Forecasting the chaotic dynamics of external cavity semiconductor lasers

Chaotic time series prediction has been paid intense attention in recent years due to its important applications. Herein, we present a single-node photonic reservoir computing approach to forecasting the chaotic behavior of external cavity semiconductor lasers using only observed data. In the reservoir, we employ a semiconductor laser with delay as the sole nonlinear physical node. By investigating the effect of the reservoir meta-parameters on the prediction performance, we numerically demonstrate that there exists an optimal meta-parameter space for forecasting optical-feedback-induced chaos. Simulation results demonstrate that using our method, the upcoming chaotic time series can be continuously predicted for a time period in excess of 2 ns with a normalized mean squared error lower than 0.1. This proposed method only utilizes simple nonlinear semiconductor lasers and thus offers a hardware-friendly approach for complex chaos prediction. In addition, this work may provide a roadmap for the meta-parameter selection of a delay-based photonic reservoir to obtain optimal prediction performance

Echo State Queueing Network: a new reservoir computing learning tool

In the last decade, a new computational paradigm was introduced in the field of Machine Learning, under the name of Reservoir Computing (RC). RC models are neural networks which a recurrent part (the reservoir) that does not participate in the learning process, and the rest of the system where no recurrence (no neural circuit) occurs. This approach has grown rapidly due to its success in solving learning tasks and other computational applications. Some success was also observed with another recently proposed neural network designed using Queueing Theory, the Random Neural Network (RandNN). Both approaches have good properties and identified drawbacks. In this paper, we propose a new RC model called Echo State Queueing Network (ESQN), where we use ideas coming from RandNNs for the design of the reservoir. ESQNs consist in ESNs where the reservoir has a new dynamics inspired by recurrent RandNNs. The paper positions ESQNs in the global Machine Learning area, and provides examples of their use and performances. We show on largely used benchmarks that ESQNs are very accurate tools, and we illustrate how they compare with standard ESNs.Comment: Proceedings of the 10th IEEE Consumer Communications and Networking Conference (CCNC), Las Vegas, USA, 201

Training Echo State Networks with Regularization through Dimensionality Reduction

In this paper we introduce a new framework to train an Echo State Network to predict real valued time-series. The method consists in projecting the output of the internal layer of the network on a space with lower dimensionality, before training the output layer to learn the target task. Notably, we enforce a regularization constraint that leads to better generalization capabilities. We evaluate the performances of our approach on several benchmark tests, using different techniques to train the readout of the network, achieving superior predictive performance when using the proposed framework. Finally, we provide an insight on the effectiveness of the implemented mechanics through a visualization of the trajectory in the phase space and relying on the methodologies of nonlinear time-series analysis. By applying our method on well known chaotic systems, we provide evidence that the lower dimensional embedding retains the dynamical properties of the underlying system better than the full-dimensional internal states of the network

Bidirectional deep-readout echo state networks

We propose a deep architecture for the classification of multivariate time series. By means of a recurrent and untrained reservoir we generate a vectorial representation that embeds temporal relationships in the data. To improve the memorization capability, we implement a bidirectional reservoir, whose last state captures also past dependencies in the input. We apply dimensionality reduction to the final reservoir states to obtain compressed fixed size representations of the time series. These are subsequently fed into a deep feedforward network trained to perform the final classification. We test our architecture on benchmark datasets and on a real-world use-case of blood samples classification. Results show that our method performs better than a standard echo state network and, at the same time, achieves results comparable to a fully-trained recurrent network, but with a faster training

Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems

A new class of non-homogeneous state-affine systems is introduced for use in reservoir computing. Sufficient conditions are identified that guarantee first, that the associated reservoir computers with linear readouts are causal, time-invariant, and satisfy the fading memory property and second, that a subset of this class is universal in the category of fading memory filters with stochastic almost surely uniformly bounded inputs. This means that any discrete-time filter that satisfies the fading memory property with random inputs of that type can be uniformly approximated by elements in the non-homogeneous state-affine family.Comment: 41 page

Toward bio-inspired information processing with networks of nano-scale switching elements

Unconventional computing explores multi-scale platforms connecting molecular-scale devices into networks for the development of scalable neuromorphic architectures, often based on new materials and components with new functionalities. We review some work investigating the functionalities of locally connected networks of different types of switching elements as computational substrates. In particular, we discuss reservoir computing with networks of nonlinear nanoscale components. In usual neuromorphic paradigms, the network synaptic weights are adjusted as a result of a training/learning process. In reservoir computing, the non-linear network acts as a dynamical system mixing and spreading the input signals over a large state space, and only a readout layer is trained. We illustrate the most important concepts with a few examples, featuring memristor networks with time-dependent and history dependent resistances

Online Learning Algorithm for Time Series Forecasting Suitable for Low Cost Wireless Sensor Networks Nodes

Time series forecasting is an important predictive methodology which can be applied to a wide range of problems. Particularly, forecasting the indoor temperature permits an improved utilization of the HVAC (Heating, Ventilating and Air Conditioning) systems in a home and thus a better energy efficiency. With such purpose the paper describes how to implement an Artificial Neural Network (ANN) algorithm in a low cost system-on-chip to develop an autonomous intelligent wireless sensor network. The present paper uses a Wireless Sensor Networks (WSN) to monitor and forecast the indoor temperature in a smart home, based on low resources and cost microcontroller technology as the 8051MCU. An on-line learning approach, based on Back-Propagation (BP) algorithm for ANNs, has been developed for real-time time series learning. It performs the model training with every new data that arrive to the system, without saving enormous quantities of data to create a historical database as usual, i.e., without previous knowledge. Consequently to validate the approach a simulation study through a Bayesian baseline model have been tested in order to compare with a database of a real application aiming to see the performance and accuracy. The core of the paper is a new algorithm, based on the BP one, which has been described in detail, and the challenge was how to implement a computational demanding algorithm in a simple architecture with very few hardware resources.Comment: 28 pages, Published 21 April 2015 at MDPI's journal "Sensors