Reservoir Computing Research Articles

Hidden data recovery using reservoir computing: Adaptive network model and experimental brain signals.

The problem of hidden data recovery is crucial in various scientific and technological fields, particularly in neurophysiology, where experimental data can often be incomplete or corrupted. We investigate the application of reservoir computing (RC) to recover hidden data from both model Kuramoto network system and real neurophysiological signals (EEG). Using an adaptive network of Kuramoto phase oscillators, we generated and analyzed macroscopic signals to understand the efficiency of RC in hidden signal recovery compared to linear regression (LR). Our findings indicate that RC significantly outperforms LR, especially in scenarios with reduced signal information. Furthermore, when applied to real EEG data, RC achieved more accurate signal reconstruction than traditional spline interpolation methods. These results underscore RC's potential for enhancing data recovery in neurophysiological studies, offering a robust solution to improve data integrity and reliability, which is essential for accurate scientific analysis and interpretation.

Coherent all Optical Reservoir Computing for Equalization of Impairments in Coherent Fiber Optic Communication Systems

Coherent all Optical Reservoir Computing for Equalization of Impairments in Coherent Fiber Optic Communication Systems

Organic Polymer-Based Photodiodes for Optoelectronic Reservoir Computing with Time-Based Coding.

The integration of optoelectronic devices with reservoir computing offers a novel and effective approach to in-sensor computing. This work presents a hybrid digital-physical solution that leverages the high-performance poly[(bithiophene)-alternate-(2,5-di(2-octyldodecyl)-3,6-di(thienyl)-pyrrolyl pyrrolidone)] (DPPT-TT) organic polymer-based photodiodes for the hardware implementation of reservoir computing system. The photodiodes demonstrate nonlinear photoelectric responses, fading memory, and cyclical stability, in relation to the temporal information on light stimuli. These attributes enable effective mapping, historical context sensitivity, and consistent performance, with time-encoded inputs, which are particularly essential for accurate and continuous processing of time series data. The optoelectronic reservoir computing system with pulse width modulation (PWM) coding demonstrates impressive performance in the prediction of chaotic sequences, achieving a normalized root-mean-square error as low as 0.095 with optimized parameters. The DPPT-TT-based photodiodes and time-based coding offer a hardware-efficient solution for reservoir computing, significantly advancing Internet of Things applications.

Thresholding Computing with Heterogeneous Integration of Memristive Kernel with Metal-Oxide-Semiconductor Capacitor for Temporal Data Analysis.

Precise event detection within time-series data is increasingly critical, particularly in noisy environments. Reservoir computing, a robust computing method widely utilized with memristive devices, is efficient in processing temporal signals. However, it typically lacks intrinsic thresholding mechanisms essential for precise event detection. This study introduces a new approach by integrating two Pt/HfO2/TiN (PHT) memristors and one Ni/HfO2/n-Si (NHS)metal-oxide-semiconductor capacitor (2M1MOS) to implement a tunable thresholding function. The current-voltage nonlinearity of memristors combined with the capacitance-voltage nonlinearity of the capacitor forms the basis of the 2M1MOS kernel system. The proposed kernel hardware effectively records feature-specified information of the input signal onto the memristors through capacitive thresholding. In electrocardiogram analysis, the memristive response exhibited a more than ten-fold difference between arrhythmia and normal beats. In isolated spoken digit classification, the kernel achieved an error rate of only 0.7% by tuning thresholds for various time-specific conditions. The kernel is also applied to biometric authentication by extracting personal features using various threshold times, presenting more complex and multifaceted uses of heartbeats and voice data as bio-indicators. These demonstrations highlight the potential of thresholding computing in a memristive framework with heterogeneous integration.

