Related papers: Data-driven characterization of spatiotemporal cha…

Probabilistic forecasting is crucial for real-world spatiotemporal systems, such as climate, energy, and urban environments, where quantifying uncertainty is essential for informed, risk-aware decision-making. While diffusion models have…

The method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems has been proposed. The application of this method is illustrated by the consideration of two different systems: i) the fluid model…

We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We…

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…

The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fundamental drivers of forecast accuracy. Here, we demonstrate…

We propose a physics-aware machine learning method to time-accurately predict extreme events in a turbulent flow. The method combines two radically different approaches: empirical modelling based on reservoir computing, which learns the…

Reservoir Computing (RC), a type of recurrent random neural network, is a powerful framework for modeling complex and chaotic dynamics. However, its autonomous (closed-loop) operation is often plagued by inherent instability. Moreover,…

Using large-scale parallel numerical simulations we explore spatiotemporal chaos in Rayleigh-B\'enard convection in a cylindrical domain with experimentally relevant boundary conditions. We use the variation of the spectrum of Lyapunov…

As an alternative approach for predicting complex dynamical systems where physics-based models are no longer reliable, reservoir computing (RC) has gained popularity. The hybrid approach is considered an interesting option for improving the…

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 Computing and Normalizing Flow to study this issue, which…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

Emergence, a global property of complex adaptive systems (CASs) constituted by interactive agents, is prevalent in real-world dynamic systems, e.g., network-level traffic congestions. Detecting its formation and evaporation helps to monitor…

We focus on chaotic dynamical systems and analyze their time series with the use of autoencoders, i.e., configurations of neural networks that map identical output to input. This analysis results in the determination of the latent space…

An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the…

Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be…

Forecasting chaotic time series requires models that can capture the intrinsic geometry of the underlying attractor while remaining computationally efficient. We introduce a novel reservoir computing (RC) framework that integrates…

Chaos is omnipresent in nature, and its understanding provides enormous social and economic benefits. However, the unpredictability of chaotic systems is a textbook concept due to their sensitivity to initial conditions, aperiodic behavior,…

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…

In this paper a new concept, namely the critical predictable time $T_c$, is introduced to give a more precise description of computed chaotic solutions of nonlinear differential equations: it is suggested that computed chaotic solutions are…

Ensemble prediction systems are an invaluable tool for weather forecasting. Practically, ensemble predictions are obtained by running several perturbations of the deterministic control forecast. However, ensemble prediction is associated…