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SUMMARY:Physics informed spatial and functional data analysis over non-Euc
 lidean domains - Laura Sangalli (Polytechnic University of Milan)
DTSTART:20230519T130000Z
DTEND:20230519T140000Z
UID:TALK199489@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:Recent years have seen an explosive growth in the recording of
  increasingly complex and high-dimensional data. Classical statistical met
 hods are often unfit to handle such data\, whose analysis calls for the de
 finition of new methods merging ideas and approaches from statistics and a
 pplied mathematics. My talk will in particular focus on spatial and functi
 onal data defined over non-Euclidean domains\, such as linear networks\, t
 wo-dimensional manifolds and non-convex volumes. I will present an innovat
 ive class of methods\, based on regularizing terms involving Partial Diffe
 rential Equations (PDEs)\, defined over the complex domains being consider
 ed. These physics-informed regression methods enable the inclusion of the 
 available problem specific information\, suitably encoded in the regulariz
 ing PDE. The proposed methods make use of advanced numerical techniques\, 
 such as finite element analysis and isogeometric analisys. A challenging a
 pplication to neuroimaging data will be illustrated. 
LOCATION:MR12\, Centre for Mathematical Sciences
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