Achieving liquid processors by colloidal suspensions for reservoir computing

The increasing use of machine learning, with its significant computational and environmental costs, has motivated the exploration of unconventional computing substrates. Liquid substrates, such as colloids, are of particular interest due to their ability to conform to various shapes while exhibiting complex dynamics resulting from the collective behaviour of the constituent colloidal particles. This study explores the potential of using a PEDOT:PSS colloidal suspension as a physical reservoir for reservoir computing in spoken digit recognition. Reservoir computing uses high-dimensional dynamical systems to perform tasks with different substrates, including physical ones. Here, a physical reservoir is implemented that encodes temporal data by exploiting the rich dynamics inherent in colloidal suspensions, thus avoiding reliance on conventional computing hardware. The reservoir processes audio input encoded as spike sequences, which are then classified using a trained readout layer to identify spoken digits. Evaluation across different speaker scenarios shows that the colloidal reservoir achieves high accuracy in classification tasks, demonstrating its viability as a physical reservoir substrate.

Experimental realization of a performance-enhanced reservoir computer based on a photonic-filter feedback laser

Experimental realization of a performance-enhanced reservoir computer based on a photonic-filter feedback laser

IGZO/PVP Composite Nanofiber Neuromorphic Transistors with Optoelectronic Synapse Emulation and Reservoir Computing.

Nanofiber neuromorphic transistors are regarded as promising candidates for mimicking brain-like learning and advancing high-performance computing. Composite nanofibers (CNFs) typically exhibit enhanced optoelectronic and mechanical properties. In this study, indium-gallium-zinc oxide (IGZO)/polyvinylpyrrolidone (PVP) CNFs were synthesized, and the neuromorphic transistor was integrated on both rigid and flexible substrates. The learning behavior, characterized by the transition from short-term plasticity (STP) to long-term plasticity, was achieved through photoelectric stimulation of the rigid neuromorphic transistor. The nonlinear STP was simulated by the flexible neuromorphic transistor through electrical pulses, matching effectively with a reservoir computing (RC) system. Hand gesture recognition with little energy consumption (49 pJ per reservoir state) and a maximum accuracy of 92.86% has been achieved by the RC system, proving the substantial potential of the IGZO/PVP CNF neuromorphic transistor for wearable intelligent processing tasks.

Physical reservoir computing on a soft bio-inspired swimmer

Bio-inspired Autonomous Underwater Vehicles with soft bodies provide significant performance benefits over conventional propeller-driven vehicles; however, it is difficult to control these vehicles due to their soft underactuated bodies. This study investigates the application of Physical Reservoir Computing (PRC) in the swimmer's flexible body to perform state estimation. This PRC informed state estimation has potential to be used in vehicle control. PRC is a type of recurrent neural network that leverages the nonlinear dynamics of a physical system to predict a nonlinear spatiotemporal input-output relationship. By embodying the neural network into the physical structure, PRC can process the response to an environment input with high computational efficiency. This study uses a soft bio-inspired propulsor embodied as a physical reservoir. We evaluate its ability to predict different state estimation tasks including hydrodynamic forces and benchmark computational tasks in response to the forcing applied to the artificial muscles during actuation. The propulsor's nonlinear fluid-structural dynamics act as the physical reservoir and the kinematic feedback serves as the reservoir readouts. We show that the bio-inspired underwater propulsor can predict the hydrodynamic thrust and benchmark tasks with high accuracy under specific input frequencies. By analyzing the frequency spectrum of the input, readouts, and target signals, we demonstrate that the system's dynamic response determines the frequency contents relevant to the task being predicted. The propulsor's ability to process information stems from its nonlinearity, as it is responsible to transform the input signal into a broader spectrum of frequency content at the readouts. This broad band of frequency content is necessary to recreate the target signal within the PRC algorithm, thereby improving the prediction performance. The spectral analysis provides a unique perspective to analyze the nonlinear dynamics of a physical reservoir and serves as a valuable tool for examining other types of vibratory systems for PRC. This work serves as a first step towards embodying computation into soft bio-inspired swimmers.

