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A topological computation method, called the MGSTD method, is applied to time-series data obtained from meteorological measurement. The method gives decomposition of the dynamics into invariant sets and gradient-like transitions between…

We consider heat fluctuations and fluctuation theorems for systems driven by multiple reservoirs. We establish a fundamental symmetry obeyed by the joint probability distribution for the heat transfers and system coordinates. The symmetry…

Quantum reservoir computing is a machine learning framework that offers ease of training compared to other quantum neural networks, as it does not rely on gradient-based optimization. Learning is performed in a single step on the output…

Reservoir computing has been shown to be a useful framework for predicting critical transitions of a dynamical system if the bifurcation parameter is also provided as an input. Its utility is significant because in real-world scenarios, the…

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…

Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has…

Reservoir computing is a relatively recent computational paradigm that originates from a recurrent neural network and is known for its wide range of implementations using different physical technologies. Large reservoirs are very hard to…

Reservoir computing is a brain-inspired machine learning framework for processing temporal data by mapping inputs into high-dimensional spaces. Physical reservoir computers (PRCs) leverage native fading memory and nonlinearity in physical…

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.…

This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…

Datasets often contain values that naturally reside in a metric space: numbers, strings, geographical locations, machine-learned embeddings in a Euclidean space, and so on. We study the computational complexity of repairing inconsistent…

Time series classification is an important task in its own right, and it is often a precursor to further downstream analytics. To date, virtually all works in the literature have used either shape-based classification using a distance…

Reservoir computing (RC) is a novel approach to time series prediction using recurrent neural networks. In RC, an input signal perturbs the intrinsic dynamics of a medium called a reservoir. A readout layer is then trained to reconstruct a…

The applicability of machine learning for predicting chaotic dynamics relies heavily upon the data used in the training stage. Chaotic time series obtained by numerically solving ordinary differential equations embed a complicated noise of…

In many scientific contexts, different investigators experiment with or observe different variables with data from a domain in which the distinct variable sets might well be related. This sort of fragmentation sometimes occurs in molecular…

We demonstrate reservoir computing with a physical system using a single autonomous Boolean logic element with time-delay feedback. The system generates a chaotic transient with a window of consistency lasting between 30 and 300 ns, which…

This paper introduces a methodology for identifying and simulating financial and economic systems using stochastically structured reservoir computers (SSRCs). The framework combines structure-preserving embeddings with graph-informed…

Many scientific areas, from computer science to the environmental sciences and finance, give rise to multivariate time series which exhibit long memory, or loosely put, a slow decay in their autocorrelation structure. Efficient modelling…

High-precision modeling of systems is one of the main areas of industrial data analysis. Models of systems, their digital twins, are used to predict their behavior under various conditions. We have developed several models of a storage…

Reservoir computers (RC) have proven useful as surrogate models in forecasting and replicating systems of chaotic dynamics. The quality of surrogate models based on RCs is crucially dependent on their optimal implementation that involves…