4 papers
Four-field mixed finite elements for incompressible nonlinear elasticity
Santiago Badia, Wei Li, Ricardo Ruiz-Baier
We present a stable finite element method for incompressible nonlinear elasticity based on a four-field mixed formulation involving the displacement, displacement gradient, first P…
Unfitted finite element interpolated neural networks
Wei Li, Alberto F. MartÃn, 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. MartÃn
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…
Adaptive Finite Element Interpolated Neural Networks
Santiago Badia, Wei Li, Alberto F. MartÃn
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…