The paper investigates how training shapes the geometry of recurrent network dynamics in Reservoir Computing (RC) networks used for temporal forecasting. It demonstrates that, in a linear continuous-time reservoir with infinite data, training data create an invariant subspace whose dimension matches the number of dominant modes. For a simplified diagonal linear reservoir, the study connects dominant eigenvalues and eigenvectors to the spectrum of a backward Dynamic Mode Decomposition matrix, providing a finite-dimensional approximation of the backward-time Koopman operator, and illustrates these phenomena through simulation while suggesting extensions to nonlinear RC.
By Noa Kaplan, Alberto Padoan, Anastasia Bizyaeva
arXiv:2607. 17858v1 Announce Type: cross Abstract: Reservoir computing exploits nonlinear dynamical systems to encode temporal inputs into high-dimensional state space representations.
By Mohab Abdalla, Damien Rontani
arXiv:2504. 17503v2 Announce Type: replace Abstract: We study how the degree of nonlinearity in the input data affects the optimal design of reservoir computers, focusing on how closely the model's nonlinearity should align with that of the data.
By Davide Prosperino, Haochun Ma, Christoph R\"ath
arXiv:2606. 09929v1 Announce Type: cross Abstract: Physical reservoir computing harnesses nonlinear mechanical dynamics but, by convention, freezes the substrate and trains only a linear readout, presuming the substrate is not usefully trainable.
By Caleb Munigety
arXiv:2607. 24420v1 Announce Type: cross Abstract: Reservoir computing has emerged as an efficient machine learning framework for predicting time series generated by dynamical systems.
By Arthur S Powanwe
arXiv:2608. 16084v1 Announce Type: new Abstract: Neural autoregressive models have rapidly emerged as powerful emulators of high-dimensional chaotic systems, yet their long-term instability and error growth remain poorly understood, leading to ad-hoc solutions.
By Conrad Ainslie, Pedram Hassanzadeh, Michael W. Mahoney, Ashesh Chattopadhyay