Uncertainty Quantification for Hyperbolic and Kinetic Equations

Shi Jin, Lorenzo Pareschi (Eds.)
SEMA SIMAI Springer Series
277 pages, 2018

This book explores recent advances in uncertainty quantification for hyperbolic, kinetic, and related problems. The contributions address a range of different aspects, including: polynomial chaos expansions, perturbation methods, multi-level Monte Carlo methods, importance sampling, and moment methods. The interest in these topics is rapidly growing, as their applications have now expanded to many areas in engineering, physics, biology and the social sciences. Accordingly, the book provides the scientific community with a topical overview of the latest research efforts.

Linear multistep methods for optimal control problems and applications to hyperbolic relaxation systems

Giacomo Albi, Michael Herty, Lorenzo Pareschi
(24/7/2018, preprint arXiv:1807.08547)

We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of accuracy for Adams-Moulton and Adams-Bashford methods, whereas BDF methods preserve high--order accuracy.

Structure preserving schemes for the continuum Kuramoto model: phase transitions

José A. Carrillo, Young-Pil Choi, Lorenzo Pareschi  (13/3/2018 preprint arXiv:1803.03886 to appear in J. Comp. Phys.)

The construction of numerical schemes for the Kuramoto model is challenging due to the structural properties of the system which are essential in order to capture the correct physical behavior, like the description of stationary states and phase transitions. Additional difficulties are represented by the high dimensionality of the problem in presence of multiple frequencies.

Kinetic models for optimal control of wealth inequalities

Bertram Düring, Lorenzo Pareschi, Giuseppe Toscani (6/3/2018, preprint arXiv:1803.02171 to appear in Eur. J. Physics B)

We introduce and discuss optimal control strategies for kinetic models for wealth distribution in a simple market economy, acting to minimize the variance of the wealth density among the population. Our analysis is based on a model predictive control approximation of the microscopic agents' dynamic and results in an alternative theoretical approach to the taxation and redistribution policy.