Total recall: Post-processing methods for delay-embedding and feature scaling of reservoir computer

Abstract Reservoir computing is a machine learning method that is well-suited for complex timeseries prediction tasks. Both delay-embedding and the projection of input data into a higher-dimensional space play important roles in enabling accurate predictions. We establish simple post-processing methods that train on past node states, chosen at either uniformly or randomly-delayed timeshifts. Reservoir computer prediction performance is improved through increased feature dimension and/or better delay-embedding. From these simple post-processing methods we introduce the multi-random-timeshifting method, which recalls previous states of reservoir nodes. Multi-random-timeshifting allows for smaller reservoirs while maintaining large feature dimensions, is computationally cheap to optimise, and is our preferred post-processing method. All our post-processing methods can be translated to readout data sampled from physical reservoirs, which we demonstrate using readout data from an experimentally-realised laser reservoir system.