The lowest-order Neural Approximated Virtual Element Method

Stefano Berrone; Davide Oberto; Moreno Pintore; Gioana Teora

The lowest-order Neural Approximated Virtual Element Method

Numerical Analysis 2023-12-01 v1 Numerical Analysis

Authors: Stefano Berrone , Davide Oberto , Moreno Pintore , Gioana Teora

Abstract

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 operators in the Virtual Element Method. In this paper, we discuss its formulation and detail the strategy for training the underlying neural network. The efficacy of this new method is tested through numerical experiments on elliptic problems.

Keywords

virtual element method neural networks finite element method

Cite

@article{arxiv.2311.18534,
  title  = {The lowest-order Neural Approximated Virtual Element Method},
  author = {Stefano Berrone and Davide Oberto and Moreno Pintore and Gioana Teora},
  journal= {arXiv preprint arXiv:2311.18534},
  year   = {2023}
}

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