Reservoir Computing Research Articles

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).

Cost‐Effective and Fully Hardware‐Oriented Reservoir Computing Based on IGZO/HZO Ferroelectric Thin‐Film Transistor with Electrically and Optically Distinguishable States

AbstractHardware‐based reservoir computing (RC) systems provide benefits like energy efficiency and effective predictability. The implementation of different switching characteristics for the reservoir and readout layers requires the use of different types of devices or additional processing. However, an RC system with distinguishable switching characteristics obtained by changing stimulation on a single device is not identified yet, but it is appealing in terms of process simplicity and efficient processing costs. This study develops an RC system that uses ferroelectric thin‐film transistor (FeTFT) devices with an indium gallium zinc oxide channel and Hf0.5Zr0.5O2 ferroelectric layer for both networks. The nonvolatile FeTFT utilizes the remnant polarization properties of the ferroelectric layer through electrical stimulation, showing stable retention characteristics (104 s) and long‐term potentiation/depression. By using optical stimulation, the volatile FeTFT demonstrates short‐term characteristics, such as paired‐pulse facilitation, and a 4‐bit RC system. This proves that it is possible to meet the functional requirements of both the reservoir and readout networks by simply varying the type of stimulation applied to a single FeTFT. Finally, the fully FeTFT‐based RC system can recognize digit patterns from the Modified National Institute of Standards and Technology database with a high accuracy of 90.5%.

Quantum next generation reservoir computing: an efficient quantum algorithm for forecasting quantum dynamics

Next Generation Reservoir Computing (NG-RC) is a modern class of model-free machine learning that enables an accurate forecasting of time series data generated by dynamical systems. We demonstrate that NG-RC can accurately predict full many-body quantum dynamics in both integrable and chaotic systems. This is in contrast to the conventional application of reservoir computing that concentrates on the prediction of the dynamics of observables. In addition, we apply a technique which we refer to as skipping ahead to predict far future states accurately without the need to extract information about the intermediate states. However, adopting a classical NG-RC for many-body quantum dynamics prediction is computationally prohibitive due to the large Hilbert space of sample input data. In this work, we propose an end-to-end quantum algorithm for many-body quantum dynamics forecasting with a quantum computational speedup via the block-encoding technique. This proposal presents an efficient model-free quantum scheme to forecast quantum dynamics coherently, bypassing inductive biases incurred in a model-based approach.

Nonlinear integrated optical resonators for optical fibre data recovery

We apply in simulation a reservoir computer based on evanescently coupled GaAs microrings for real-time compensation of a nonlinear distortion of a 50 Gbaud 16-QAM signal with the launch power up to 14 dBm in a standard single-mode optical fibre. We clearly evidence the crucial role of fast nonlinear response in enabling all-optical signal recovery in real time. With our system we are able to recover from linear and nonlinear distortion caused by a 20 km fibre and 12 dBm launch power below the forward error correction limit.

Novel efficient reservoir computing methodologies for regular and irregular time series classification

AbstractTime series is a data structure prevalent in a wide range of fields such as healthcare, finance and meteorology. It goes without saying that analyzing time series data holds the key to gaining insight into our day-to-day observations. Among the vast spectrum of time series analysis, time series classification offers the unique opportunity to classify the sequences into their respective categories for the sake of automated detection. To this end, two types of mainstream approaches, recurrent neural networks and distance-based methods, have been commonly employed to address this specific problem. Despite their enormous success, methods like Long Short-Term Memory networks typically require high computational resources. It is largely as a consequence of the nature of backpropagation, driving the search for some backpropagation-free alternatives. Reservoir computing is an instance of recurrent neural networks that is known for its efficiency in processing time series sequences. Therefore, in this article, we will develop two reservoir computing based methods that can effectively deal with regular and irregular time series with minimal computational cost, both while achieving a desirable level of classification accuracy.