Dynamical predictive coding with reservoir computing performs noise-robust multi-sensory speech recognition.

Multi-sensory integration is a perceptual process through which the brain synthesizes a unified perception by integrating inputs from multiple sensory modalities. A key issue is understanding how the brain performs multi-sensory integrations using a common neural basis in the cortex. A cortical model based on reservoir computing has been proposed to elucidate the role of recurrent connectivity among cortical neurons in this process. Reservoir computing is well-suited for time series processing, such as speech recognition. This inquiry focuses on extending a reservoir computing-based cortical model to encompass multi-sensory integration within the cortex. This research introduces a dynamical model of multi-sensory speech recognition, leveraging predictive coding combined with reservoir computing. Predictive coding offers a framework for the hierarchical structure of the cortex. The model integrates reliability weighting, derived from the computational theory of multi-sensory integration, to adapt to multi-sensory time series processing. The model addresses a multi-sensory speech recognition task, necessitating the management of complex time series. We observed that the reservoir effectively recognizes speech by extracting time-contextual information and weighting sensory inputs according to sensory noise. These findings indicate that the dynamic properties of recurrent networks are applicable to multi-sensory time series processing, positioning reservoir computing as a suitable model for multi-sensory integration.

Intermittent dynamics identification and prediction from experimental data of discrete-mode semiconductor lasers by reservoir computing

Analysis of intermittent dynamics from experimental data is essential to promote the understanding of practical complex nonlinear systems and their underlying physical mechanisms. In this paper, reservoir computing enabled dynamics prediction, and identification of two types of intermittent switching using experimental data from discrete-mode semiconductor lasers are rigorously studied and demonstrated. The results show that, for the dynamics prediction task, both regular and irregular intermittent switching can be predicted reliably by reservoir computing, achieving the average normalized mean-square error of less than 0.015. Additionally, the impact of the number of virtual nodes in the reservoir layer, as well as the train-test split ratio on prediction performance, is explored. For the dynamic identification task, a 2-class classification test is adopted, and the corresponding binary accuracy is calculated to evaluate the identification performance. The results demonstrate that the accuracy of identifying both regular and irregular intermittent switching exceeds 0.996. Compared with the conventional amplitude threshold identification method, the reservoir computing-driven dynamics identification method exhibits superior accuracy, especially in the intermittent transient transition regions.

A photonic integrated chip for distinguishing the optical wave packets based on a neural-network

In this work, we use an optical-neural network to recognize a series of optical triangular and square wave packets. This chip is designed based on the reservoir computing, consisting of the directional couplers, phase shifters, Mach-Zehnder modulators, spiral waveguide and grating couplers. The non-linear activation function is obtained by the directional couplers. The optimization of the optical reservoir computing system is performed by tuning the voltage on the phase shifters to obtain the largest extinction ratio of the output signals for different input wave packets. The photonic integrated chip is fabricated on silicon-on-insulator and is characterized at an operation frequency of 3 GHz. The results demonstrate that the photonic integrated chip can efficiently distinguish between optical triangular and square wave packets.

Evaporated Copper‐Based Perovskite Dynamic Memristors for Reservoir Computing Systems

AbstractDynamic memristors are considered as the optimal hardware devices for reservoir computing (RC) enabled by their nonlinear conductance variations. This significantly reduces the extensive training workload typically required by traditional neural networks. Lead halide perovskites, with their tunable band structure and active ion migration properties, have emerged as highly promising materials for developing dynamic memristors. However, large‐scale and consistently stable production remains a challenge for perovskite functional films, while lead elements' toxicity and environmental impact also partly restrict their practical device utilization. In this work, lead‐free copper‐based perovskite (i.e., CsCu2I3) films are prepared by thermal evaporation for constructing dynamic memristors. The effective conductivity modulation of CsCu2I3‐based memristor can be utilized in artificial neural networks, achieving a high handwritten digit recognition accuracy of 91.2%. In addition, the RC system is also constructed based on the dynamic behavior of the devices, by which a letter recognition accuracy of 98.2% with simple training is achieved. This technology provides a feasible pathway to construct copper‐based perovskite dynamic memristors for future neural network information processing.

