Publications related to Quotient Submanifolds for Static Feedback Linearization

On the stability of blowup solutions for the critical corotational wave-map problem

We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter

λ(t)=t−1−ν

is sufficiently close to ...

2020

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Jan Sickmann Hesthaven

The homotopy continuation method has been widely used to compute multiple solutions of nonlinear differential equations, but the computational cost grows exponentially based on the traditional finite difference and finite element discretizations. In this w ...

SPRINGER/PLENUM PUBLISHERS2020

Machine learning for fast and reliable solution of time-dependent differential equations

Alfio Quarteroni, Francesco Regazzoni

We propose a data-driven Model Order Reduction (MOR) technique, based on Artificial Neural Networks (ANNs), applicable to dynamical systems arising from Ordinary Differential Equations (ODEs) or time-dependent Partial Differential Equations (PDEs). Unlike ...

2019

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

David Valentin Strütt

In this thesis, we study two distinct problems. The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...

EPFL2018

A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems

Fabio Nobile, Simone Brugiapaglia

We present a theoretical analysis of the CORSING (COmpRessed SolvING) method for the numerical approximation of partial differential equations based on compressed sensing. In particular, we show that the best s-term approximation of the weak solution of a ...

2018

A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics

Alfio Quarteroni, Niccolò Dal Santo

The aim of this work is to propose and analyse a new high-order discontinuous Galerkin finite element method for the time integration of a Cauchy problem for second-order ordinary differential equations. These equations typically arise after space semidisc ...

OXFORD UNIV PRESS2018

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Fei Pu

In this thesis, we study systems of linear and/or non-linear stochastic heat equations and fractional heat equations in spatial dimension

1

driven by space-time white noise. The main topic is the study of hitting probabilities for the solutions to these ...

EPFL2018

Some Remarks on the Lie Derivative and the Pullback Equation for Contact Forms

Bernard Dacorogna, Olivier Kneuss

Given the contact forms f and g, and the 1-form h, we discuss the existence of a vector field u verifying L-u(f)= d(u (right perpendicular) f)+ u (right perpendicular) df = h. This is closely related to the pullback equation, where we seek for a diffeomorp ...

Walter De Gruyter Gmbh2017

Large-scale neural networks implemented with non-volatile memory as the synaptic weight element: impact of conductance response

Yusuf Leblebici, Irem Boybat Kara, Alessandro Fumarola, Severin Sidler

We assess the impact of the conductance response of Non-Volatile Memory (NVM) devices employed as the synaptic weight element for on-chip acceleration of the training of large-scale artificial neural networks (ANN). We briefly review our previous work towa ...

Ieee2016

Isogeometric Analysis for second order Partial Differential Equations on surfaces

Alfio Quarteroni, Luca Dede'

We consider the numerical solution of second order Partial Differential Equations (PDEs) on lower dimensional manifolds, specifically on surfaces in three dimensional spaces. For the spatial approximation, we consider Isogeometric Analysis which facilitate ...

Elsevier2015

Quotient Submanifolds for Static Feedback Linearization

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On the stability of blowup solutions for the critical corotational wave-map problem

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Machine learning for fast and reliable solution of time-dependent differential equations

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems

A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Some Remarks on the Lie Derivative and the Pullback Equation for Contact Forms

Large-scale neural networks implemented with non-volatile memory as the synaptic weight element: impact of conductance response

Isogeometric Analysis for second order Partial Differential Equations on surfaces

Isogeometric Analysis for second order Partial Differential Equations on surfaces

On the stability of blowup solutions for the critical corotational wave-map problem

A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics

A Homotopy Method with Adaptive Basis Selection for Computing Multiple Solutions of Differential Equations

Machine learning for fast and reliable solution of time-dependent differential equations

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems

The stochastic heat equation: hitting probabilities and the probability density function of the supremum via Malliavin calculus

Some Remarks on the Lie Derivative and the Pullback Equation for Contact Forms

Large-scale neural networks implemented with non-volatile memory as the synaptic weight element: impact of conductance response