Fig. 2: Schematic illustration of spin-wave reservoir computing using micromagnetic simulation and prediction of NARMA10 task.

Input signals U are transformed into the piece-wise constant input U(t), multiplied by binary mask \({{{{\mathcal{B}}}}}_{i}(t)\), and transformed into injected current \(j(t)=2{j}_{c}{\tilde{U}}_{i}(t)\) with \({\tilde{U}}_{i}={{{{\mathcal{B}}}}}_{i}(t)U(t)\) for the ith physical node. Current is injected into each physical node with the cylindrical region to apply spin-transfer torque and to excite spin-wave. Higher damping regions in the edges of the rectangle are set to avoid reflection of spin-waves. The x-component of magnetization m_x at each physical and virtual node are collected and the extended state \(\tilde{\tilde{{{{\bf{X}}}}}}\) is constructed from m_x and \({m}_{x}^{2}\). Output weights are trained by linear regression. The labels (1) to (6) correspond to step 1 to step 6 in Section Learning with reservoir computing, respectively.