30 citations · 109 across the 14 of their papers we have counts for
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Combinatorial Mori-Zwanzig Theory
Yuanran Zhu
We introduce a combinatorial version Mori-Zwanzig theory and develop from it a family of self-consistent evolution equations for the correlation function or Green's function of int…
A simple hypocoercivity analysis for the effective Mori-Zwanzig equation
Yuanran Zhu
We provide a simple hypocoercivity analysis for the effective Mori-Zwanzig equation governing the time evolution of noise-averaged observables in a stochastic dynamical system. Und…
Effective Mori-Zwanzig equation for the reduced-order modeling of stochastic systems
Yuanran Zhu, Huan Lei
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…
Hypoellipticity and the Mori-Zwanzig formulation of stochastic differential equations
Yuanran Zhu, Daniele Venturi
We develop a thorough mathematical analysis of the effective Mori-Zwanzig (EMZ) equation governing the dynamics of noise-averaged observables in stochastic differential equations d…
Faber approximation to the Mori-Zwanzig equation
Yuanran Zhu, Daniele Venturi
We develop a new effective approximation of the Mori-Zwanzig equation based on operator series expansions of the orthogonal dynamics propagator. In particular, we study the Faber s…