STOCHASTICS WITH APPLICATIONS Seminar

 

PROGRAM

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Predavanja možete pratiti i online putem MITEAM stranice seminara Stohastika sa primenama:
https://miteam.mi.sanu.ac.rs/asset/n4AMxqgneB2qxFuT2

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Plan rada seminara Stohastika sa primenama za NOVEMBAR 2026.

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Četvrtak, 26.11.2026. u 11:15, Online
Michael Oberguggenberger, University of Innsbruck, Austria
BAYESIAN SOLUTION TO INVERSE PROBLEMS FOR PARTIAL DIFFERENTIAL EQUATIONS
Well-known (ill-posed) inverse problems are the reconstruction of the heat source from the terminal temperature distribution in the heat equation, the reconstruction of potentials in diffusion equations, or the reconstruction of source terms in elliptic equations. The past decade has seen widespread interest in solving such inverse problems by Bayesian methods. The sources/potentials are members of an infinite dimensional Hilbert space. Their reconstruction requires Gaussian measures on Hilbert spaces as well as an infinite dimensional version of Bayes' rule. Given a prior Gaussian measure, a physics-informed likelihood function, and observations of the terminal temperature, the solution of the inverse problem for the heat equation consists in the posterior measure obtained from the Bayesian procedure. The source/potential is realized as a random field whose probability distribution is the posterior measure. We intend to give an overview of these rather new methods and show an application to the linear heat equation, the Poisson equation and a semilinear diffusion equation.

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