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SUMMARY:Machine Learning-Enhanced Refinement and Agglomeration Strategies 
 for Polygonal and Polyhedral Methods
DTSTART:20230126T161500
DTEND:20230126T171500
DTSTAMP:20260502T105946Z
UID:a5e43d4f759eda23bdb7e0414112319fe1ba2dada34f6aa1433ea4a2
CATEGORIES:Conferences - Seminars
DESCRIPTION:Paola Antonietti (Politecnico di Milano)\nIn this talk we disc
 uss how to enhance the accuracy and performance of Polyhedral Finite Eleme
 nt Methods based on designing suitable Machine Learning-aided numerical al
 gorithms to handle the process of grid refinement and agglomeration. More 
 specifically\, we propose new strategies to handle polytopal grid refineme
 nt\, to be employed within an adaptive framework. Specifically\, Convoluti
 onal Neural Networks are employed to classify the “shape” of an elemen
 t so as to apply “ad-hoc” refinement criteria or to enhance existing r
 efinement strategies at a low online computational cost. We test the propo
 sed algorithms considering two families of finite element methods that sup
 port arbitrarily shaped polytopal elements\, namely the Virtual Element me
 thod and the Polytopal Discontinuous Galerkin method. In the second part o
 f the talk ML-aided grid agglomeration techniques are presented. Mesh aggl
 omeration strategies are important both within adaptive refinement algorit
 hms and to construct multilevel algebraic solvers. We propose to use Graph
  Neural Networks (GNNs) to automatically perform grid agglomeration. GNNs 
 have the advantage to process naturally and simultaneously both the graph 
 structure of mesh and the geometrical information. We assess the performan
 ce of the proposed agglomeration algorithm and demonstrate its effectivene
 ss when employed within multigrid solvers in a Polytopal Discontinuous Gal
 erkin framework.
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021
STATUS:CONFIRMED
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