The ability of machine learning (ML) models to “extrapolate” to situations outside of the
range spanned by their training data is crucial for predicting the long-term behavior of non …

We develop and test machine learning techniques for successfully using past state time
series data and knowledge of a time-dependent system parameter to predict the evolution of …

In this topical review, we present a brief overview of the different methods and measures to
detect the occurrence of critical transitions in complex systems. We start by introducing the …

Forecasting is an extensive field of study, which tries to avoid injuries, diseases, and
damages but also can help in energy production, finance investments, etc. Two mathematics …

Multifunctional biological neural networks exploit multistability in order to perform multiple
tasks without changing any network properties. Enabling artificial neural networks (ANNs) to …

Tipping points are abrupt, drastic, and often irreversible changes in the evolution of non-
stationary and chaotic dynamical systems. For instance, increased greenhouse gas …

Abstract Model-free and data-driven prediction of tipping point transitions in nonlinear
dynamical systems is a challenging and outstanding task in complex systems science. We …

The prediction of stochastic dynamical systems and the capture of dynamical behaviors are
profound problems. In this article, we propose a data-driven framework combining Reservoir …

Echo-state networks are simple models of discrete dynamical systems driven by a time
series. By selecting network parameters such that the dynamics of the network is contractive …

Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in
and are driven by temporally varying environments. Such systems can show multiple …