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Uncertainty quantification for kinetic equations of collective behavior

Mattia Zanella, Politecnico di Torino

n this seminar we concentrate on collocation and stochastic Galerkin methods for the uncertainty quantification of Vlasov--Fokker--Planck (VFP) equations with nonlocal flux. In particular, we develop methods that preserve their structural properties and that are spectrally accurate in the random space. In contrast to a direct application of classical uncertainty quantification methods, which are typically lead to the loss of positivity and of entropy properties, the proposed schemes are capable to achieve high accuracy in the random space without losing non-negativity of the solution, which dissipates the entropy under suitable assumptions. Applications of the developed methods will be presented in the context of social and traffic dynamics.

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Short Bio:

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Mattia Zanella obtained his PhD in 2017 with a thesis entitled ``Boltzmann--type and meanfield modeling of social dynamics: numerics, control, uncertainty quantification'' under the direction of Prof. Lorenzo Pareschi. He is actually Assistant Professor (Ricercatore a Tempo Determinato di tipo A) at the Department of Mathematical Sciences ``G. L. Lagrange'', Politecnico di Torino. His research interests are focused on uncertainty quantification for kinetic equations, optimal control methods  and kinetic models for collective phenomena. 

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