Noise resistance of next-generation reservoir computing: a comparative study with high-order correlation computation

Reservoir computing (RC) methods have received more and more attention and applications in chaotic time series prediction with their simple structure and training method. Recently, the next-generation reservoir computing (NG-RC) method has been proposed by Gauthier et al. (Nat Commun 12:5564, 2021) with less training cost and better time series predictions. Nevertheless, in practice, available data on dynamic systems are contaminated with noise. Though NG-RC is shown highly efficient in learning and predicting, its noise resistance captivity is not clear yet, limiting its use in practical problems. In this paper, we study the noise resistance of the NG-RC method, taking the well-known denoising method, the high-order correlation computation (HOCC) method, as a reference. Both methods have similar procedures in respect of function bases and regression processes. With the simple ridge regression method, the NG-RC method has a strong noise resistance for white noise, even better than the HOCC method. Besides, the NG-RC method also shows a good prediction ability for small colored noise, while it does not provide correct reconstruct dynamics. In this paper, other than reconstruction parameters, four numerical indicators are used to check the noise resistance comprehensively, such as the training error, prediction error, prediction time, and auto-correlation prediction error, for both the short-time series and long climate predictions. Our results provide a systematic estimation of NG-RC’s noise resistance capacity, which is helpful for its applications in practical problems.