Publications associées à Équation différentielle homogène

Stable cones in the thin one-phase problem

The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one -phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n >= 3 is completely open. In this context, axial ...

Johns Hopkins Univ Press2024

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

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

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Giancarlo Ferrari Trecate, Luca Furieri, Clara Lucía Galimberti, Liang Xu

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem from the discretiz ...

2023

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Le Chen, Cheuk Yin Lee, David Jean-Michel Candil

We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...

New York2023

An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics

Junming Duan

The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an ordinary differe ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Microscopic field theory for structure formation in systems of self-propelled particles with generic torques

Ignacio Pagonabarraga Mora, Elena Sesé Sansa

We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques ind ...

AIP Publishing2022

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Équation différentielle homogène

Stable cones in the thin one-phase problem

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

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

Anomalous dissipation and other non-smooth phenomena in fluids

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

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Homogeneous catalysis with nitrous oxide

An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics

Microscopic field theory for structure formation in systems of self-propelled particles with generic torques

Graph Chatbot

Chattez avec Graph Search

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

An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics

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

Anomalous dissipation and other non-smooth phenomena in fluids

Stable cones in the thin one-phase problem

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Homogeneous catalysis with nitrous oxide

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

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Microscopic field theory for structure formation in systems of self-propelled particles with generic torques