25 citations · 39 across the 8 of their papers we have counts for
8 papers
Multi-level Neural Networks for Accurate Solutions of Boundary-Value Problems
Ziad Aldirany, Régis Cottereau, Marc Laforest +1
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their…
Operator approximation of the wave equation based on deep learning of Green's function
Ziad Aldirany, Régis Cottereau, Marc Laforest +1
Deep operator networks (DeepONets) have demonstrated their capability of approximating nonlinear operators for initial- and boundary-value problems. One attractive feature of DeepO…
Optimal Design of Validation Experiments for the Prediction of Quantities of Interest
Antonin Paquette-Rufiange, Serge Prudhomme, Marc Laforest
Numerical predictions of quantities of interest measured within physical systems rely on the use of mathematical models that should be validated, or at best, not invalidated. Model…
Thin-Shell Approach for Modeling Superconducting Tapes in the - Finite-Element Formulation
Bruno de Sousa Alves, Valtteri Lahtinen, Marc Laforest +1
This paper presents a novel finite-element approach for the electromagnetic modeling of superconducting coated conductors. We combine a thin-shell (TS) method to the - formul…
The mathematical theory of splitting-merging patterns in phase transition dynamics
Eva Kardhashi, Marc Laforest, Philippe G. LeFloch
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between…
The -CurlCurl : Spaces, traces, coercivity and a Helmholtz decomposition in
Marc Laforest
This work provides the foundation for the finite element analysis of an elliptic problem which is the rotational analogue of the -Laplacian and which appears as a model of the m…
A Posteriori Error Estimation for the p-curl Problem
Andy T. S. Wan, Marc Laforest
We derive a posteriori error estimates for a semi-discrete finite element approximation of a nonlinear eddy current problem arising from applied superconductivity, known as the …
Diminishing functionals for nonclassical entropy solutions selected by kinetic relations
Marc Laforest, Philippe G. LeFloch
We consider nonclassical entropy solutions to scalar conservation laws with concave-convex flux functions, whose set of left- and right-hand admissible states across undercompressi…