Micromagnetic analysis of magnetic vortex dynamics for reservoir computing

Reservoir computing (RC) has generated significant interest for its ability to reduce computational costs compared to traditional neural networks. The performance of the RC element is quantified by its memory capacity (MC) and prediction capability. In this study, we utilize micromagnetic simulations to investigate a magnetic vortex based on a permalloy ferromagnetic layer and its dynamics in RC. The nonlinear dynamics of the vortex core (VC), driven by continuous oscillating magnetic fields and binary digit data as spin-polarized current pulses, are analyzed. The highest MC observed is 4.1, corresponding to the nonlinear VC dynamics. Additionally, the prediction capability is evaluated using the Nonlinear Auto-Regressive Moving Average 2 task, demonstrating a normalized mean squared error of 0.0241 highlighting the time-series data prediction performance of the vortex as a reservoir.

Network Structure and Reservoir Computing in Cultured Neuronal Networks

Network Structure and Reservoir Computing in Cultured Neuronal Networks

A sensitivity analysis of cellular automata and heterogeneous topology networks: partially-local cellular automata and homogeneous homogeneous random boolean networks

ABSTRACT Elementary Cellular Automata (ECA) are well-studied computational universes capable of impressive computational variety, but harnessing their potential has been challenging. When combined with Reservoir Computing (RC), harnessing this computation becomes feasible, and furthermore enables energy efficient AI. This study compares ECA reservoirs to topological heterogeneous and more biological plausible counterparts of Partially-Local CA (PLCA) and Homogeneous Homogeneous Random Boolean Networks (HHRBN). Using the 5-bit memory benchmark, Temporal Derrida plots and collapse rate, finding are that more disordered topology does not equate to more disordered computation and moreover the evidence suggest this heterogeneity shrinks the critical range.

Versatile NbOx‐Based Volatile Memristor for Artificial Intelligent Applications

AbstractTo achieve cost‐effectiveness, researchers are exploring various memristors for their adaptation in neuromorphic computing. Recent studies have focused on developing versatile functioning singular memristors, such as those involved in on‐receptor computing, which integrates sensory functions into current neuromorphic computing paradigms. Additionally, adaptations like reservoir computing are being investigated for computing systems. In this study, a memristor composed of a stack of Ti/NbOx/Pt layers is fabricated to explore multifunctional behaviors within a single memristor. By applying bias toward the top Ti electrode, gradual current changes with volatile features are demonstrated, revealing an ion‐migration‐based nonfilamentary switching memristor. Leveraging this volatile functionality, an artificial nociceptor is first implemented, demonstrating key functions of biological nociceptors including thresholding, relaxation, no‐adaptation, and sensitization. Subsequently, synapse emulation akin to the biological brain is achieved through easy conductance potentiation and depression with diverse synapse functions, enabling the memristor to mimic learning activities with spike firing. Lastly, computational applications are explored by adapting edge computing and multi‐bit reservoir computing, expanding the memristor's applications across diverse fields with versatile behaviors.

Strain-mediated reservoir computing with temporal and spatial co-multiplexing in multiferroic heterostructures

Physical reservoir computing (PRC), a brain-inspired computing method known for its efficient information processing and low training requirements, has attracted significant attention. The key factor lies in the number of computational nodes within the reservoir for its computational capability. Here, we explore co-multiplexing reservoirs that leverage both temporal and spatial strategies. Temporal multiplexing virtually expands the node count through the use of masking techniques, while spatial multiplexing utilizes multiple physical locations (e.g., Hall bars) to achieve an increase in the number of real nodes. Our experiment employs a strain-mediated reservoir based on multiferroic heterostructures. By applying a single voltage across the PMN-PT substrate (acting as global input) and measuring the output Hall voltages from four Hall bars (real nodes), we achieve significant efficiency gains. This co-multiplexing approach results in a reduction in the normalized root mean square error from 0.5 to 0.23 for a 20-step prediction task of a Mackey–Glass chaotic time series. Furthermore, the single input and four independent outputs lead to a fourfold reduction in energy consumption compared to the strain-mediated PRC with temporal multiplexing solely. This research paves the way for future energy saving PRC implementations utilizing co-multiplexing, promoting a resource-efficient paradigm in reservoir computing.