PINNs and GaLS: An Priori Error Estimates for Shallow Physically Informed Neural Network Applied to Elliptic Problems. - Umberto Zerbinati (CoRR, 2022)

When rational functions meet virtual elements: The lightning Virtual Element Method. - Manuel Luigi Trezzi; Umberto Zerbinati (CoRR, 2023)

PETScML: Second-Order Solvers for Training Regression Problems in Scientific Machine Learning. - Stefano Zampini; Umberto Zerbinati; George Turkiyyah; David E. Keyes (PASC, 2024)

A nodal ghost method based on variational formulation and regular square grid for elliptic problems on arbitrary domains in two space dimensions. - Clarissa Astuto; Daniele Boffi; Giovanni Russo; Umberto Zerbinati (CoRR, 2024)

An adaptive mesh refinement strategy to ensure quasi-optimality of the conforming finite element method for the Helmholtz equation via T-coercivity. - Tim van Beeck; Umberto Zerbinati (CoRR, 2024)

A comparison of the Coco-Russo scheme and [ghost]-FEM for elliptic equations in arbitrary domains. - Clarissa Astuto; Armando Coco; Umberto Zerbinati (CoRR, 2024)

Kinetic Derivation of an Inviscid Compressible Leslie-Ericksen Equation for Rarified Calamitic Gases. - Patrick E. Farrell; Giovanni Russo; Umberto Zerbinati (Multiscale Model. Simul., 2024)

ngsPETSc: A coupling between NETGEN/NGSolve and PETSc. - Jack D. Betteridge; Patrick E. Farrell; Matthias Hochsteger; Christopher Lackner; Joachim Schöberl; Stefano Zampini; Umberto Zerbinati (J. Open Source Softw., 2024)

Preconditioned normal equations for solving discretised partial differential equations. - Lorenzo Lazzarino; Yuji Nakatsukasa; Umberto Zerbinati (CoRR, 2025)

Analysis and numerical analysis of the Helmholtz-Korteweg equation. - Patrick E. Farrell; Tim van Beeck; Umberto Zerbinati (CoRR, 2025)