MEAN-FIELD CONTROL VARIATE METHODS FOR KINETIC EQUATIONS WITH UNCERTAINTIES AND APPLICATIONS TO SOCIOECONOMIC SCIENCES
| Autor: | Torsten Trimborn, Lorenzo Pareschi, Mattia Zanella |
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| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
Control and Optimization uncertainty quantification Computer science Monte Carlo method FOS: Physical sciences stochastic sampling Space (mathematics) Control variates NO FOS: Mathematics control variate methods Discrete Mathematics and Combinatorics Applied mathematics Mathematics - Numerical Analysis Uncertainty quantification Condensed Matter - Statistical Mechanics Statistical Mechanics (cond-mat.stat-mech) Numerical analysis kinetic equations Monte Carlo methods Numerical Analysis (math.NA) Boltzmann equation Nonlinear Sciences - Adaptation and Self-Organizing Systems multi-fidelity methods Modeling and Simulation Phase space mean field approximations Direct simulation Monte Carlo Adaptation and Self-Organizing Systems (nlin.AO) |
| Zdroj: | International Journal for Uncertainty Quantification. 12:61-84 |
| ISSN: | 2152-5080 |
| DOI: | 10.1615/int.j.uncertaintyquantification.2021037960 |
| Popis: | In this paper, we extend a recently introduced multi-fidelity control variate for the uncertainty quantification of the Boltzmann equation to the case of kinetic models arising in the study of multiagent systems. For these phenomena, where the effect of uncertainties is particularly evident, several models have been developed whose equilibrium states are typically unknown. In particular, we aim to develop efficient numerical methods based on solving the kinetic equations in the phase space by Direct Simulation Monte Carlo (DSMC) coupled to a Monte Carlo sampling in the random space. To this end, exploiting the knowledge of the corresponding mean-field approximation we develop novel mean-field Control Variate (MFCV) methods that are able to strongly reduce the variance of the standard Monte Carlo sampling method in the random space. We verify these observations with several numerical examples based on classical models , including wealth exchanges and opinion formation model for collective phenomena. |
| Databáze: | OpenAIRE |
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