Minimal Reservoir Computing

Kurzfassung

Reservoir computers are powerful machine learning algorithms for predicting nonlinear systems. However, the traditional reservoir computer uses random matrices to define the underlying recurrent neural network and has a large number of hyperparameters to optimize. Here, we show that a few simple modifications to the traditional reservoir computer architecture, which eliminate randomness and minimize computational resources, lead to significant and robust improvements in short- and long-term predictive performance compared to similar models, while requiring minimal amount of training data. Specifically, the adjacency matrix of the reservoir becomes a block diagonal matrix, where each block is the same matrix with all elements being one. Further, we omit the nonlinear activation function. The nonlinearity is only introduced by also taking higher powers of the reservoir response. Thus, this new architecture open new avenues to explainable and interpretable reservoir computing. For certain parameterizations, we find that the predictions are accurate for more than 10 Lyapunov times and that ordinary least squares regression directly on the embedded data can predict the long-term climate of chaotic systems [1]. [1] H.Ma et al., Sci. Rep., 13, 12970 (2023)