Ai Proff. Ordinari Ai Proff. Associati Ai Ricercatori ________________________ Gentili colleghe/i, ricevo e vi giro la comunicazione con argomento in oggetto. Cordialmente, Prof. Lucio Cerrito Coordinatore della Macroarea di Scienze MM.FF.NN. ________ Gentili Colleghe e Colleghi, il terzo colloquio interdipartimentale sui nuovi metodi computazionali si svolgerà in aula T7, a partire dalle 14:30 di lunedì 6 maggio 2024. L'oratore sarà Alessio Troiani del Dipartimento di Matematica e Informatica dell'Università di Perugia, che ci parlerà di "Minimizing multivariate functions through Natively Parallel Markov Chains". Il riassunto del contenuto del seminario è riportato alla fine del presente messaggio. Con i nostri più cordiali saluti, Gianfranco Bocchinfuso (Dip. di Scienze e Tecnologie Chimiche), Michele Buzzicotti (Dip. di Fisica), Dario Del Moro (Dip. di Fisica), Ugo Locatelli (Dip. di Matematica), Blasco Morozzo Della Rocca (Dip. di Biologia), Gerardo Pepe (Dip. di Biologia). %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Author: Alessio Troiani Dipartimento di Matematica e Informatica Università di Perugia Title: "Minimizing multivariate functions through Natively Parallel Markov Chains" Abstract. Consider the problem of minimizing an objective function f of several variables where each variable can take a finite number of values. The total number of values f can take is finite and, in principle, this problem can be solved by direct inspection. However, the number of possible values for f grows exponentially fast and this approach becomes rapidly unfeasible as the number of variables becomes large. One of the several methods developed to tackle problems of this type, coming from statistical mechanics, is Markov Chain Monte Carlo (MCMC). The idea behind MCMC consists of defining a Markov Chain whose state space coincides with the domain of the objective function and whose stationary distribution gives high probability to the states corresponding to small values of $f$. If the chain is run for a sufficiently long time, the chain will likely visit such states. To minimize functions with the MCMC approach, one typically defines a Markov Chain which, at each step, tries to change the value of a single variable. This way of proceeding allows fine-tuning the stationary distribution of the chain but uses the parallel computing architectures available nowadays rather poorly. In this talk, I will present a class of Markov Chains where multiple variables are updated at each step and such that the stationary measure is concentrated on the minima of the objective function thus providing a naturally parallel algorithm to minimize f which exploits parallel computing at its fullest. |
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