5 papers
Two continuous extensions of the Neural Approximated Virtual Element Method
Stefano Berrone, Moreno Pintore, Gioana Teora
We propose two globally continuous neural-based variants of the Neural Approximated Virtual Element Method (NAVEM), termed B-NAVEM and P-NAVEM. Both approaches construct local basi…
The Zipped Finite Element Method: High-order Shape Functions for Polygons
Stefano Berrone, Lorenzo Neva, Moreno Pintore +2
In this paper, we present a new polygonal finite element method, called the Zipped Finite Element Method, for star-shaped polygons. The proposed approach constructs high-order shap…
The Neural Approximated Virtual Element Method for Elasticity Problems
Stefano Berrone, Moreno Pintore, Gioana Teora
We present the Neural Approximated Virtual Element Method to numerically solve elasticity problems. This hybrid technique combines classical concepts from the Finite Element Method…
A 3D Machine Learning based Volume Of Fluid scheme without explicit interface reconstruction
Moreno Pintore, Bruno Després
We present a machine-learning based Volume Of Fluid method to simulate multi-material flows on three-dimensional domains. One of the novelties of the method is that the flux fracti…
Computable Lipschitz Bounds for Deep Neural Networks
Moreno Pintore, Bruno Després
Deriving sharp and computable upper bounds of the Lipschitz constant of deep neural networks is crucial to formally guarantee the robustness of neural-network based models. We anal…