Finite Element Neural Network Interpolation. Part I: Interpretable and Adaptive Discretization for Solving PDEs

K Škardová, A Daby-Seesaram, M Genet - arxiv preprint arxiv:2412.05719, 2024 - arxiv.org
We present the Finite Element Neural Network Interpolation (FENNI) framework, a sparse
neural network architecture extending previous work on Embedded Finite Element Neural …

Unfitted finite element interpolated neural networks

W Li, AF Martín, S Badia - arxiv preprint arxiv:2501.17438, 2025 - arxiv.org
We present a novel approach that integrates unfitted finite element methods and neural
networks to approximate partial differential equations on complex geometries. Easy-to …