Related papers: On Dominant Manifolds in Reservoir Computing Netwo…

Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and…

Quantum reservoir computing has emerged as a promising paradigm for harnessing quantum systems to process temporal data efficiently by bypassing the costly training of gradient-based learning methods. Here, we demonstrate the capability of…

Reservoir Computing is a machine learning approach that uses the rich repertoire of complex system dynamics for function approximation. Current approaches to reservoir computing use a network of coupled integrating neurons that require a…

We introduce a novel class of untrained Recurrent Neural Networks (RNNs) within the Reservoir Computing (RC) paradigm, called Residual Reservoir Memory Networks (ResRMNs). ResRMN combines a linear memory reservoir with a non-linear…

There is a growing interest in the development of artificial neural networks that are implemented in a physical system. A major challenge in this context is that these networks are difficult to train since training here would require a…

Recurrent neural networks are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here…

This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…

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 study the learning dynamics of self-predictive learning for reinforcement learning, a family of algorithms that learn representations by minimizing the prediction error of their own future latent representations. Despite its recent…

Rayleigh-Benard convection (RBC) is a canonical system for buoyancy-driven turbulence and heat transport, central to geophysical and industrial flows. Developing efficient control strategies remains challenging at high Rayleigh numbers,…

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model…

Reservoir computing is a promising approach for harnessing the computational power of recurrent neural networks while dramatically simplifying training. This paper investigates the application of integrate-and-fire neurons within reservoir…

Discovering governing equations from data, in particular high dimensional data, is challenging in various fields of science and engineering, and it has potential to revolutionise the science and technology in this big data era. This paper…

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…

The human brain's synapses have remarkable activity-dependent plasticity, where the connectivity patterns of neurons change dramatically, relying on neuronal activities. As a biologically inspired neural network, reservoir computing (RC)…

The reservoir computing networks (RCNs) have been successfully employed as a tool in learning and complex decision-making tasks. Despite their efficiency and low training cost, practical applications of RCNs rely heavily on empirical…

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…

Learning tractable linear representations of nonlinear dynamical systems via Koopman operator theory is often hindered by dictionary selection, temporal memory encoding, and numerical ill-conditioning. Inspired by Reservoir Computing (RC)…

Forecasting nonlinear time series with multi-scale temporal structures remains a central challenge in complex systems modeling. We present a novel reservoir computing framework that combines delay embedding with random Fourier feature (RFF)…