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Post-processing Methods for Delay Embedding and Feature Scaling of Reservoir Computers

Communications Engineering(2025)

Technische Universität Ilmenau

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Abstract
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. Jonnel Jaurigue and co-authors improve the performance of reservoir computing by training on past node states. Their multi-random-timeshifting method can be translated to physical reservoir readout data as showcased in the experimental demonstration.
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