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SUMMARY:AInstein: Machine Learning "Special" (Pseudo)-Riemannian Metrics
DTSTART:20251215T130000Z
DTEND:20251215T150000Z
DTSTAMP:20260509T130200Z
UID:indico-event-49679@agenda.infn.it
DESCRIPTION:Speakers: Tancredi Schettini Gherardini (Queen Mary University
  of London)\n\nA numerical scheme based on semi-supervised machine learnin
 g\, "AInstein"\, was recently introduced (see https://iopscience.iop.org/
 article/10.1088/3050-287X/ae1117) to approximate generic Riemannian Einste
 in metrics on a given manifold. Its versatility stems from encoding the di
 fferentiable structure directly in the loss function\, making the method a
 pplicable to manifolds constructed in a "bottom-up" fashion that admit no 
 natural embedding in R^n. A limitation\, however\, is that the resulting n
 umerical metric is not inherently global.To address this\, we introduce a 
 new approach for all real (n-1)-dimensional manifolds that can be embedded
  in R^n\, in which the neural-network ansatz is automatically globally def
 ined. After a brief review of the original AInstein model\, the talk prese
 nts novel results obtained with the new architecture\, including applicati
 ons to two open problems: the Kazdan–Warner (prescribed curvature) probl
 em on S^2 and the search for negative-curvature metrics on S^4 and S^5. Fi
 nally\, we focus on a further extension of the method to Lorentzian metric
 s\, presenting some preliminary results concerning black holes.\n\nhttps:/
 /agenda.infn.it/event/49679/
LOCATION:Sala Paoluzi
URL:https://agenda.infn.it/event/49679/
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