We develop an auto-reservoir computing framework, Auto-Reservoir Neural Network (ARNN), to efficiently and accurately make multi-step-ahead predictions based on a short-term high-dimensional time series. Different from traditional reservoir computing whose reservoir is an external dynamical system irrelevant to the target system, ARNN directly transforms the observed high-dimensional dynamics as its reservoir, which maps the high-dimensional/spatial data to the future temporal values of a target variable based on our spatiotemporal information (STI) transformation. Thus, the multi-step prediction of the target variable is achieved in an accurate and computationally efficient manner. ARNN is successfully applied to both representative models and real-world datasets, all of which show satisfactory performance in the multi-step-ahead prediction, even when the data are peturbed by noise and when the system is time-varying. Actually, such ARNN transformation equivalently expands the sample size and thus has great potential in practical applications in artificial intelligence and machine learning.

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Learning rate is arguably the most important hyper-parameter to tune when training a neural network. As manually setting right learning rate remains a cumbersome process, adaptive learning rate algorithms aim at automating such a process. Motivated by the success of the Barzilai–Borwein (BB) step-size method in many gradient descent methods for solving convex problems, this paper aims at investigating the potential of the BB method for training neural networks. With strong motivation from related convergence analysis, the BB method is generalized to adaptive learning rate of mini-batch gradient descent. The experiments showed that, in contrast to many existing methods, the proposed BB method is highly insensitive to initial learning rate, especially in terms of generalization performance. Also, the BB method showed its advantages on both learning speed and generalization performance over other available methods.