Data assimilation (DA) and uncertainty quantification (UQ) are extensively used in analysing
and reducing error propagation in high-dimensional spatial-temporal dynamics. Typical …

Computational models in neuroscience usually take the form of systems of differential
equations. The behaviour of such systems is the subject of dynamical systems theory …

We examine the efficiency of Recurrent Neural Networks in forecasting the spatiotemporal
dynamics of high dimensional and reduced order complex systems using Reservoir …

Causal inference in complex systems has been largely promoted by the proposal of some
advanced temporal causation models. However, temporal models have serious limitations …

We develop a methodology to construct low-dimensional predictive models from data sets
representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic …

We use recent advances in the machine learning area known as “reservoir computing” to
formulate a method for model-free estimation from data of the Lyapunov exponents of a …

Spectral decomposition of the Koopman operator is attracting attention as a tool for the
analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular …

Numerical approximation methods for the Koopman operator have advanced considerably
in the last few years. In particular, data-driven approaches such as dynamic mode …

We establish the convergence of a class of numerical algorithms, known as dynamic mode
decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite …

A machine-learning approach called “reservoir computing” has been used successfully for
short-term prediction and attractor reconstruction of chaotic dynamical systems from time …