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SUMMARY:From Surrogate Solvers to PINNs and Beyond Classical Methods - Car
 lo Nitsch  (University of Naples Federico II)
DTSTART:20260420T110000Z
DTEND:20260420T114500Z
UID:TALK244912@talks.cam.ac.uk
DESCRIPTION:Starting from surrogate models and PINN-based approaches\, I w
 ill discuss how neural methods may help move beyond some classical framewo
 rks in shape optimization\, such as shape derivatives\, level-set methods\
 , and other smooth parametrizations of the domain. In particular\, neural 
 representations suggest new ways to handle topological changes\, complex g
 eometries\, and free boundaries\, where more rigid classical approaches ma
 y become restrictive.The price to pay is that\, at present\, the mathemati
 cal theory is still incomplete: compared with classical methods\, there is
  no equally systematic understanding of convergence\, stability\, or appro
 ximation properties in the relevant variational settings. For this reason\
 , the talk will emphasize perspectives rather than definitive answers.This
  talk is not intended as a survey of fully established results\, but rathe
 r as an overview of possible directions.
LOCATION:Seminar Room 1\, Newton Institute
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