Embedding theory of reservoir computing and reducing reservoir network using 
time delays

Duan, Xing-Yue; Ying, Xiong; Leng, Si-Yang; Kurths, Jürgen; Lin, Wei; Ma, Huan-Fei

doi:10.1103/PhysRevResearch.5.L022041

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Embedding theory of reservoir computing and reducing reservoir network using time delays

Authors

Duan, Xing-Yue
External Organizations;

Ying, Xiong
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Leng, Si-Yang
External Organizations;

/persons/resource/Juergen.Kurths

Kurths, Jürgen
Potsdam Institute for Climate Impact Research;

Lin, Wei
External Organizations;

Ma, Huan-Fei
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Citation

Duan, X.-Y., Ying, X., Leng, S.-Y., Kurths, J., Lin, W., Ma, H.-F. (2023): Embedding theory of reservoir computing and reducing reservoir network using time delays. - Physical Review Research, 5, 2, L022041.
https://doi.org/10.1103/PhysRevResearch.5.L022041

Cite as: https://publications.pik-potsdam.de/pubman/item/item_29451

Abstract

Reservoir computing (RC), a particular form of recurrent neural network, is under explosive development due to its exceptional efficacy and high performance in reconstruction and/or prediction of complex physical systems. However, the mechanism triggering such effective applications of RC is still unclear, awaiting deep and systematic exploration. Here, combining the delayed embedding theory with the generalized embedding theory, we rigorously prove that RC is essentially a high-dimensional embedding of the original input nonlinear dynamical system. Thus, using this embedding property, we unify into a universal framework the standard RC and the time-delayed RC where we introduce time delays only into the network's output layer, and we further find a trade-off relation between the time delays and the number of neurons in RC. Based on these findings, we significantly reduce the RC's network size and promote its memory capacity in completing systems reconstruction and prediction. More surprisingly, only using a single-neuron reservoir with time delays is sometimes sufficient for achieving reconstruction and prediction tasks, while the standard RC of any large size but without time delay cannot complete them yet.