75 citations · 219 across the 10 of their papers we have counts for
12 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…
The lowest-order Neural Approximated Virtual Element Method on polygonal elements
Stefano Berrone, Moreno Pintore, Gioana Teora
The lowest-order Neural Approximated Virtual Element Method on polygonal elements is proposed here. This method employs a neural network to locally approximate the Virtual Element…
Meshfree Variational Physics Informed Neural Networks (MF-VPINN): an adaptive training strategy
Stefano Berrone, Moreno Pintore
In this paper, we introduce a Meshfree Variational-Physics-Informed Neural Network. It is a Variational-Physics-Informed Neural Network that does not require the generation of the…
The lowest-order Neural Approximated Virtual Element Method
Stefano Berrone, Davide Oberto, Moreno Pintore +1
We introduce the Neural Approximated Virtual Element Method, a novel polygonal method that relies on neural networks to eliminate the need for projection and stabilization operator…
Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks
S. Berrone, C. Canuto, M. Pintore +1
In this paper, we present and compare four methods to enforce Dirichlet boundary conditions in Physics-Informed Neural Networks (PINNs) and Variational Physics-Informed Neural Netw…
Solving PDEs by Variational Physics-Informed Neural Networks: an a posteriori error analysis
Stefano Berrone, Claudio Canuto, Moreno Pintore
We consider the discretization of elliptic boundary-value problems by variational physics-informed neural networks (VPINNs), in which test functions are continuous, piecewise linea…
Variational Physics Informed Neural Networks: the role of quadratures and test functions
Stefano Berrone, Claudio Canuto, Moreno Pintore
In this work we analyze how quadrature rules of different precisions and piecewise polynomial test functions of different degrees affect the convergence rate of Variational Physics…
Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method
Moreno Pintore, Federico Pichi, Martin Hess +2
The majority of the most common physical phenomena can be described using partial differential equations (PDEs). However, they are very often characterized by strong nonlinearities…