Second-order Time Delay Reservoir Computing for Nonlinear Time Series Problems

Time Delay Reservoir (TDR) leverages delay differential equations (DDEs) for high dimensionality and short-term memory, with hardware-friendly attributes. However, its predictive performance and memory capacity are limited by the hyperparameters of the oscillation function. We identify the limitations' causes as the trade-off between self-feedback and neighboring-feedback due to neuron separation, and unsuitable nonlinear function order in DDE. To address these, we introduce a second-order time delay TDR for enhanced flexibility and a parameter-free nonlinear function to reduce dependency on parameters. Our experiments demonstrate improved performance and memory capacity over the standard TDR and six other approaches in time series prediction and recognition tasks.