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In light of the challenges posed by climate change and the goals of the Paris Agreement, electricity generation is shifting to a more renewable and decentralized pattern, while the operation of systems like buildings is increasingly electrified. This calls ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

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 ...

Literature on linear induction motors (LIMs) has proposed several approaches to model the behavior of such devices for different applications. In terms of accuracy and fidelity, field analysis-based models are the most relevant. Closed-form or numerical so ...

Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

Time-domain solutions of Maxwell’s equations in homogeneous and isotropic media are paramount to studying transient or broadband phenomena. However, analytical solutions are generally unavailable for practical applications, while numerical solutions are co ...

Modern power distribution systems are experiencing a large-scale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). Their presence complicates the analysis and mitigation of harmonics, whose creation and propagation may be amplified ...

The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

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 ...

This paper presents the new 2D electrostatic particle -in -cell code FENNECS developed to study the formation of magnetized non -neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gyrotron electron gun desi ...

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

In this thesis, we propose to formally derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they respond to harmonic or stochastic forcing, or to an initial condition. This approach reconciles the non-mo ...

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that th ...

Metal-organic frameworks (MOFs) are a rapidly growing class of materials that offer great promise in various applications. However, the synthesis remains challenging: for example, a range of crystal structures can often be accessed from the same building b ...

In this paper, we study sampling from a posterior derived from a neural network. We propose a new probabilistic model consisting of adding noise at every pre- and post-activation in the network, arguing that the resulting posterior can be sampled using an ...

Two -particle Bose-Einstein momentum correlation functions are studied for charged-hadron pairs in lead -lead collisions at a center -of -mass energy per nucleon pair of .'/sNN = 5.02 TeV. The data sample, containing 4.27 x 109 minimum bias events correspo ...

The field of biometrics, and especially face recognition, has seen a wide-spread adoption the last few years, from access control on personal devices such as phones and laptops, to automated border controls such as in airports. The stakes are increasingly ...

When two objects slide against each other, wear and friction occur at their interface. The accumulation of wear forms what is commonly referred to as a ``third-body''. Understanding third-body evolution has significant applications in industry, where contr ...

Regularized Interpolation for Noisy Images

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Quantifying the Unknown: Data-Driven Approaches and Applications in Energy Systems

From low-rank retractions to dynamical low-rank approximation and back

Stability: a search for structure

Pseudo-Three-Dimensional Analytical Model of Linear Induction Motors for High-Speed Applications

Reliable data-driven decision-making through optimal transport

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

The time-domain Cartesian multipole expansion of electromagnetic fields

Unified Harmonic Power-Flow and Stability Analysis of Power Grids with Converter-Interfaced Distributed Energy Resources

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

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

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Non-normal forms

Transportation-based functional ANOVA and PCA for covariance operators

On the Generalization of Stochastic Gradient Descent with Momentum

How Reproducible is the Synthesis of Zr-Porphyrin Metal-Organic Frameworks? An Interlaboratory Study

Gibbs sampling the posterior of neural networks

Two-particle Bose-Einstein correlations and their Lévy parameters in PbPb collisions at √sNN=5.02 TeV

Performing and Detecting Backdoor Attacks on Face Recognition Algorithms

Modeling friction and wear using an adaptive discrete-continuum coupling