Klaus Hasselmann's revolutionary intuition in climate science was to use the stochasticity
associated with fast weather processes to probe the slow dynamics of the climate system …

A reduced basis method based on a physics-informed machine learning framework is
developed for efficient reduced-order modeling of parametrized partial differential equations …

Closure modeling based on the Mori-Zwanzig formalism has proven effective to improve the
stability and accuracy of projection-based model order reduction. However, closure models …

Closure problems are omnipresent when simulating multiscale systems, where some
quantities and processes cannot be fully prescribed despite their effects on the simulation's …

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by
reducing the unnecessary degrees of freedom of the fine-grained (FG) system while …

Complex dynamical systems are used for predictions in many domains. Because of
computational costs, models are truncated, coarsened or aggregated. As the neglected and …

For over a century, reduced order models (ROMs) have been a fundamental discipline of
theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr …

This paper series aims to establish a complete correspondence between fine-grained (FG)
and coarse-grained (CG) dynamics by way of excess entropy scaling (introduced in Paper I) …

The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess
entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems …

This work introduces a method for learning low-dimensional models from data of high-
dimensional black-box dynamical systems. The novelty is that the learned models are …