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Article
Computer Science, Artificial Intelligence
Felix Koester et al.
Summary: This paper analyzes the memory capacity of a delay-based reservoir computer using a Hopf normal form as nonlinearity, and calculates its linear as well as higher order recall capabilities. The results show that the total memory capacity is dependent on the ratio between the information input period and the time delay in the system.
COGNITIVE COMPUTATION
(2023)
Article
Mathematics, Applied
Kohei Tsuchiyama et al.
Summary: Reservoir computing is a machine learning paradigm that utilizes a reservoir structure with nonlinearities and short-term memory. It has expanded to various functions including autonomous generation of chaotic time series, time series prediction, and classification. Sampling plays a crucial role in physical reservoir computers, but finding the suitable sampling frequency is essential for effectively regenerating chaotic time series.
Article
Mathematics, Applied
T. Alberti et al.
Summary: Natural systems exhibit emergent phenomena at different scales, with chaotic behavior at large scales and randomness at small scales. The properties of the underlying attractor, which hosts the system trajectories, are usually studied quantitatively to understand these features. However, the multi-scale nature of natural systems makes it difficult to obtain a clear picture of the attracting set. In this study, we use an adaptive decomposition method and extreme value theory to analyze the scale-dependent dimension of the attractor, showing that it can discriminate between different types of noise.
Article
Nanoscience & Nanotechnology
Tobias Huelser et al.
Summary: This article investigates the relationship between information processing capacity and task performance, finding poor correlation between them. A new method for calculating task mean square error is proposed, and it is found that there is good consistency between predicted and actual errors as long as the task input sequences do not have long autocorrelation times.
Article
Physics, Multidisciplinary
Yuanzhao Zhang et al.
Summary: Reservoir computing is a model-free framework for predicting the behavior of nonlinear dynamical systems. However, it struggles to learn the dynamics of some systems unless key information is known. Next-generation reservoir computing can accurately predict the basins of attraction of a system, but small uncertainty in nonlinearity can reduce the prediction accuracy.
PHYSICAL REVIEW RESEARCH
(2023)
Article
Mathematics, Applied
T. L. Carroll
Summary: A reservoir computer is a computational approach that utilizes a high dimensional dynamical system by connecting nonlinear nodes into a network, allowing for memory and feedback. The fading memory duration is crucial for the reservoir computer's ability to solve specific problems effectively and efficiently.
Article
Meteorology & Atmospheric Sciences
Troy Arcomano et al.
Summary: This paper describes the implementation of a combined hybrid-parallel prediction approach on a low-resolution atmospheric global circulation model. The hybrid model, which combines a physics-based numerical model with a machine learning component, produces more accurate forecasts for various atmospheric variables compared to the host model. Furthermore, the hybrid model exhibits smaller systematic errors and more realistic temporal variability in simulating the climate.
JOURNAL OF ADVANCES IN MODELING EARTH SYSTEMS
(2022)
Review
Computer Science, Interdisciplinary Applications
Ahmad Alsahref et al.
Summary: Time-series forecasting is an important discipline in data modeling that utilizes past observations to predict future values. This article reviews the methods of analyzing time series, from traditional linear modeling techniques to automated machine learning (AutoML) frameworks and deep learning models. The objective is to identify the challenges of time-series forecasting and the techniques used to address them. The article serves as a guide and reference for researchers and industries using AutoML for forecasting, while also highlighting gaps in previous works and forecasting techniques.
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING
(2022)
Article
Multidisciplinary Sciences
Peter J. Baddoo et al.
Summary: Research in modern data-driven dynamical systems tackles the challenges of high dimensionality, unknown dynamics, and nonlinearity. This work presents a kernel method for learning interpretable data-driven models for high-dimensional, nonlinear systems. The method efficiently handles high-dimensional data and incorporates partial knowledge of system physics.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Zhou Wu et al.
Summary: In this article, a new chain-structure echo state network (CESN) is proposed for multivariate time series prediction, utilizing the philosophy of "divide and conquer" to divide input vectors into clusters. The network is trained using least-squares regression and stochastic local search (SLS) to optimize the output weights and minimize the loss function, effectively preventing overfitting. The effectiveness and robustness of CESN and SLS-CESN are verified through chaos prediction benchmarks and real applications.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Mathematics, Applied
Thomas L. Carroll et al.
