MOOC
Warm-up for EPFL
Related publications (1,000)
A Combination Technique for Optimal Control Problems Constrained by Random PDEs
We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...
2024Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs
Fernando José Henriquez Barraza
We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...
New York2024Pseudo-Three-Dimensional Analytical Model of Linear Induction Motors for High-Speed Applications
Mario Paolone, André Hodder, Lucien André Félicien Pierrejean, Simone Rametti
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 ...
2024Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE
Marco Picasso, Alexandre Caboussat, Maude Girardin
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 ...
Lausanne2024Randomized flexible GMRES with deflated restarting
For a high dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in computational costs as well as numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g. to the generaliz ...
Springer2024Generalization of Scaled Deep ResNets in the Mean-Field Regime
Volkan Cevher, Grigorios Chrysos, Fanghui Liu
Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...
2024Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise
We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...
London2024Experimental Investigation on Size-Effect of Rubble Stone Masonry Walls Under In-Plane Horizontal Loading: Overview and Preliminary Results
Katrin Beyer, Savvas Saloustros
Rubble stone masonry is a common construction typology of historical city centres and vernacular architecture. While past earthquakes have shown that it is one of the most vulnerable masonry construction typologies, there are few experimental campaigns giv ...
2024The time-domain Cartesian multipole expansion of electromagnetic fields
Marcos Rubinstein, Farhad Rachidi-Haeri, Elias Per Joachim Le Boudec, Chaouki Kasmi, Nicolas Mora Parra, Emanuela Radici
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 ...
2024An integrated heart-torso electromechanical model for the simulation of electrophysiological outputs accounting for myocardial deformation
Alfio Quarteroni, Francesco Regazzoni
When generating in-silico clinical electrophysiological outputs, such as electrocardiograms (ECGs) and body surface potential maps (BSPMs), mathematical models have relied on single physics, i.e. of the cardiac electrophysiology (EP), neglecting the role o ...
Elsevier Science Sa2024