Publications associées à Discrétisation

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...

Walter De Gruyter Gmbh2024

An adaptive space-time algorithm for the incompressible Navier-Stokes equations

Marco Picasso, Samuel Dubuis

A space-time adaptive algorithm is presented to solve the incompressible Navier-Stokes equations. Time discretization is performed with the BDF2 method while continuous, piecewise linear anisotropic finite elements are used for the space discretization. Th ...

Academic Press Inc Elsevier Science2023

Discontinuous Galerkin methods for Fisher-Kolmogorov equation with application to a-synuclein spreading in Parkinson's disease

Alfio Quarteroni, Francesca Bonizzoni

This spreading of prion proteins is at the basis of brain neurodegeneration. This paper deals with the numerical modelling of the misfolding process of a-synuclein in Parkinson's disease. We introduce and analyse a discontinuous Galerkin method for the sem ...

Elsevier Science Sa2023

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

Alfio Quarteroni, Luca Dede'

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our mod ...

Wiley2023

lifex-cfd: An open-source computational fluid dynamics solver for cardiovascular applications

Alfio Quarteroni, Luca Dede', Marco Fedele

Computational fluid dynamics (CFD) is an important tool for the simulation of the cardiovascular function and dysfunction. Due to the complexity of the anatomy, the transitional regime of blood flow in the heart, and the strong mutual influence between the ...

Elsevier2023

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Giancarlo Ferrari Trecate, Luca Furieri, Clara Lucía Galimberti, Liang Xu

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem from the discretiz ...

2023

Mean Field Type Control With Species Dependent Dynamics via Structured Tensor Optimization

Isabel Haasler, Axel Ringh, Yiqiang Chen

In this letter we consider mean field type control problems with multiple species that have different dynamics. We formulate the discretized problem using a new type of entropy-regularized multimarginal optimal transport problems where the cost is a decomp ...

2023

Functional data analysis with rough sample paths?

Victor Panaretos, Neda Mohammadi Jouzdani

Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is imposed to allow for ...

TAYLOR & FRANCIS LTD2024

Lattice Green's function method for Atomistic/Continuum coupling

Ankit Gupta

Metal plasticity is an inherently multiscale phenomenon due to the complex long-range field of atomistic dislocations that are the primary mechanism for plastic deformation in metals. Atomistic/Continuum (A/C) coupling methods are computationally efficient ...

EPFL2023

Efficient lattice Green's function method for bounded domain problems

William Curtin, Max Ludwig Hodapp, Ankit Gupta

The lattice Green's function method (LGFM) is the discrete counterpart of the continuum boundary element method and is a natural approach for solving intrinsically discrete solid mechanics problems that arise in atomistic-continuum coupling methods. Here, ...

Wiley2022

Variational Methods For Continuous-Domain Inverse Problems: the Quest for the Sparsest Solution

Thomas Jean Debarre

The goal of this thesis is to study continuous-domain inverse problems for the reconstruction of sparse signals and to develop efficient algorithms to solve such problems computationally. The task is to recover a signal of interest as a continuous function ...

EPFL2022

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Andreas Loukas, Nikolaos Karalias

Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (I) not naturally amenable to gradient-based optimization, and (II) incompatible with deep lear ...

2022

A smooth basis for atomistic machine learning

Michele Ceriotti, Kevin Kazuki Huguenin-Dumittan, Filippo Bigi

Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighborhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to ...

AIP Publishing2022

Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals

Michaël Unser, Shayan Aziznejad, Thomas Jean Debarre

We present a novel framework for the reconstruction of 1D composite signals assumed to be a mixture of two additive components, one sparse and the other smooth, given a finite number of linear measurements. We formulate the reconstruction problem as a cont ...

2021

Numerical simulation of sediment dynamics with free surface flows

Arwa Mrad

We present a numerical model for the simulation of 3D mono-dispersed sediment dynamics in a Newtonian flow with free surfaces. The physical model is a macroscopic model for the transport of sediment based on a sediment concentration with a single momentum ...

EPFL2021

Optimal Policies for Age and Distortion in a Discrete-Time Model

Emre Telatar, Yunus Inan, Reka Inovan

We propose a simple model to study the tradeoff between timeliness and distortion, where different pieces of data have a different cost of not being sent. We pose the question of finding the optimal tradeoff as a policy design problem amenable to dynamic p ...

IEEE2021

A Space-Time Adaptive Algorithm to Illustrate the Lack of Collision of a Rigid Disk Falling in an Incompressible Fluid

Marco Picasso, Samuel Dubuis, Peter Wittwer

A space-time adaptive algorithm to solve the motion of a rigid disk in an incompressible Newtonian fluid is presented, which allows collision or quasi-collision processes to be computed with high accuracy. In particular, we recover the theoretical result p ...

WALTER DE GRUYTER GMBH2021

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Giacomo Garegnani

In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...

EPFL2021

Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

Dimitrios Gourzoulidis

This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...

EPFL2021

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Sebastian Krumscheid, Matthieu Claude Martin

We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

2021