Summary: A reservoir computer is a powerful computing system constructed by connecting a large number of nonlinear nodes, which can achieve accurate results and operate at high speeds. However, the complexity of its construction and the requirement for a high number of nonlinear nodes make it challenging. This study proposes a time-shifting technique that divides the reservoir computer into a small set of nonlinear nodes and a separate set of time-shifted reservoir output signals, which greatly simplifies the construction process and improves the performance of the reservoir computer.
Article
Mathematics, Applied
Daniel J. Gauthier et al.
Summary: Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. The next-generation reservoir computing approach simplifies training further and exhibits higher accuracy in predicting attractor characteristics compared to traditional approaches.
Article
Mathematics, Applied
Mousumi Roy et al.
Summary: In this article, a data-driven approach using echo state network (ESN) is investigated to infer the dynamics of multistable systems. The machine is able to predict diverse dynamics for different parameter values, even at distant parameters from the training dynamics. The whole bifurcation diagram can also be accurately predicted. Additionally, the study extends to exploring the dynamics of co-existing attractors at unknown parameter values and identifying the basins for different attractors.
Article
Mathematics, Applied
Wendson A. S. Barbosa et al.
Summary: Forecasting the behavior of high-dimensional dynamical systems using machine learning requires efficient methods to learn the underlying physical model. This study demonstrates spatiotemporal chaos prediction using a machine learning architecture combined with a next-generation reservoir computer, which achieves state-of-the-art performance with significantly faster training process and smaller training data set compared to other machine learning algorithms. The computational cost and training data are further reduced by exploiting the translational symmetry of the model.
Article
Optics
Kazutaka Kanno et al.
Summary: In this study, reservoir computing based on a single semiconductor laser with optical feedback modulation is investigated numerically and experimentally. The results show that the performance of the phase modulation scheme is better than that of the intensity modulation scheme, and the prediction error improves for large injection currents. The physical origin of the superior performance of the phase modulation scheme is analyzed using steady-state analysis in the phase space.
Article
Physics, Multidisciplinary
Yujie You et al.
Summary: This study proposes a novel spatiotemporal transformer neural network (STNN) for efficient prediction of high-dimensional short-term time-series, which utilizes a continuous attention mechanism and various attention mechanisms to integrate and predict effective information. Experimental results demonstrate that STNN significantly outperforms existing methods in multi-step forecasting.
Proceedings Paper
Computer Science, Artificial Intelligence
Lina C. Jaurigue et al.
Summary: This article discusses the performance of photonic reservoir computing, focusing on the impact of delay lines and the interplay between coupling topology and performance for various benchmark tasks. The study shows that additional delayed input can be beneficial for reservoir computing setups, as it provides an easy tuning parameter to improve the performance on a range of tasks.
EMERGING TOPICS IN ARTIFICIAL INTELLIGENCE (ETAI) 2022
(2022)
Article
Computer Science, Artificial Intelligence
Felix Koester et al.
Summary: This study demonstrates that delay-based reservoir computers can be characterized by a universal master memory function (MMF) and provides linear memory capacity. An analytical description of the MMF is proposed for efficient computing and can be applied to various reservoir scenarios.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Physics, Multidisciplinary
Lina Jaurigue et al.
Summary: Reservoir computing is a machine learning method that utilizes the response of a dynamical system to solve tasks, particularly suited for hardware implementation and effective in time series prediction tasks. While still requiring parameter optimization, including a time-delayed version of the input can improve performance significantly.
Article
Multidisciplinary Sciences
Ryan Pyle et al.
Summary: Recent advancements in computing algorithms and hardware have led to increased interest in developing high-accuracy, low-cost surrogate models for simulating physical systems. The echo state network (ESN) technique has gained popularity within the weather and climate modeling community. A study found that state-of-the-art LSR-ESNs reduce to a polynomial regression model called D2R2, which outperforms other approaches significantly in computational savings.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Mathematics, Applied
Allen G. Hart et al.
