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arXiv · 2601.09595

Two continuous extensions of the Neural Approximated Virtual Element Method

Stefano Berrone·Moreno Pintore·Gioana Teora
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Abstract

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 basis functions using pre-trained fully connected neural networks while ensuring exact continuity across adjacent mesh elements. B-NAVEM leverages a Physics-Informed Neural Network to approximately solve the local Laplace problem that defines the virtual element basis functions, whereas P-NAVEM directly enforces polynomial reproducibility via a tailored loss function, without requiring harmonicity within the element interior. Numerical experiments assess the methods in terms of computational cost, memory usage, and accuracy during both training and testing phases.

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Stefano Berrone, Moreno Pintore, Gioana Teora. 2026-01-14. Two continuous extensions of the Neural Approximated Virtual Element Method. https://arxiv.org/abs/2601.09595

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