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The prediction of time series is a challenging task relevant in such diverse applications as analyzing financial data, forecasting flow dynamics or understanding biological processes. Especially chaotic time series that depend on a long…

Reservoir computing (RC) is a machine learning paradigm that harnesses dynamical systems as computational resources. In its quantum extension -- quantum reservoir computing (QRC) -- these principles are applied to quantum systems, whose…

Multifunctionality is ubiquitous in biological neurons. Several studies have translated the concept to artificial neural networks as well. Recently, multifunctionality in reservoir computing (RC) has gained the widespread attention of…

Reservoir Computing (RC) has become popular in recent years thanks to its fast and efficient computational capabilities. Standard RC has been shown to be equivalent in the asymptotic limit to Recurrent Kernels, which helps in analyzing its…

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…

This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space…

It is well known that chaotic dynamic systems (such as three-body system, turbulent flow and so on) have the sensitive dependence on initial conditions (SDIC). Unfortunately, numerical noises (such as truncation error and round-off error)…

Neural systems are well known for their ability to learn and store information as memories. Even more impressive is their ability to abstract these memories to create complex internal representations, enabling advanced functions such as the…

Reservoir computing provides a time and cost-efficient alternative to traditional learning methods.Critical regimes, known as the "edge of chaos," have been found to optimize computational performance in binary neural networks. However,…

As artificial intelligence continues to push into real-time, edge-based and resource-constrained environments, there is an urgent need for novel, hardware-efficient computational models. In this study, we present and validate a neuromorphic…

Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…

Model Predictive Control (MPC) is a powerful control strategy; however, its reliance on online optimization poses significant challenges for implementation on systems with limited computational resources. One possible approach to address…

A Lyapunov design method is used to analyze the nonlinear stability of a generic reservoir computer for both the cases of continuous-time and discrete-time dynamics. Using this method, for a given nonlinear reservoir computer, a radial…

Reservoir computing is a novel machine learning algorithm that uses a nonlinear dynamical system to efficiently learn complex temporal patterns from data. The objective of this thesis is to investigate the principles of reservoir computing…

A robust Learning Model Predictive Controller (LMPC) for uncertain systems performing iterative tasks is presented. At each iteration of the control task the closed-loop state, input and cost are stored and used in the controller design.…

We numerically investigate a time-delayed reservoir computer architecture based on a single mode laser diode with optical injection and optical feedback. Through a high-resolution parametric analysis, we reveal unforeseen regions of high…

Recurrent neural networks (RNNs) are wide-spread machine learning tools for modeling sequential and time series data. They are notoriously hard to train because their loss gradients backpropagated in time tend to saturate or diverge during…

Recurrent neural networks (RNNs) are known to be universal approximators of dynamic systems under fairly mild and general assumptions. However, RNNs usually suffer from the issues of vanishing and exploding gradients in standard RNN…

Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep…

Physical reservoir computing is a computational framework that offers an energy- and computation-efficient alternative to conventional training of neural networks. In reservoir computing, input signals are mapped into the high-dimensional…