Summary: Echo State Networks (ESNs) are single-layer recurrent neural networks trained by regularised linear least squares regression, which can approximate target functions effectively. The numerical experiments on the Lorenz system demonstrate the validity and feasibility of ESN.
PHYSICA D-NONLINEAR PHENOMENA
(2021)
Article
Mathematics, Applied
Alexander Wikner et al.
Summary: This study discusses the forecasting of chaotic dynamical systems using noisy partial measurements data, with a focus on combining machine learning with knowledge-based models to improve predictions. By assimilating synthetic data and training machine learning models with partial measurements, it shows potential to correct imperfections in knowledge-based models and improve forecasting accuracy.
Article
Engineering, Electrical & Electronic
Julian Bueno et al.
Summary: Optical neural networks using Reservoir Computing technology combined with Vertical Cavity Surface Emitting Lasers show high performance and potential in optical neural network implementations. VCSELs have unique advantages for future photonic neural networks, such as high speed, low power consumption, reduced cost, and ease of integration.
IEEE PHOTONICS TECHNOLOGY LETTERS
(2021)
Article
Multidisciplinary Sciences
Daniel J. Gauthier et al.
Summary: Reservoir computers are artificial neural networks that can be trained on small data sets with large random matrices and numerous metaparameters. Nonlinear vector autoregression is a superior machine learning algorithm compared to reservoir computing, requiring fewer training data sets and training time.
NATURE COMMUNICATIONS
(2021)
Article
Computer Science, Artificial Intelligence
Jason Z. Kim et al.
Summary: Computational systems are designed to store and manipulate information, while neurobiological systems adapt to perform similar functions without explicit engineering. Recent research has shown that recurrent neural networks (RNNs) can learn to modify complex information representations using examples and control signals, allowing for continuous interpolation and extrapolation of these representations far beyond the training data. Furthermore, RNNs can infer bifurcation structures and chaos routes, as well as extrapolate non-dynamical trajectories.
NATURE MACHINE INTELLIGENCE
(2021)
Article
Optics
Felix Koester et al.
Summary: This paper provides a deep insight into the computation capability of delay based reservoir computing through an eigenvalue analysis and finds a connection between task-independent memory capacity and the eigenvalue spectrum of the dynamical system. The performance of reservoir computing can be predicted by analyzing the small signal response of the reservoir. Analysis can be applied to any dynamical system used as a reservoir.
JOURNAL OF PHYSICS-PHOTONICS
(2021)
Article
Mathematics, Applied
Yanne K. Chembo
Article
Multidisciplinary Sciences
Philipp Neumann et al.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2019)
Article
Mathematics, Applied
Jaideep Pathak et al.
Article
Optics
Yoma Kuriki et al.
Article
Physics, Multidisciplinary
Jaideep Pathak et al.
PHYSICAL REVIEW LETTERS
(2018)
Article
Multidisciplinary Sciences
Pantelis R. Vlachas et al.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2018)
Article
Optics
Kosuke Takano et al.
Article
Physics, Fluids & Plasmas
Piotr Antonik et al.
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Computer Science, Artificial Intelligence
Shisheng Zhong et al.
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Computer Science, Artificial Intelligence
Silvia Ortin et al.
COGNITIVE COMPUTATION
(2017)
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Computer Science, Artificial Intelligence
Lars Keuninckx et al.
COGNITIVE COMPUTATION
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Mathematics, Applied
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Optics
Joma Nakayama et al.
Article
Multidisciplinary Sciences
Steven L. Brunton et al.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
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Article
Multidisciplinary Sciences
Lyudmila Grigoryeva et al.
SCIENTIFIC REPORTS
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Multidisciplinary Sciences
Daniel Brunner et al.
NATURE COMMUNICATIONS
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Optics
L. Larger et al.
Article
Multidisciplinary Sciences
Y. Paquot et al.
SCIENTIFIC REPORTS
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Article
Multidisciplinary Sciences
Joni Dambre et al.
SCIENTIFIC REPORTS
(2012)
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Multidisciplinary Sciences
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NATURE COMMUNICATIONS
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Mathematics, Applied
AK Kassam et al.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
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Article
Computer Science, Artificial Intelligence
W Maass et al.
NEURAL COMPUTATION
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