Faber approximation to the Mori-Zwanzig equation
Provides a novel, provably optimal approximation method for the Mori-Zwanzig equation, relevant for reducing computational complexity in molecular dynamics and other linear systems.
The paper introduces a Faber series approximation for the Mori-Zwanzig equation, achieving asymptotically optimal convergence (at least R-superlinear) for linear dynamical systems, and demonstrates its effectiveness on random wave propagation and harmonic oscillator chains.
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 series, which yields asymptotically optimal approximations converging at least $R$-superlinearly with the polynomial order for linear dynamical systems. We provide a through theoretical analysis of the new method and present numerical applications to random wave propagation and harmonic chains of oscillators interacting on the Bethe lattice and on graphs with arbitrary topology.