Post-processing methods for delay embedding and feature scaling of reservoir computers

Reservoir computing is a machine learning method that is well-suited for complex time series 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 at uniformly or randomly-delayed timeshifts. These methods improve reservoir computer prediction performance through increased feature dimension and/or better delay embedding. Here we introduce the multi-random-timeshifting method that randomly recalls previous states of reservoir nodes. The use of multi-random-timeshifting allows for smaller reservoirs while maintaining large feature dimensions, is computationally cheap to optimise, and is our preferred post-processing method. For experimentalists, 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.