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The projection method for dynamical systems and kinetic equations modelling interacting agents in high-dimension

Mercoledi' 21 Settembre 2011 - Massimo Fornasier

ARGOMENTI: Seminari

SEMINARIO AMEC (congiunto di Analisi, MEccanica e Calcolo),
Mercoledi` 21 Settembre 2011, Massimo Fornasier (Technical University of Munich) terra' in Sala Riunioni VII dalle 11:00 alle 11:30 il prologo e in aula 1C150 alle ore 12:15 il seminario dal titolo "The projection method for dynamical systems and kinetic equations modelling interacting agents in high-dimension".

-Abstract
In this talk we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain dynamical systems modeling complex interactions. In such systems, one has to deal with a large number of agents (typically millions) in spaces of parameters describing each agent of high dimension (thousands or more). Even with todays powerful computers, numerical simulations of such systems are prohibitively expensive. We propose an approach for the simulation of dynamical systems governed by functions of adjacency matrices in high dimension, by random projections via Johnson-Lindenstrauss embeddings, and recovery by compressed sensing techniques. We show how these concepts can be generalized to work for associated kinetic equations, by addressing the phenomenon of the delayed curse of dimension, known in information-based complexity for optimal measure quantization in high dimension. This is a joint work with Jan Haskovec and Jan Vybiral.

Nel prologo di mezz'ora il conferenziere presentera' l'argomento del successivo seminario per permettere a tutti gli interessati una migliore comprensione del problema trattato, con particolare attenzione per i dottorandi e giovani ricercatori.

Rif. int. M. Bardi, C. Marchi, M. Novaga

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