Multi-scale variance reduction methods based on multiple control\n variates for kinetic equations with uncertainties

2018/12/12 by Giacomo Dimarco, Lorenzo Pareschi, Dimarco, Giacomo +1 · 4 citations
Computer Science · Decision Sciences · Physics and Astronomy · #65C05 #65M75 #76P05 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design

paper · pdf · doi:10.48550/arxiv.1812.05485

openalex publication_date 2018/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The development of efficient numerical methods for kinetic equations with\nstochastic parameters is a challenge due to the high dimensionality of the\nproblem. Recently we introduced a multiscale control variate strategy which is\ncapable to accelerate considerably the slow convergence of standard Monte Carlo\nmethods for uncertainty quantification. Here we generalize this class of\nmethods to the case of multiple control variates. We show that the additional\ndegrees of freedom can be used to improve further the variance reduction\nproperties of multiscale control variate methods.\n

Citations

• Optimal Model Management for Multifidelity Monte Carlo Estimation

Cited by

• Efficient numerical methods for the uncertain Boltzmann equation based on a hybrid solver
• Structure and asymptotic preserving deep neural surrogates for uncertainty quantification in multiscale kinetic equations
• Robust feedback control of collisional plasma dynamics in presence of uncertainties
• Control variates with neural surrogates for uncertainty quantification in kinetic equations

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