14 citations · 26 across the 6 of their papers we have counts for
6 papers
Unfitted finite element interpolated neural networks
Wei Li, Alberto F. Martín, Santiago Badia
We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generat…
Compatible finite element interpolated neural networks
Santiago Badia, Wei Li, Alberto F. Martín
We extend the finite element interpolated neural network (FEINN) framework from partial differential equations (PDEs) with weak solutions in to PDEs with weak solutions in $H…
STLCutters.jl: A scalable geometrical framework library for unfitted finite element discretisations
Pere A. Martorell, Santiago Badia
Approximating partial differential equations for extensive industrial and scientific applications requires leveraging the power of modern high-performance computing. In large-scale…
Adaptive Finite Element Interpolated Neural Networks
Santiago Badia, Wei Li, Alberto F. Martín
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised…
Space-time unfitted finite elements on moving explicit geometry representations
Santiago Badia, Pere A. Martorell, Francesc Verdugo
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the pro…
High order unfitted finite element discretizations for explicit boundary representations
Pere A. Martorell, Santiago Badia
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also…