Prediction And Analysis Of High Dimensional Dynamic System Based On Integrated Predictor With Auto-reservoir Structure

Compared with feedforward neural network,reservoir computing(RC)evolves freely according to its own dynamic properties and its interactions with the input data,for which it has outstanding performance in handling high-dimensional time-varying information and also provides efficient operation.Therefore,this paper combines RC with the auto-reservoir neural network(ARNN)and proposes a novel integrated predictor of highdimensional dynamical system(Hereinafter referred to as integrated predictor).Instead of the feedforward neural network in ARNN,integrated predictor applies reservoir computing with the STI transformation to predict multi-step-ahead states of various systems.And in account of robustness and accuracy,integrated predictor will perform internal predictions for 10000 times,and the final output signals rely on the distribution of the predicted values.This paper provides a comprehensive guide to set up the integrated predictor,and demonstrates detailed operation processes of integrated predictor.First of all,under hyperparameters setting,a reservoir network is randomly generated to prepare for the next forecasting processes.Secondly,input the known time series into the reservoir network in chronological order,and calculate the output of reservoir at each time point according to the reservoir evolution.Then,the output of reservoir,regarded as known information,is substituted into Spatiotemporal Information(STI)Transformation equations.The predicted values could be obtained by solving the equations in a form similar to " encoding and decoding".Finally,repeat the previous three steps for N times,and determine the final output of integrated predictor according to the distribution of the predicted values.In order to verify effectiveness of integrated predictor,it is applied to the high-dimensional Lorenz 96 system and two real data sets.The results show that the Pearson correlation coefficients between the predicted values and the real values are all higher than 0.85,and the corresponding p values are much smaller than 0.01,which indicates that the integrated predictor has good prediction ability.Not only that,for short-term forecasting and long-term forecasting situations,the prediction performance of integrated predictor in different data sets is also better than other common forecasting methods.Finally,this paper takes the 40 dimensional Lorenz 96 system as an example to show the entire prediction process of integrated predictor in detail,and illustrates the robustness of integrated predictor from several perspectives.First,for systems with different degrees of complexity,the prediction results of integrated predictor can always be consistent with the real data basically.In addition,the predicted values of integrated predictor can be concentrated in a small interval,even integrated predictor set with different internal prediction times N.Besides,under different hyperparameters setting,the predictions for target variables of integrated predictor is approaching to each other.Finally,for a certain range of prediction step L,integrated predictor with the optimal training length m can accurately predict over 60%samples.