Publications

New preprints

1. Stefano Berrone, Moreno Pintore, and Gioana Teora. Two continuous extensions of the Neural Approximated Virtual Element Method. ArXiv preprint arXiv:2601.09595, (2026). [link]

2. Moreno Pintore, and Bruno Després. Computable Lipschitz Bounds for Deep Neural Networks. ArXiv preprint arXiv:2410.21053, (2024). [link]

Published journal papers

1. 1. Moreno Pintore, and Bruno Després. A Posteriori Lipschitz Bounds for Deep Neural Networks. SIAM Journal on Numerical Analysis, 64(3), (2026). [link]

   2. Stefano Berrone, Lorenzo Neva, Moreno Pintore, Gioana Teora, and Fabio Vicini. The Zipped Finite Element Method: High-order Shape Functions for Polygons. Computer Methods in Applied Mechanics and Engineering, 458:119060, (2026). [link]

   3. Moreno Pintore, and Bruno Després. A 3D Machine Learning based Volume Of Fluid scheme without explicit interface reconstruction. Computers & Fluids, 314:107112, (2026). [link]

   4. Stefano Berrone, Moreno Pintore, and Gioana Teora. The neural approximated virtual element method for elasticity problems. Finite Elements in Analysis and Design, 252:104467 (2025). [link]

   5. Stefano Berrone, Moreno Pintore, and Gioana Teora. The lowest-order Neural Approximated Virtual Element Method on polygonal elements. Computers & Structures, 314:107753 (2025). [link]

   6. Stefano Berrone and Moreno Pintore. Meshfree Variational-Physics-Informed Neural Networks (MF-VPINN): an adaptive training strategy. Algorithms, 17(9), 415, (2024). [link]

   7. Stefano Berrone, Claudio Canuto, Moreno Pintore, and Natarajan Sukumar. Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks. Heliyon, 9(8):e18820, (2023). [link]

   8. Stefano Berrone, Claudio Canuto, and Moreno Pintore. Solving PDEs by variational physics-informed neural networks: an a posteriori error analysis. Annali dell’Università di Ferrara, 68:575--595, (2022). [link]

   9. Stefano Berrone, Claudio Canuto, and Moreno Pintore. Variational physics informed neural networks: the role of quadratures and test functions. Journal of Scientific Computing, 92(3):1--27, (2022). [link]

   10. Moreno Pintore, Federico Pichi, Martin Hess, Gianluigi Rozza, and Claudio Canuto. Efficient computation of bifurcation diagrams with a deflated approach to reduced basis spectral element method. Advances in Computational Mathematics, 47:1--39, (2021). [link]

Published conference papers

1. 1. Stefano Berrone, Davide Oberto, Moreno Pintore, and Gioana Teora. The lowest-order Neural Approximated Virtual Element Method. Numerical Mathematics and Advanced Applications ENUMATH 2023, 1:129--138 (2025). [link]

Theses

1. 1. Ph.D. thesis: Variational physics-informed neural networks: theory and applications. [link]

   2. Master's thesis: Efficient computation of bifurcation diagrams with spectral element method and reduced order models. [link]

Open source software

1. 1. NAVEM-library (main contributor, together with Gioana Teora).
      Official repository for the Neural Approximated Virtual Element Method. [link]