BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.8//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news1722@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20241213T192424 DTSTART;TZID=Europe/Zurich:20241213T110000 SUMMARY:Seminar in Numerical Analysis: Robert Scheichl (Heidelberg Universi ty) DESCRIPTION:The fast simulation of Gaussian random fields (GRFs) plays a pi votal role in many research areas such as uncertainty quantification\, dat a science and spatial statistics. In theory\, it is a well understood and solved problem\, but in practice the efficiency and performance of traditi onal sampling procedures degenerates quickly when the random field is disc retised on a grid with spatial resolution going to zero. Most existing alg orithms\, such as Cholesky factorisation samplers\, do not scale well on l arge-scale parallel computers. On the other hand\, stationary\, iterative approaches such as the Gibbs sampler become extremely inefficient at high grid resolution. Already in the late 1980s\, Goodman\, Sokal and their co llaborators wrote a series of papers aimed at accelerating the Gibbs sampl er using multigrid ideas. The key observation is the intricate connection of random samplers\, such as the Gibbs method\, with iterative solvers for linear systems. They proposed the so-called multigrid Monte Carlo (MGMC) method - a random analogue of the multigrid method for solving discretised PDEs. We revisit the MGMC algorithm and provide rigorous theoretical jus tifications for the optimal scalability of the method for large scale prob lems\, with a cost growing linearly with problem size. Most importantly we extend the method and the analysis to the Bayesian setting\, i.e.\, GRFs conditioned on noisy data. By using bespoke\, conditioned variants of the Gibbs sampler on each level of the multigrid hierarchy we are able to samp le directly from the posterior with a fixed\, grid-independent integrated autocorrelation time. Our theoretical analysis is confirmed by numerical experiments. We further generalise the approach by exploiting more flexibl e and robust grid hierarchies that were developed in the context of Algeb raic Multigrid solvers. Finally\, using existing PDE libraries\, such as PETSs\, the sampler is easily parallelised and scales optimally to large p rocessor numbers.\\r\\n\\r\\nFor further information about the seminar\, p lease visit this webpage [t3://page?uid=1115]. X-ALT-DESC:

The fast simulation of Gaussian random fields (GRFs) plays a pivotal role in many research areas such as uncertainty quantification\, d ata science and spatial statistics. In theory\, it is a well understood an d solved problem\, but in practice the efficiency and performance of tradi tional sampling procedures degenerates quickly when the random field is di scretised on a grid with spatial resolution going to zero. Most existing a lgorithms\, such as Cholesky factorisation samplers\, do not scale well on large-scale parallel computers. On the other hand\, stationary\, iterativ e approaches such as the Gibbs sampler become extremely inefficient at hig h grid resolution. \;Already in the late 1980s\, Goodman\, Sokal and t heir collaborators wrote a series of papers aimed at accelerating the Gibb s sampler using multigrid ideas. The key observation is the intricate conn ection of random samplers\, such as the Gibbs method\, with iterative solv ers for linear systems. They proposed the so-called multigrid Monte Carlo (MGMC) method - a random analogue of the multigrid method for solving disc retised PDEs. \;We revisit the MGMC algorithm and provide rigorous the oretical justifications for the optimal scalability of the method for larg e scale problems\, with a cost growing linearly with problem size. Most im portantly we extend the method and the analysis to the Bayesian setting\, i.e.\, GRFs conditioned on noisy data. By using bespoke\, conditioned vari ants of the Gibbs sampler on each level of the multigrid hierarchy we are able to sample directly from the posterior with a fixed\, grid-independent integrated autocorrelation time. \;Our theoretical analysis is confir med by numerical experiments. We further generalise the approach by exploi ting more flexible and robust grid hierarchies that were developed in the context of \;Algebraic Multigrid solvers. \;Finally\, using existi ng PDE libraries\, such as PETSs\, the sampler is easily parallelised and scales optimally to large processor numbers.

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For further informa tion about the seminar\, please visit this webpage.

DTEND;TZID=Europe/Zurich:20241213T120000 END:VEVENT END:VCALENDAR