Publications related to Differential equation

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

Jan Sickmann Hesthaven, Niccolo' Discacciati

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

Lausanne2024

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

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

Alfio Quarteroni, Francesco Regazzoni, Stefano Pagani

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 ...

Nature Portfolio2024

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

Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti

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 ...

Springer2024

Shape 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 York2024

Generalization 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 ...

2024

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

Stefano Alberti, Jean-Philippe Hogge, Joaquim Loizu Cisquella, Jérémy Genoud, Francesco Romano

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

2024

Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations

Katie Sabrina Catherine Rosie Marsden

In this thesis we will present two results on global existence for nonlinear dispersive equations with data at or below the scaling regularity. In chapter 1 we take a probabilistic perspective to study the energy-critical nonlinear Schrödinger equation in ...

EPFL2024

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Differential equation

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

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

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

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Generalization of Scaled Deep ResNets in the Mean-Field Regime

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

Soliton gas: Theory, numerics, and experiments

Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations

Graph Chatbot

Chat with Graph Search

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

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

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Soliton gas: Theory, numerics, and experiments

A Combination Technique for Optimal Control Problems Constrained by Random PDEs

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

Generalization of Scaled Deep ResNets in the Mean-Field Regime

Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations

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