Estimation of AMOC transition probabilities using a machine learning based rare-event algorithm

Abstract The Atlantic Meridional Overturning Circulation (AMOC) is an important component of the global climate, known to be a tipping element, as it could collapse under global warming. The main objective of this study is to compute the probability that the AMOC collapses within a specified time window, using a rare-event algorithm called Trajectory-Adaptive Multilevel Splitting (TAMS). However, the efficiency and accuracy of TAMS depend on the choice of the score function. Although the definition of the optimal score function, called “committor function” is known, it is impossible in general to compute it a priori. Here, we combine TAMS with a Next-Generation Reservoir Computing technique that estimates the committor function from the data generated by the rare-event algorithm. We test this technique in a stochastic box model of the AMOC for which two types of transition exist, the so-called F(ast)-transitions and S(low)-transitions. Results for the F-transtions compare favorably with those in the literature where a physically-informed score function was used. We show that coupling a rare-event algorithm with machine learning allows for a correct estimation of transition probabilities, transition times, and even transition paths for a wide range of model parameters. We then extend these results to the more difficult problem of S-transitions in the same model. In both cases of F-transitions and S-transitions, we also show how the Next-Generation Reservoir Computing technique can be interpreted to retrieve an analytical estimate of the committor function.

Gesture recognition with Brownian reservoir computing using geometrically confined skyrmion dynamics

Physical reservoir computing leverages the dynamical properties of complex physical systems to process information efficiently, significantly reducing training efforts and energy consumption. Magnetic skyrmions, topological spin textures, are promising candidates for reservoir computing systems due to their enhanced stability, non-linear interactions and low-power manipulation. Traditional spin-based reservoir computing has been limited to quasi-static detection or real-world data must be rescaled to the intrinsic timescale of the reservoir. We address this challenge by time-multiplexed skyrmion reservoir computing, that allows for aligning the reservoir’s intrinsic timescales to real-world temporal patterns. Using millisecond-scale hand gestures recorded with Range-Doppler radar, we feed voltage excitations directly into our device and detect the skyrmion trajectory evolution. This method scales down to the nanometer level and demonstrates competitive or superior performance compared to energy-intensive software-based neural networks. Our hardware approach’s key advantage is its ability to integrate sensor data in real-time without temporal rescaling, enabling numerous applications.

Dynamical analysis, control, boundedness, and prediction for a fractional-order financial risk system

Abstract This paper delves into the dynamical analysis, chaos control, Mittag–Leffler boundedness (MLB), and forecasting a fractional-order financial risk (FOFR) system through an absolute function term. To this end, the FOFR system is first proposed, and the adomian decomposition method (ADM) is employed to resolve this fractional-order system. The stability of equilibrium points and the corresponding control schemes are assessed, and several classical tools such as Lyapunov exponents (LE), bifurcation diagrams, complexity analysis (CA), and 0–1 test are further extended to analyze the dynamical behaviors of FOFR. Then the global Mittag–Leffler attractive set (MLAS) and Mittag–Leffler positive invariant set (MLPIS) for the proposed financial risk (FR) system are discussed. Finally, a proficient reservoir-computing (RC) method is applied to forecast the temporal evolution of the complex dynamics for the proposed system, and some simulations are carried out to show the effectiveness and feasibility of the present scheme.

