Fig. 5: Prediction of time-series data for the Lorenz system using reservoir computing with micromagnetic simulations.

The parameters are θ = 0.4 ns and α = 5.0 × 10⁻⁴. a The ground truth (A₁(t), A₂(t), A₃(t)) and the estimated time series \((\hat{{A}_{1}}(t),\hat{{A}_{1}}(t),\hat{{A}_{3}}(t))\) are shown in blue and red, respectively. The training steps are during t < 0, whereas the prediction steps are during t > 0. b The attractor in the A₁A₃ plane for the ground truth and during the prediction steps. c Schematics of the training and prediction steps for this task. During the training step, RC estimates the time series of the next time step \({\hat{A}}_{i}(t+\Delta t)\) (i = 1, 2, 3) from the input time series A_i(t) (i = 1, 2, 3) by optimizing the readout weights so that the estimated \({\hat{A}}_{i}(t+\Delta t)\) approximates the ground truth A_i(t + Δt). During the prediction step after the training step, using the optimized readout weights, the estimated \({\hat{A}}_{i}(t)\) is transformed into the time series at the next step \({\hat{A}}_{i}(t+\Delta t)\), which is further used for the estimation at future time steps t + 2Δt,t + 3Δt,…. The ground truth time series is no longer used during the prediction step except at the initial time step.