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 …

The climate is a forced and dissipative nonlinear system featuring nontrivial dynamics on a
vast range of spatial and temporal scales. The understanding of the climate's structural and …

This paper has two interrelated foci:(i) obtaining stable and efficient data-driven closure
models by using a multivariate time series of partial observations from a large-dimensional …

This paper introduces coordinate-independent methods for analyzing multiscale dynamical
systems using numerical techniques based on the transfer operator and its adjoint. In …

We formulate a new projection-based reduced-order modeling technique for non-linear
dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov …

Reduced models of nonlinear dynamical systems require closure, or the modelling of the
unresolved modes. The Mori–Zwanzig procedure can be used to derive formally closed …

This work uses the Mori-Zwanzig (MZ) formalism, a concept originating from nonequilibrium
statistical mechanics, as a basis for the development of coarse-grained models of …

Developing suitable approximate models for analyzing and simulating complex nonlinear
systems is practically important. This paper aims at exploring the skill of a rich class of …

The development of reduced models for complex multiscale problems remains one of the
principal challenges in computational physics. The optimal prediction framework of Chorin et …

We present a general numerical approach for constructing governing equations for unknown
dynamical systems when data on only a subset of the state variables are available. The …