Publications related to A posteriori error estimates for the finite element approximation of the Stokes problem

Anomalous dissipation and other non-smooth phenomena in fluids

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

EPFL2024

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

Pakshal Narendra Bohra

In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

EPFL2024

Spectral Estimators for High-Dimensional Matrix Inference

Farzad Pourkamali

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

EPFL2024

Stability: a search for structure

Wouter Jongeneel

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

EPFL2024

A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set

Daniel Kuhn, Viet Anh Nguyen, Yves Rychener

The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either chosen heuristically ...

2024

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

Paride Passelli

The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...

EPFL2024

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Simone Deparis, Riccardo Tenderini, Nicholas Mueller

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

Philadelphia2024

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov, Scott William Pesme

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

2024

A Method of Moments Estimator for Interacting Particle Systems and their Mean Field Limit

Andrea Zanoni, Grigorios A. Pavliotis

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction, and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear sys ...

Siam Publications2024

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

Roya Moghaddasi Fereidani

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

A posteriori error estimates for the finite element approximation of the Stokes problem

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Anomalous dissipation and other non-smooth phenomena in fluids

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

Spectral Estimators for High-Dimensional Matrix Inference

Stability: a search for structure

A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

A Method of Moments Estimator for Interacting Particle Systems and their Mean Field Limit

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

Anomalous dissipation and other non-smooth phenomena in fluids

Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

Stability: a search for structure

Spectral Estimators for High-Dimensional Matrix Inference

A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Set

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

A Method of Moments Estimator for Interacting Particle Systems and their Mean Field Limit

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