Modeling and analysis of natural time series based on a combination of cognitive decision rules and KAN neural network

A method for modeling and analyzing natural time series based on a combination of cognitive decision rules with the Kolmogorov-Arnold neural network (KAN) is proposed. The problem of approximating the data time changes of the galactic cosmic ray flux variations is considered. Anomalous changes in the galactic cosmic ray flux indicate disturbances in the near-Earth space and are an important factor in space weather. The non-stationary structure of data of the cosmic ray flux variations, limited data samples, and a high proportion of incomplete a priori knowledge reduce the efficiency of existing data analysis methods, including the latest developments in machine learning and artificial intelligence. The cognitive rules developed by the authors are based on the synthesis of risk theory elements with adaptive threshold wavelet estimates. They allow suppressing interference (including correlated interference) and detecting an information signal at the rate of data receipt by the processing system. The obtained estimates showed that the combination of cognitive rules with the KAN neural network makes it possible to improve the qualitative characteristics of the KAN network. Application of the method allowed us to obtain an adequate model of the data time changes of cosmic ray variations (the MSE model values of the best network NN8_filt is 0.84633 and errors are white Gaussian noise), giving a forecast with a lead step of 10 counts. The example of the event on May 10, 2024 shows the prospects of using the developed method for the task of describing anomalous changes in the rate of cosmic ray arrival to the Earth based on the data from high-latitude neutron monitors. The efficiency and accuracy of the method were also confirmed by the estimates of the deviations in the L2 norm of the true (observed) values from the values obtained by the network (with the use of cognitive rules E~L2~=^2.0136, without cognitive rules E~L2~=^3.8538).