Related papers: Predicting Critical Transitions in Multiscale Dyna…
Reservoir computing is an emerging, but very successful approach towards processing and classification of various signals. It can be described as a model of a transient computation, where influence of input changes internal dynamics of…
Reservoir computing is a recently introduced, highly efficient bio-inspired approach for processing time dependent data. The basic scheme of reservoir computing consists of a non linear recurrent dynamical system coupled to a single input…
Reservoir computing is a machine learning paradigm that uses a structure called a reservoir, which has nonlinearities and short-term memory. In recent years, reservoir computing has expanded to new functions such as the autonomous…
Closed quantum systems exhibit different dynamical regimes, like Many-Body Localization or thermalization, which determine the mechanisms of spread and processing of information. Here we address the impact of these dynamical phases in…
Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that…
Reservoir computing has proven effective for tasks such as time-series prediction, particularly in the context of chaotic systems. However, conventional reservoir computing frameworks often face challenges in achieving high prediction…
Reservoir Computing (RC) is a simple and efficient model-free framework for forecasting the behavior of nonlinear dynamical systems from data. Here, we show that there exist commonly-studied systems for which leading RC frameworks struggle…
Exploring nonlinear chemical dynamic systems for information processing has emerged as a frontier in chemical and computational research, seeking to replicate the brain's neuromorphic and dynamic functionalities. We have extensively…
Mechanical systems exhibit complex dynamical behavior from harmonic oscillations to chaotic motion. The dynamics undergo qualitative changes due to changes to internal system parameters like stiffness and changes to external forcing.…
Reservoir computing is a machine learning algorithm that excels at predicting the evolution of time series, in particular, dynamical systems. Moreover, it has also shown superb performance at solving partial differential equations. In this…
We establish the potential of continuous-variable Gaussian states of linear dynamical systems for machine learning tasks. Specifically, we consider reservoir computing, an efficient framework for online time series processing. As a…
Reservoir Computing is a relatively new framework created to allow the usage of powerful but complex systems as computational mediums. The basic approach consists in training only a readout layer, exploiting the innate separation and…
Reservoir computing - information processing based on untrained recurrent neural networks with random connections - is expected to depend on the nonlinear properties of the neurons and the resulting oscillatory, chaotic, or fixpoint…
Reservoir computing is a best-in-class machine learning algorithm for processing information generated by dynamical systems using observed time-series data. Importantly, it requires very small training data sets, uses linear optimization,…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
In a Nature article, Scheffer et al. presented a novel data-driven framework to predict critical transitions in complex systems. These transitions, which may stem from failures, degradation, or adversarial actions, have been attributed to…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian,…
Reservoir computing (RC) is a state-of-the-art machine learning method that makes use of the power of dynamical systems (the reservoir) for real-time inference. When using biological complex systems as reservoir substrates, it serves as a…
We tested the performance of reservoir computing (RC) in predicting the dynamics of a certain non-autonomous dynamical system. Specifically, we considered a van del Pol oscillator subjected to periodic external force with frequent phase…