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SUMMARY:Uncertainty quantification for kinetic equations of emergent pheno
 mena - Mattia Zanella	 (Università degli Studi di Pavia)
DTSTART:20220412T135000Z
DTEND:20220412T143500Z
UID:TALK172508@talks.cam.ac.uk
DESCRIPTION:Kinetic equations play a leading role in the modelling of larg
 e systems of interacting particles/agents with a recognized effectiveness 
 in describing real world phenomena ranging from plasma physics to multi-ag
 ent dynamics. The derivation of these models has often to deal with physic
 al\, or even social\, forces that are deduced empirically and of which we 
 have limited information. Hence\, to produce realistic descriptions of the
  underlying systems it is of paramount importance to consider the effects 
 of uncertain quantities as a structural feature in the modelling process.\
 nIn this talk\, we focus on a class of numerical methods that guarantee th
 e preservation of main physical properties of kinetic models with uncertai
 nties. In contrast to a direct application of classical uncertainty quanti
 fication methods\, typically leading to the loss of positivity of the nume
 rical solution of the problem\, we discuss the construction of novel schem
 es that are capable of achieving high accuracy in the random space without
  losing nonnegativity of the solution [1\,3]. Applications of the develope
 d methods are presented in the classical RGD framework and in related mode
 ls in life sciences. In particular\, we concentrate on the interplay of th
 is class of models with mathematical epidemiology where the assessment of 
 uncertainties in data assimilation is crucial to design efficient interven
 tions\, see [2].\n&nbsp\;\nBibliography:\n[1] J. A. Carrillo\, L. Pareschi
 \, M. Zanella. Particle based gPC methods for mean-field models of swarmin
 g with uncertainty. Commun. Comput. Phys.\, 25(2): 508-531\, 2019.&nbsp\;\
 n[2] G. Dimarco\, B. Perthame\, G. Toscani\, M. Zanella. Kinetic models fo
 r epidemic dynamics with social heterogeneity. J. Math. Biol.\, 83\, 4\, 2
 021.&nbsp\;&nbsp\;\n[3] L. Pareschi\, M. Zanella. Monte Carlo stochastic G
 alerkin methods for the Boltzmann equation with uncertainties: space-homog
 eneous case. J. Comput. Phys. 423:109822\, 2020.
LOCATION:Seminar Room 2\, Newton Institute
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