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The lowest-order Neural Approximated Virtual Element Method

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arxiv 2311.18534 v1 pith:BFYDIFYN submitted 2023-11-30 math.NA cs.NA

Stefano Berrone , Davide Oberto , Moreno Pintore , Gioana Teora This is my paper · ORCID
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keywords methodneuralelementvirtualapproximateddetaildiscussefficacy
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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.

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Cited by 1 Pith paper

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  1. A 3D-1D Virtual Element Method for Modeling Root Water Uptake

    math.NA 2024-12 conditional novelty 4.0 of 10

    A new numerical scheme couples nonlinear soil water flow with a growing root network by combining virtual element methods with an optimization-based 3D-1D coupling, validated on a manufactured solution and on stony-so...

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