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SUMMARY:Probabilistic Learning on Manifolds (with Applications) - Christia
 n Soize (Université Gustave Eiffel)
DTSTART:20230714T080000Z
DTEND:20230714T090000Z
UID:TALK193924@talks.cam.ac.uk
DESCRIPTION:Lecture: Friday 14 July 2023\, 9:00 &ndash\; 10:00Title: Proba
 bilistic learning on manifolds (PLoM)Presenter: Christian SOIZE\n1. Settin
 g the problem of the probabilistic learning on manifolds (PLoM)- Statistic
 al surrogate model of a parameterized solution of a stochastic computation
 al model.- Training dataset and random vector X.- Role played by the learn
 ed dataset generated by probabilistic learning in the construction of a st
 atistical surrogate model.- Proposed probabilistic learning on manifolds.-
  Illustration of a scattering of learned realizations.\n2. Methodology and
  algorithm of the probabilistic learning on manifolds- Methodology\, steps
  of the algorithm.- A few mathematical results.\n3. Illustrations- Illustr
 ation 1: manifold as a helical in 3D Euclidean space.- Illustration 2: ana
 lysis of a petro-physics experimental database.- Illustration 3: optimizat
 ion under uncertainties using a limited number of function evaluations.\n4
 . Probabilistic learning on manifolds under constraints- Example: probabil
 istic learning inference for stochastic boundary value problem.- Formulati
 on of PLoM under constraints using the Kullback-Leibler divergence minimiz
 ation principle.- Methodology for solving the Kullback minimization proble
 m.- Types of constraints and their consideration in PLoM algorithm.\n5. Pr
 obabilistic learning inference for 3D stochastic homogenization of heterog
 eneous material- Framework: non-separation case of mesoscale with macrosca
 le.- Stochastic elliptic boundary value problem.- Prior random elasticity 
 field and learning inference.- Numerical results and validation.\nA few pa
 pers related to Probabilistic Learning on Manifolds (PLoM)
LOCATION:Seminar Room 1\, Newton Institute
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