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SUMMARY:Machine Learning-aided enhancement and acceleration techniques for
  Polyhedral Finite Element methods
DTSTART:20220517T111500
DTEND:20220517T121500
DTSTAMP:20260404T041500Z
UID:f4683304504b845b1c10817c66a8e0beeae914a03b078ffceea22dfa
CATEGORIES:Conferences - Seminars
DESCRIPTION:Paola F. Antonietti (Polytecnico di Milano)\nThe new paradigm 
 of Polygonal Finite Element Methods (PolyFEMs) has been introduced in the 
 last years. PolyFEMs are Galerkin-type projection methods where the finite
 -dimensional discretization space is built by employing a computational gr
 id of arbitrarily shaped polygonal/polyhedral (polytopic\, for short) elem
 ents. This talk discusses how to enhance their accuracy and performance ba
 sed on designing suitable Machine Learning-aided numerical algorithms. Mor
 e specifically\, we propose new strategies to handle polygonal and polyhed
 ral grid refinement\, to be employed within an adaptive framework.  Speci
 fically\, Convolutional Neural Networks (CNNs) are employed to classify th
 e “shape” of an element so as to apply “ad-hoc” refinement criteri
 a or to enhance existing refinement strategies at a low online computation
 al cost.  The k-means clustering algorithm is used to refine polytopes wi
 th unknown shapes in a robust manner.  We test the proposed algorithms co
 nsidering two families of finite element methods that support arbitrarily 
 shaped polytopal elements\, namely the Virtual Element Method and the Poly
 topal Discontinuous Galerkin method. We demonstrate that these strategies 
 do preserve the structure and the quality of the underlying grids\, reduci
 ng the overall computational cost and mesh complexity. Some recent results
  on ML-aided grid agglomeration techniques will also be discussed.
LOCATION:MED 2 1522 https://plan.epfl.ch/?room==MED%202%201522
STATUS:CANCELLED
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