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Related publications (50)

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

San Diego2024

Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

Gaspard Ohlmann

We are interested in the well posedness of quasilinear partial differential equations of order two. Motivated by the study of the Einstein equation in relativity theory, there are a number of works dedicated to the local well-posedness issue for the quasil ...

EPFL2021

Physics Informed Neural Networks for Surrogate Modelling and Inverse Problems in Geotechnics

Finite elements methods (FEMs) have benefited from decades of development to solve partial differential equations (PDEs) and to simulate physical systems. In the recent years, machine learning (ML) and artificial neural networks (ANN) have shown great pote ...

2021

Time-independent feedbacks for the null controllability of homogeneous quasilinear hyperbolic systems in one dimensional space

Hoài-Minh Nguyên

We consider the null controllability of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks for the null-controllability for

C^1

-solutions at any ...

2020

On Classical Global Solutions of Nonlinear Wave Equations with Large Data

Shuang Miao

This article studies the Cauchy problem for systems of semi-linear wave equations on R3+1 with nonlinear terms satisfying the null conditions. We construct future global-in-time classical solutions with arbitrarily large initial energy. The choice of the l ...

OXFORD UNIV PRESS2019

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

Multi space reduced basis preconditioners for parametrized partial differential equations

Niccolò Dal Santo

The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...

EPFL2018

Silencing the second harmonic generation from plasmonic nanodimers: A comprehensive discussion

Olivier Martin, Jérémy Butet, Gabriel David Bernasconi

The silencing of the second harmonic generation process from plasmonic nanostructures corresponds to the limited far-field second harmonic radiation despite the huge fundamental electric field enhancement in the interstice between two plasmonic nanoparticl ...

BEILSTEIN-INSTITUT2018

Isogeometric analysis and proper orthogonal decomposition for parabolic problems

Alfio Quarteroni, Shengfeng Zhu

We investigate the combination of Isogeometric Analysis (IGA) and proper orthogonal decomposition (POD) based on the Galerkin method for model order reduction of linear parabolic partial differential equations. For the proposed fully discrete scheme, the a ...

Springer Heidelberg2017

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Jean-Philippe Lucien Montillet

Families of energy operators and generalized energy operators have recently been introduced in the definition of the solutions of linear Partial Differential Equations (PDEs) with a particular application to the wave equation [ 15]. To do so, the author ha ...

Int Center Scientific Research & Studies2017

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Time-independent feedbacks for the null controllability of homogeneous quasilinear hyperbolic systems in one dimensional space

Hoài-Minh Nguyên

C^1

-solutions at any ...

2020