Related papers: Predicting Critical Transitions in Multiscale Dyna…

Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…

Nonlinear dynamical systems exposed to changing forcing can exhibit catastrophic transitions between alternative and often markedly different states. The phenomenon of critical slowing down (CSD) can be used to anticipate such transitions…

A reservoir computer is a dynamical system that may be used to perform computations. A reservoir computer usually consists of a set of nonlinear nodes coupled together in a network so that there are feedback paths. Training the reservoir…

Reconstructing the KAM dynamics diagram of Hamiltonian system from the time series of a limited number of parameters is an outstanding question in nonlinear science, especially when the Hamiltonian governing the system dynamics are unknown.…

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…

We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development…

Quantum reservoir computing is an emergent field in which quantum dynamical systems are exploited for temporal information processing. In previous work, it was found a feature that makes a quantum reservoir valuable: contractive dynamics of…

Quantum reservoir computing has emerged as a promising machine learning paradigm for processing temporal data on near-term quantum devices, as it allows for exploiting the large computational capacity of the qubits without suffering from…

Forecasting dynamical systems is of importance to numerous real-world applications. When possible, dynamical systems forecasts are constructed based on first-principles-based models such as through the use of differential equations. When…

Key components of the Earth system can undergo abrupt and potentially irreversible transitions when the magnitude or rate of external forcing exceeds critical thresholds. In this study, we use the example of the Atlantic Meridional…

Several recent papers have shown that reservoir computers are useful for analyzing and predicting dynamical systems. Reservoir computers have also been shown to be useful for various classification problems. In this work, a reservoir…

Reservoir Computing is a relatively recent computational framework based on a large Recurrent Neural Network with fixed weights. Many physical implementations of Reservoir Computing have been proposed to improve speed and energy efficiency.…

I give an overview of rare event simulation techniques to generate dynamical pathways across high free energy barriers. The methods on which I will concentrate are the reactive flux approach, transition path sampling, (replica-exchange)…

Many turbulent flows undergo drastic and abrupt configuration changes with huge impacts. As a paradigmatic example we study the multistability of jet dynamics in a barotropic beta plane model of atmosphere dynamics. It is considered as the…

Reservoir computing (RC) is a machine learning algorithm that can learn complex time series from data very rapidly based on the use of high-dimensional dynamical systems, such as random networks of neurons, called "reservoirs." To implement…

We propose a new reservoir computing method for forecasting high-resolution spatiotemporal datasets. By combining multi-resolution inputs from coarser to finer layers, our architecture better captures both local and global dynamics. Applied…

The rising computational and energy demands of artificial intelligence systems urge the exploration of alternative software and hardware solutions that exploit physical effects for computation. According to machine learning theory, a neural…

Stemming from physics and later applied to other fields such as ecology, the theory of critical transitions suggests that some regime shifts are preceded by statistical early warning signals. Reddit's r/place experiment, a large-scale…

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 mechanisms that trigger critical transitions, and how…

A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…