Data-driven learning of Mori–Zwanzig operators for isotropic turbulence

Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori-Zwanzig (MZ) formalism provides mathematically formal procedure constructing representations high-dimensional dynamical systems, where effect due to unresolved are captured in memory kernel and orthogonal dynamics. Turbulence based on MZ have been scarce limited knowledge operators, originates from difficulty deriving kernels complex nonlinear systems. this work, we apply recently developed data-driven learning algorithm, Koopman's description systems Mori's linear projection operator, set fully-resolved isotropic turbulence datasets extract operators. With data augmentation using known symmetries, extracted Markov term, kernel, statistically converged Generalized Fluctuation-Dissipation Relation can be verified. The properties dynamics, their dependence choices observables investigated address modeling assumptions that commonly used MZ-based models. A series numerical experiments then constructed evaluate effects predictions. Results show prediction errors strongly affected by choice further reduced including past history kernel.