Open AccessEffective Mori-Zwanzig equation for the reduced-order modeling of stochastic systems
Author(s) -
Yuanran Zhu,
Huan Lei
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021096
Subject(s) - observable , kernel (algebra) , statistical physics , langevin equation , mathematics , parametrization (atmospheric modeling) , monte carlo method , convergence (economics) , hypoelliptic operator , physics , mathematical analysis , pure mathematics , partial differential equation , statistics , quantum mechanics , linear differential equation , economic growth , economics , radiative transfer
Built upon the hypoelliptic analysis of the effective Mori-Zwanzig (EMZ) equation for observables of stochastic dynamical systems, we show that the obtained semigroup estimates for the EMZ equation can be used to derive prior estimates of the observable statistics for systems in the equilibrium and nonequilibrium state. In addition, we introduce both first-principle and data-driven methods to approximate the EMZ memory kernel and prove the convergence of the data-driven parametrization schemes using the regularity estimate of the memory kernel. The analysis results are validated numerically via the Monte-Carlo simulation of the Langevin dynamics for a Fermi-Pasta-Ulam chain model. With the same example, we also show the effectiveness of the proposed memory kernel approximation methods.