterization with log-normal distribution of these uncertainties is introduced. Deriving from a deterministic one-dimensional fluid-structure interaction model, we establish the stochastic model as a coupled hyperbolic system incorporated with parametric uncertainties to describe the blood flow and pressure wave propagation in the arterial network.

Model reduction techniques for fast blood flow simulation in parametrized geometries.

In this paper, we propose a new model reduction technique aimed at real-time blood flow simulations on a given family of geometrical shapes of arterial vessels. Our approach is based on the combination of a low-dimensional shape parametrization of the computational domain and the reduced basis method to solve the associated parametrized flow equations. We propose a preliminary analysis carried on a set of arterial vessel geometries, described by means of a radial basis functions parametrization.