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Register a new userRobust Forecasting through Generalized Synchronization in Reservoir Computing
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Reservoir computers (RC) are a form of recurrent neural network (RNN) used for forecasting timeseries data. As with all RNNs, selecting the hyperparameters presents a challenge when training onnew inputs. We present a method based on generalized synchronization (GS) that gives direction in designing and evaluating the architecture and hyperparameters of an RC. The auxiliary method for detecting GS provides a computationally efficient pre-training test that guides hyperparameterselection. Furthermore, we provide a metric for RC using the reproduction of the input systems Lyapunov exponentsthat demonstrates robustness in prediction.
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Reservoir computers (RC) are a form of recurrent neural network (RNN) used for forecasting time series data. As with all RNNs, selecting the hyperparameters presents a challenge when training on new inputs. We present a method based on generalized synchronization (GS) that gives direction in designing and evaluating the architecture and hyperparameters of a RC. The auxiliary method for detecting GS provides a pre-training test that guides hyperparameter selection. Furthermore, we provide a metric for a well trained RC using the reproduction of the input systems Lyapunov exponents.
We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and induces critical transitions. By taking advantage of recent advances in reservoir computing, we present a data-driven method to predict the future evolution of the state. We show that our method is capable of predicting a critical transition event at least several numerical time steps in advance. We demonstrate the success as well as the limitations of our method using numerical experiments on three examples of systems, ranging from low dimensional to high dimensional. We discuss the mathematical and broader implications of our results.
Closed quantum systems exhibit different dynamical regimes, like Many-Body Localization or thermalization, which determine the mechanisms of spread and processing of information. Here we address the impact of these dynamical phases in quantum reservoir computing, an unconventional computing paradigm recently extended into the quantum regime that exploits dynamical systems to solve nonlinear and temporal tasks. We establish that the thermal phase is naturally adapted to the requirements of quantum reservoir computing and report an increased performance at the thermalization transition for the studied tasks. Uncovering the underlying physical mechanisms behind optimal information processing capabilities of spin networks is essential for future experimental implementations and provides a new perspective on dynamical phases.
Many neural networks use the tanh activation function, however when given a probability distribution as input, the problem of computing the output distribution in neural networks with tanh activation has not yet been addressed. One important example is the initialization of the echo state network in reservoir computing, where random initialization of the reservoir requires time to wash out the initial conditions, thereby wasting precious data and computational resources. Motivated by this problem, we propose a novel solution utilizing a moment based approach to propagate uncertainty through an Echo State Network to reduce the washout time. In this work, we contribute two new methods to propagate uncertainty through the tanh activation function and propose the Probabilistic Echo State Network (PESN), a method that is shown to have better average performance than deterministic Echo State Networks given the random initialization of reservoir states. Additionally we test single and multi-step uncertainty propagation of our method on two regression tasks and show that we are able to recover similar means and variances as computed by Monte-Carlo simulations.
This work describes preliminary steps towards nano-scale reservoir computing using quantum dots. Our research has focused on the development of an accumulator-based sensing system that reacts to changes in the environment, as well as the development of a software simulation. The investigated systems generate nonlinear responses to inputs that make them suitable for a physical implementation of a neural network. This development will enable miniaturisation of the neurons to the molecular level, leading to a range of applications including monitoring of changes in materials or structures. The system is based around the optical properties of quantum dots. The paper will report on experimental work on systems using Cadmium Selenide (CdSe) quantum dots and on the various methods to render the systems sensitive to pH, redox potential or specific ion concentration. Once the quantum dot-based systems are rendered sensitive to these triggers they can provide a distributed array that can monitor and transmit information on changes within the material.
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