Fig. 3: Modeling of a sophisticated spintronic task, Mackey-Glass time series prediction with skyrmion systems, using Neural ODEs.
From: Forecasting the outcome of spintronic experiments with Neural Ordinary Differential Equations
a Schematic graph of the procedure for doing the prediction task. The purpose is to predict the Mackey-Glass time series at a future time. The input signal, preprocessed through a read-in matrix Win, is fed into the reservoir, which is a skyrmion system modeled by the trained Neural ODE or micromagnetic simulations. A trained output matrix Wout is used for reading out the reservoir states and providing the predicted signal. b, c Selected testing (green dashed) results for prediction horizontal step H = 1 (for short-term prediction) and H = 25 (for long-term prediction), predicted by the one-skyrmion system modeled by micromagnetic simulations in b and the Neural ODE in c, in comparison with the true trajectory (blue) of Mackey-Glass time series. The red curves show the prediction error compared to the true trajectory. d, e Normalized root mean square error (NRMSE) as a function of prediction horizontal step H, in log scale, for the testing set by using the trained Neural ODE (orange) and micromagnetic simulations (blue) for the one-skyrmion system in d and the multi-skyrmions system in e.
