Manjunath, Gandhi2022-04-042022-04-042022-06G. Manjunath, "An Echo State Network Imparts a Curve Fitting," in IEEE Transactions on Neural Networks and Learning Systems, vol. 33, no. 6, pp. 2596-2604, doi: 10.1109/TNNLS.2021.3099091.2162-237X (online)2162-2388 (print)10.1109/TNNLS.2021.3099091http://hdl.handle.net/2263/84771Recurrent neural networks (RNNs) are successfully employed in processing information from temporal data. Approaches to training such networks are varied and reservoir computing-based attainments, such as the echo state network (ESN), provide great ease in training. Akin to many machine learning algorithms rendering an interpolation function or fitting a curve, we observe that a driven system, such as an RNN, renders a continuous curve fitting if and only if it satisfies the echo state property. The domain of the learned curve is an abstract space of the left-infinite sequence of inputs and the codomain is the space of readout values. When the input originates from discrete-time dynamical systems, we find theoretical conditions under which a topological conjugacy between the input and reservoir dynamics can exist and present some numerical results relating the linearity in the reservoir to the forecasting abilities of the ESNs.en© 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.Recurrent neural network (RNN)Echo state network (ESN)Task analysisReservoirsTrainingMathematical modelDynamical systemsNeuronsCurve fittingEcho state property (ESP)LearningNonautonomous dynamical systemsPostprint Article