On the Sensitivity of Next Generation Reservoir Computing

A Catch-22 of Reservoir Computing

Data-driven predictions of nonlinear dynamical systems are a promising approach for learning complex dynamical systems.Recently, nextgeneration reservoir computing (ngrc) has emerged as an especially attractive variant of model-free model-free framework for data-driven predictions of nonlinear dynamical systems.Here, using paradigmatic multistable systems including magneticpendulums and coupled kuramoto oscillators, we show that the performance of nextgeneration reservoir computing models can be extremely sensitive to the choice of readout nonlinearity.In particular, by incorporating the exact nonlinearity from the original equations, models trained on a single trajectory can predict pseudo-fractal basins with almost perfect accuracy.However, even a small uncertainty on the exact nonlinearity can completely break the model, rendering the prediction accuracy no better than chance.Our results highlight the challenges faced by data-driven methods in learning complex dynamical systems.