4 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…
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…