Context-dependent time-series prediction via HyperReservoirs

Time series prediction is a common application of reservoir computing. When the training and testing time series data contains multiple dynamical regimes, because an underlying parameter is changing, or the data in fact consists of multiple distinct systems, simple application of the reservoir computing principle produces high prediction errors. Here, we propose a HyperReservoir as an extended model of reservoir computing especially designed for such cases. The HyperReservoir combines a main reservoir with a smaller context reservoir, where the latter modulates the output weights of the former. This structure resembles the hypernetworks from deep neural network literature. However, in contrast, HyperReservoirs retain the simple training via linear regression of standard reservoir computing. We compare the proposed architecture with a conventional ESN, in which context acts at the input, and a full-matrix Conceptor, in which context modulates the reservoir state space. We evaluate all three models on time-series prediction tasks based on Lorenz and R"ossler systems, including for varying bifurcation parameters and time sampling scales. We find that the HyperReservoir achieves the lowest mean test error in all three tasks, and particularly outperforms conceptors on data that is sampled from the same attractor but at different time scales.