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We introduce the lowest-order 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 viability of the new method is tested through numerical experiments on elliptic problems.

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The Lowest-Order Neural Approximated Virtual Element Method

  • 会议论文

  • 发表日期：

    2025年

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  • Stefano Berrone,
  • Davide Oberto,
  • Moreno Pintore,
  • Gioana Teora

摘要

We introduce the lowest-order 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 viability of the new method is tested through numerical experiments on elliptic problems.