Noise Resistance Of Reservoir Computing

Reservoir computing(RC)methods have received more and more attention and applications in chaotic time series prediction with their simple structure and training method.Traditional RC method has been used in many fields.At the same time,in 2021,the next generation reservoir computing(NG-RC)method(Nature Communications,12:5564,2021)has been proposed by Gauthier et al.with less training cost and better time-series predictions.Nevertheless,in practice,available data on dynamic systems are contaminated with noise.Though the traditional RC and 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 traditional RC and NG-RC method,taking the well-known denoising method,the high-order correlation computation(HOCC)method,as a reference.It provides a foundation for the establishment of data analysis methods for complex systems with better noise resistance performanceThe first part of this thesis explores the performance and characteristics of the traditional RC method.We use the control variable method to test the influence of training steps,noise intensity,sampling interval and noise type on the noise resistance ability of the traditional RC method.It is found that when other variables are the same,the noise resistance ability of the traditional RC increases with the increase of the training steps,decreases with the increase of the noise intensity,and decreases with the increase of the sampling interval.Meanwhile,The prediction ability of traditional RC for white noise-driven system is similar to that for colored noise-driven system,but both are weaker than HOCC method.The second part of this thesis explores the performance and characteristics of the NG-RC method.Unlike traditional RC method,NG-RC method rely on eigenvectors,which is similar to HOCC method using function bases.Therefore,we theoretically explore the similarities and differences between the two method,and find that the two method have similarities in the selection of basis function and regression solution,but use different methods in noise resistance.Next,by comparing with the HOCC method,the noise resistance performance of the NG-RC method without and with time-delay bases is comprehensively tested by using four indexes,such as the training error,prediction error,prediction time,and auto-correlation prediction error,for both the short-time series and long climate predictions.It is found that NG-RC method without time-delay bases has strong noise resistance performance,even better than HOCC method.In addition,it also has a good prediction ability for the colored-noise drive system with small noise intensity,but the effect is worse than that of HOCC method.At the same time,the NG-RC method with time-delay bases can improve its noise resistance ability,but the effect of the colored noise-drive system is still inferior to the HOCC method.In short,by comparing HOCC algorithm,this paper systematically analyzes the noise resistance ability and performance characteristics of the traditional RC and NG-RC algorithm theoretically and numerically,which has some reference value for the improvement of the noise resistance capability of the RC algorithm and the research on the noise resistance capability of other algorithms.