Sequential Reservoir Computing for Log File‐Based Behavior Process Data Analyses

AbstractThe use of process data in assessment has gained attention in recent years as more assessments are administered by computers. Process data, recorded in computer log files, capture the sequence of examinees' response activities, for example, timestamped keystrokes, during the assessment. Traditional measurement methods are often inadequate for handling this type of data. In this paper, we proposed a sequential reservoir method (SRM) based on a reservoir computing model using the echo state network, with the particle swarm optimization and singular value decomposition as optimization. Designed to regularize features from process data through a computational self‐learning algorithm, this method has been evaluated using both simulated and empirical data. Simulation results suggested that, on one hand, the model effectively transforms action sequences into standardized and meaningful features, and on the other hand, these features are instrumental in categorizing latent behavioral groups and predicting latent information. Empirical results further indicate that SRM can predict assessment efficiency. The features extracted by SRM have been verified as related to action sequence lengths through the correlation analysis. This proposed method enhances the extraction and accessibility of meaningful information from process data, presenting an alternative to existing process data technologies.

Highly textured CMOS-compatible hexagonal boron nitride-based neuristor for reservoir computing

Significant advancements in artificial neural networks (ANNs) have driven the rapid progress of artificial intelligence and machine learning. While current feedforward neural networks primarily handle static data, recurrent neural networks (RNNs) are designed for dynamical systems. However, RNNs demand extensive training on specific tasks, limiting their scalability and affordability for edge computing. Physical reservoir computing (RC) offers an alternative approach by mapping inputs into high-dimensional states, allowing for pattern analysis within a fixed reservoir. Unlike RNNs, RC is well-suited for temporal and sequential data processing with rapid speed and low training costs. This makes RC suitable for hardware implementation across various research domains. Nonetheless, existing demonstrations of RC remain constrained to small-scale device arrays. As electronic synapse arrays aim to approach very large-scale and highly complex hardware as in the human brain, managing heat dissipation becomes a formidable challenge. In this work, we successfully developed the neuristors based on textured h-BN films, prepared using a CMOS-compatible technique, and constructed a physical RC system based on as-fabricated devices. Our approach leverages vertically aligned BN to provide aligned diffusion paths for the reproducible migration process of metal ions from the electrodes and offers a potential solution for thermal management in electronic devices. This achievement highlights the promising potential of our neuristors for future high-density and energy-efficient neuromorphic computing.

Minimal model for reservoir computing

A minimal model for reservoir computing is studied. We demonstrate that a reservoir computer exists that emulates given coupled maps by constructing a modularised network. We describe a possible mechanism for collapses of the emulation in the reservoir computing by introducing a measure of finite scale deviation. Such transitory behaviour is caused by either (i) an escape from a finite-time stagnation near an unstable chaotic set, or (ii) a critical transition driven by the effective parameter drift. Our approach reveals the essential mechanism for reservoir computing and provides insights into the design of reservoir computer for practical applications.

Physical Reservoir Computing Devices Utilizing Nanomaterial Random Network and Its Sensing Application

Physical Reservoir Computing Devices Utilizing Nanomaterial Random Network and Its Sensing Application

Reservoir computing with logistic map.

Recent studies on reservoir computing essentially involve a high-dimensional dynamical system as the reservoir, which transforms and stores the input as a higher-dimensional state for temporal and nontemporal data processing. We demonstrate here a method to predict temporal and nontemporal tasks by constructing virtual nodes as constituting a reservoir in reservoir computing using a nonlinear map, namely, the logistic map, and a simple finite trigonometric series. We predict three nonlinear systems, namely, Lorenz, Rössler, and Hindmarsh-Rose, for temporal tasks and a seventh-order polynomial for nontemporal tasks with great accuracy. Also, the prediction is made in the presence of noise and found to closely agree with the target. Remarkably, the logistic map performs well and predicts close to the actual or target values. The low values of the root mean square error confirm the accuracy of this method in terms of efficiency. Our approach removes the necessity of continuous dynamical systems for constructing the reservoir in reservoir computing. Moreover, the accurate prediction for the three different nonlinear systems suggests that this method can be considered a general one and can be applied to predict many systems. Finally, we show that the method also accurately anticipates the time series of the all the three variable of Rössler system for the future (self-prediction).