On the estimation of the Mori-Zwanzig memory integral
Abstract
We develop a thorough mathematical analysis to deduce conditions for the accuracy and convergence of different approximations of the memory integral in the Mori-Zwanzig (MZ) equation. In particular, we derive error bounds and sufficient convergence conditions for short-memory approximations, the t-model, and hierarchical (finite-memory) approximations. In addition, we derive useful upper bounds for the MZ memory integral, which allow us to estimate a priori the contribution of the MZ memory to the dynamics. Such upper bounds are easily computable for systems with finite-rank projections. Numerical examples are presented and discussed for linear and nonlinear dynamical systems evolving from random initial states.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 21, 2018
- Source ID
- 10.1063/1.5003467
Entities
People
- Daniele Venturi
- Jason M. Dominy
- Yuanran Zhu
Organizations
- Air Force Office of Scientific Research
- University of California