Publications associées à Méthode de variation des constantes

High-order geometric integrators for the variational Gaussian wavepacket dynamics and application to vibronic spectra at finite temperature

Molecular quantum dynamics simulations are essential for understanding many fundamental phenomena in physics and chemistry. They often require solving the time-dependent Schrödinger equation for molecular nuclei, which is challenging even for medium-sized ...

EPFL2024

Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls

Boris Buffoni

Using a variational method, we prove the existence of heteroclinic solutions for a 6-dimensional system of ordinary differential equations. We derive this system from the classical Benard-Rayleigh problem near the convective instability threshold. The cons ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

Julien Gilles Edgar Gateau

This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated homeostatic systems experiencing multiple excitations. It focuses on the evolution of a signal (e.g., heart rate) before, during, and after e ...

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD2020

Numerical methods for deterministic and stochastic differential equations with multiple scales and high contrasts

Giacomo Rosilho De Souza

Mathematical models involving multiple scales are essential for the description of physical systems. In particular, these models are important for the simulation of time-dependent phenomena, such as the heat flow, where the Laplacian contains mixed and ind ...

EPFL2020

Range-based underwater target localization using an autonomous surface vehicle: Observability analysis

In the field of marine robotics, the problem of range based underwater target localization can be defined as that of localizing an unknown - fixed or moving - target from a surface vehicle called the tracker, using range information available about the tar ...

2018

Redefining solubility parameters: Bulk and surface properties from unified molecular descriptors

Vassily Hatzimanikatis

The central objective of this work is to revisit the development of the widely used solubility parameters and linear solvation energy relationships (LSER) and seek interconnections and possibilities for secure exchange of information. Partial solvation par ...

Academic Press Ltd- Elsevier Science Ltd2017

Dynamical Low Rank approximation of PDEs with random parameters

Eleonora Musharbash

In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...

EPFL2017

Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

Michaël Unser, Julien René Pierre Fageot, John Paul Ward

Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total variation by con ...

2017

Molecular thermodynamics of metabolism: hydration quantities and the equation-of-state approach

Vassily Hatzimanikatis, Meriç Ataman, Noushin Hadadi

The present work is part of a series of papers aiming at a thorough understanding of the thermodynamics of metabolism over a broad range of external conditions. The focus here is on the systematic study of solvation/hydration of a variety of fluids via an ...

Royal Soc Chemistry2016

Multi-index Monte Carlo: when sparsity meets sampling

Fabio Nobile

We propose and analyze a novel Multi Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a s ...

Springer2016

Characterization of the Solution of Linear Inverse Problems with Generalized TV Regularization

Michaël Unser

Ill-posed inverse problems are often constrained by imposing a bound on the total variation of the solution. Here, we consider a generalized version of total-variation regularization that is tied to some differential operator L. We then show that the gener ...

OSA2016

Directional Input Adaptation in Parametric Optimal Control Problems

Dominique Bonvin, Benoît Chachuat, Saurabh Anand Deshpande

This paper deals with input adaptation in dynamic processes in order to guarantee feasible and optimal operation despite the presence of uncertainty. The proposed adaptation consists in using the nominal optimal inputs and adding appropriately designed inp ...

Society for Industrial and Applied Mathematics2012

Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications

Michaël Unser, Aurélien Bourquard, Stamatios Lefkimmiatis

We present nonquadratic Hessian-based regularization methods that can be effectively used for image restoration problems in a variational framework. Motivated by the great success of the total-variation (TV) functional, we extend it to also include second- ...

IEEE2012

Localization of Diffusive Sources Using Spatiotemporal Measurements

Martin Vetterli, Pier Luigi Dragotti, Yue Lu

Consider a diffusion field induced by a finite number of localized and instantaneous sources. In this paper, we study the problem of estimating these sources (including their intensities, spatial locations, and activation time) from the spatiotemporal samp ...

2011

Sparse Source Recovery from Boundary Measurements using an Extension of Prony's Method for the Poisson Equation

Djano Kandaswamy

Electroencephalography (EEG) is a key modality to monitor brain activity with high temporal resolution. EEG makes use of an array of electrodes to measure the electrical potential on the scalp. While most traditional EEG analyses have looked at EEG rhythms ...

EPFL2011

A Signal Processing Approach to Generalized 1-D Total Variation

Dimitri Nestor Alice Van De Ville, Fikret Isik Karahanoglu, Ilker Bayram

Total variation (TV) is a powerful method that brings great benefit for edge-preserving regularization. Despite being widely employed in image processing, it has restricted applicability for 1-D signal processing since piecewise-constant signals form a rat ...

Institute of Electrical and Electronics Engineers2011

Parametric Resonance in Time-Dependent Networks of Hopf Oscillators

Max-Olivier Hongler, Julio Rodriguez

We study a collection of limit cycle oscillators with different frequencies interacting via networks. With static networks, our specific class of models produces a frequency learning mechanism leading the collection of oscillators to ultimately adopt a sin ...

2010

Plenoptic based super-resolution for omnidirectional image sequences

Pascal Frossard, Pierre Vandergheynst, Luigi Bagnato

This paper addresses the reconstruction of high resolution omnidirectional images from a low resolution video acquired by an omnidirectional camera moving in a static scene. In order to exploit the additional information provided by the side images in the ...

2010