2017/12/05 by José A. Carrillo, Lorenzo Pareschi, Carrillo, J. A. +3 · 3 citations
Biochemistry, Genetics and Molecular Biology · Decision Sciences · Mathematics · Physics and Astronomy · #35Q83 #65C05 #65M70 #Adaptation and Self-Organizing Systems (nlin.AO) #Analysis of PDEs (math.AP) #Applied mathematics #Computational Physics (physics.comp-ph) #Diffusion and Search Dynamics #FOS: Mathematics #FOS: Physical sciences #Mathematical analysis #Mathematical optimization #Mathematics #Mean field theory #Monte Carlo method #Numerical Analysis (math.NA) #Physics #Polynomial #Polynomial chaos #Probabilistic and Robust Engineering Design #Random field #Statistical physics #Statistics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1712.01677
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2017/12/05 · openalex created_date 2017/12/22 · openalex updated_date 2026/08/05
In this work we focus on the construction of numerical schemes for the approximation of stochastic mean--field equations which preserve the nonnegativity of the solution. The method here developed makes use of a mean-field Monte Carlo method in the physical variables combined with a generalized Polynomial Chaos (gPC) expansion in the random space. In contrast to a direct application of stochastic-Galerkin methods, which are highly accurate but lead to the loss of positivity, the proposed schemes are capable to achieve high accuracy in the random space without loosing nonnegativity of the solution. Several applications of the schemes to mean-field models of collective behavior are reported.