output
20092025
most citedThermodynamics-based Artificial Neural Networks for constitutive modeling

421 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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16 papers · 1 filter

math.NA2025

Data-driven material identification in micromorphic continua

Jacinto Ulloa, Laurent Stainier

We introduce a data-driven framework for identifying material behavior from full-field kinematics and external force measurements in generalized (micromorphic) continua. The aim is…

math.NA2024

Sparse approximations for contact mechanics

Kiran Sagar Kollepara, José V. Aguado, Yves Le Guennec +2

Low-rank model order reduction strategies for contact mechanics show limited dimensionality reduction due to linear inseparability of contact pressure field. Therefore, a dictionar…

math.NA2024★ 18 cited

Data-driven micromorphic mechanics for materials with strain localization

Jacinto Ulloa, Laurent Stainier, Michael Ortiz +1

This paper explores the role of generalized continuum mechanics, and the feasibility of model-free data-driven computing approaches thereof, in solids undergoing failure by strain…

math.NA2022★ 4 cited

A two-scale solver for linear elasticity problems in the context of parallel message passing

Alexis Salzman, Nicolas Moës

This paper pushes further the intrinsic capabilities of the GFEM global-local approach introduced initially in [1]. We develop a distributed computing approach using MPI (Me…

math.NA2021★ 124 cited

Residual-based adaptivity for two-phase flow simulation in porous media using Physics-informed Neural Networks

John M. Hanna, Jose V. Aguado, Sebastien Comas-Cardona +2

This paper aims to provide a machine learning framework to simulate two-phase flow in porous media. The proposed algorithm is based on Physics-informed neural networks (PINN). A no…

math.NA2020★ 12 cited

Scaling laws for the rigid-body response of masonry structures under blast loads

Filippo Masi, Ioannis Stefanou, Victor Maffi-Berthier

The response of masonry structures to explosions can be hardly investigated relying only on numerical and analytical tools. Experimental tests are of paramount importance for impro…

math.NA2018

Tensor-based numerical method for stochastic homogenisation

Quentin Ayoul-Guilmard, Anthony Nouy, Christophe Binetruy

This paper addresses the complexity reduction of stochastic homogenisation of a class of random materials for a stationary diffusion equation. A cost-efficient approximation of the…

math.NA2017★ 3 cited

Tensor-based multiscale method for diffusion problems in quasi-periodic heterogeneous media

Quentin Ayoul-Guilmard, Anthony Nouy, Christophe Binetruy

This paper proposes to address the issue of complexity reduction for the numerical simulation of multiscale media in a quasi-periodic setting. We consider a stationary elliptic dif…

math.NA2016★ 7 cited

Projection based model order reduction methods for the estimation of vector-valued variables of interest

Olivier Zahm, Marie Billaud-Friess, Anthony Nouy

We propose and compare goal-oriented projection based model order reduction methods for the estimation of vector-valued functionals of the solution of parameter-dependent equations…

math.NA2015★ 28 cited

Low-rank methods for high-dimensional approximation and model order reduction

Anthony Nouy

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These metho…

math.NA2015★ 10 cited

Geometric Structures in Tensor Representations (Final Release)

Antonio Falco, Wolfgang Hackbusch, Anthony Nouy

The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-cal…

math.NA2014★ 18 cited

To be or not to be intrusive? The solution of parametric and stochastic equations --- Proper Generalized Decomposition

Loïc Giraldi, Dishi Liu, Hermann G. Matthies +1

A numerical method is proposed to compute a low-rank Galerkin approximation to the solution of a parametric or stochastic equation in a non-intrusive fashion. The considered nonlin…

math.NA2013★ 25 cited

Simulation of sharp interface multi-material flows involving an arbitrary number of components through an extended five-equation model

Marie Billaud Friess, Samuel Kokh

In this paper, we present an anti-diffusive method dedicated to the simulation of interface flows on Cartesian grids involving an arbitrary number m of compress- ible components. O…

math.NA2013★ 12 cited

Low-rank approximate inverse for preconditioning tensor-structured linear systems

Loic Giraldi, Anthony Nouy, Gregory Legrain

In this paper, we propose an algorithm for the construction of low-rank approximations of the inverse of an operator given in low-rank tensor format. The construction relies on an…

math.NA2013★ 41 cited

A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems

Marie Billaud-Friess, Anthony Nouy, Olivier Zahm

In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation forma…

math.NA2011★ 11 cited

Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces

Antonio Falco, Anthony Nouy

Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of…