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Andrea Manzoni

Cette personne a quitté l’EPFL

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Publications associées (42)

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Efficient approximation of cardiac mechanics through reduced-order modeling with deep learning-based operator approximation

Alfio Quarteroni, Andrea Manzoni

Reducing the computational time required by high-fidelity, full-order models (FOMs) for the solution of problems in cardiac mechanics is crucial to allow the translation of patient-specific simulations into clinical practice. Indeed, while FOMs, such as th ...

Wiley2023

Reduced Models for Optimal Control, Shape Optimization and Inverse Problems in Haemodynamics

Andrea Manzoni

The objective of this thesis is to develop reduced models for the numerical solution of optimal control, shape optimization and inverse problems. In all these cases suitable functionals of state variables have to be minimized. State variables are solutions ...

EPFL2012

An Adjoint-Based Method For The Numerical Approximation Of Shape Optimization Problems In Presence Of Fluid-Structure Interaction

Andrea Manzoni

In this work, we propose both a theoretical framework and a numerical method to tackle shape optimization problems related with fluid dynamics applications in presence of fluid-structure interactions. We present a general framework relying on the solution ...

EDP SCIENCES S A2018

An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

In this paper we propose a new, purely algebraic, Petrov-Galerkin reduced basis (RB) method to solve the parametrized Stokes equations, where parameters serve to identify the (variable) domain geometry. Our method is obtained as an algebraic least squares ...

ELSEVIER SCIENCE SA2019

The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications

Alfio Quarteroni, Andrea Manzoni, Christian Vergara

Mathematical and numerical modelling of the cardiovascular system is a research topic that has attracted remarkable interest from the mathematical community because of its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseas ...

Cambridge Univ Press2017

Model order reduction in fluid dynamics: challenges and perspectives

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni, Toni Mikael Lassila

This chapter reviews techniques of model reduction of fluid dynamics systems. Fluid systems are known to be difficult to reduce efficiently due to several reasons. First of all, they exhibit strong nonlinearities – which are mainly related either to nonlin ...

Springer2013

POD-Enhanced Deep Learning-Based Reduced Order Models for the Real-Time Simulation of Cardiac Electrophysiology in the Left Atrium

Alfio Quarteroni, Andrea Manzoni

The numerical simulation of multiple scenarios easily becomes computationally prohibitive for cardiac electrophysiology (EP) problems if relying on usual high-fidelity, full order models (FOMs). Likewise, the use of traditional reduced order models (ROMs) ...

FRONTIERS MEDIA SA2021

Fast simulations of patient-specific haemodynamics of coronary artery bypass grafts based on a POD-Galerkin method and a vascular shape parametrization

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni, Elena Faggiano

In this work a reduced-order computational framework for the study of haemodynamics in three-dimensional patient-specific configurations of coronary artery bypass grafts dealing with a wide range of scenarios is proposed. We combine several efficient algor ...

Elsevier2016

A matrix DEIM technique for model reduction of nonlinear parametrized problems in cardiac mechanics

Alfio Quarteroni, Andrea Manzoni

When relying on Newton iterations to solve nonlinear problems in the context of Reduced Basis (RB) methods, the assembling of the RB arrays during the online stage depends on the dimension of the underlying high-fidelity approximation. This is more of an i ...

Elsevier Science Sa2017

Hyper-reduced order models for parametrized unsteady Navier-Stokes equations on domains with variable shape

Andrea Manzoni, Niccolò Dal Santo

In this work, we set up a new, general, and computationally efficient way to tackle parametrized fluid flows modeled through unsteady Navier-Stokes equations defined on domains with variable shape, when relying on the reduced basis method. We easily descri ...

SPRINGER2019

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

Andrea Manzoni

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential ...

Iop Publishing Ltd2017

A reduced-order strategy for solving inverse Bayesian shape identication problems in physiological flows

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni, Toni Mikael Lassila

A reduced-order strategy based on the reduced basis (RB) method is developed for the efficient numerical solution of statistical inverse problems governed by PDEs in domains of varying shape. Usual discretization techniques are infeasible in this context, ...

Springer2013

Multi space reduced basis preconditioners for parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

We introduce a two-level preconditioner for the efficient solution of large scale saddle point linear systems arising from the finite element (FE) discretization of parametrized Stokes equations. This preconditioner extends the Multi Space Reduced Basis (M ...

PERGAMON-ELSEVIER SCIENCE LTD2019

Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni, Toni Mikael Lassila

We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting ar ...

EDP Sciences2013

Efficient model reduction of parametrized systems by matrix discrete empirical interpolation

Andrea Manzoni, Federico Negri

In this work, we apply a Matrix version of the so-called Discrete Empirical Interpolation (MDEIM) for the efficient reduction of nonaffine parametrized systems arising from the discretization of linear partial differential equations. Dealing with affinely ...

Elsevier2015

Data integration for the numerical simulation of cardiac electrophysiology

Alfio Quarteroni, Andrea Manzoni, Luca Dede', Stefano Pagani

The increasing availability of extensive and accurate clinical data is rapidly shaping cardiovascular care by improving the understanding of physiological and pathological mechanisms of the cardiovascular system and opening new frontiers in designing thera ...

WILEY2021

A Computational Study of the Electrophysiological Substrate in Patients Suffering From Atrial Fibrillation

Alfio Quarteroni, Andrea Manzoni

In the context of cardiac electrophysiology, we propose a novel computational approach to highlight and explain the long-debated mechanisms behind atrial fibrillation (AF) and to reliably numerically predict its induction and sustainment. A key role is pla ...

FRONTIERS MEDIA SA2021

Deep learning-based reduced order models in cardiac electrophysiology

Alfio Quarteroni, Andrea Manzoni, Luca Dede'

Predicting the electrical behavior of the heart, from the cellular scale to the tissue level, relies on the numerical approximation of coupled nonlinear dynamical systems. These systems describe the cardiac action potential, that is the polarization/depola ...

2020

A numerical investigation of multi space reduced basis preconditioners for parametrized elliptic advection-diffusion equations

Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

We analyze the numerical performance of a preconditioning technique recently proposed in [1] for the efficient solution of parametrized linear systems arising from the finite element (FE) discretization of parameter-dependent elliptic partial differential ...

Walter de Gruyter GmbH2017

Reduced basis approximation and a posteriori error estimation for Stokes flows in parametrized geometries: roles of the inf-sup stability constants

Gianluigi Rozza, Andrea Manzoni

In this paper we review and we extend the reduced basis approximation and a posteriori error estimation for steady Stokes flows in affinely parametrized geometries, focusing on the role played by the Brezzi's and Babuska's stability constants. The crucial ...

Springer2013